Merge bf47181a90 into 26a5fc70e4

## Summary of Changes

Check that `open()` worked to avoid warnings
[here](https://cgal.geometryfactory.com/CGAL/testsuite/CGAL-6.2-Ic-50/Lab_Demo/TestReport_cgaltest_ArchLinux-clang-CXX20-Release.gz).

## Release Management

* Affected package(s): Lab

* License and copyright ownership: unchanged

.clang-format

@@ -1,35 +1,63 @@
 ---
+# CGAL clang-format configuration
+# This file defines the code formatting style for C++ files in the CGAL project.
+
 Language:        Cpp
 BasedOnStyle:  LLVM
-AccessModifierOffset: -2
-AllowShortFunctionsOnASingleLine: true
-BinPackParameters: false
-BreakConstructorInitializers: BeforeComma
+
+# Indentation
+AccessModifierOffset: -2  # Indent public:/private:/protected: 2 spaces to the left
+
+# Function formatting
+AllowShortFunctionsOnASingleLine: Inline  # Allow short inline/member functions on one line, but not free functions
+AlwaysBreakAfterReturnType: None  # Don't force return type on separate line
+
+# Parameter and argument formatting
+BinPackParameters: false  # Put each parameter on its own line for better readability
+
+# Constructor formatting
+BreakConstructorInitializers: BeforeComma  # Put comma before each initializer: `MyClass() \n  , member1(val1) \n  , member2(val2)`
+
+# Brace wrapping configuration
 BreakBeforeBraces: Custom
 BraceWrapping:
-  AfterCaseLabel:  false
-  AfterClass:      true
-  AfterControlStatement: MultiLine
-  AfterEnum:       false
-  AfterFunction:   false
-  AfterNamespace:  false
-  AfterObjCDeclaration: false
-  AfterStruct:     true
-  AfterUnion:      false
-  AfterExternBlock: false
-  BeforeCatch:     false
-  BeforeElse:      false
-  BeforeLambdaBody: false
-  BeforeWhile:     false
-  IndentBraces:    false
-  SplitEmptyFunction: false
-  SplitEmptyRecord: false
-  SplitEmptyNamespace: false
-ColumnLimit:     120
-# Force pointers to the type for C++.
+  AfterCaseLabel:  false       # Don't put brace on new line after case labels
+  AfterClass:      true        # Put opening brace on new line after class definition
+  AfterControlStatement: MultiLine  # Only break before braces if the control statement spans multiple lines
+  AfterEnum:       false       # Don't break after enum
+  AfterFunction:   false       # Don't break after function declaration (keep on same line)
+  AfterNamespace:  false       # Don't break after namespace
+  AfterObjCDeclaration: false  # Objective-C related (not used in CGAL)
+  AfterStruct:     true        # Put opening brace on new line after struct definition
+  AfterUnion:      false       # Don't break after union
+  AfterExternBlock: false      # Don't break after extern "C" blocks
+  BeforeCatch:     false       # Don't put catch on new line
+  BeforeElse:      false       # Don't put else on new line
+  BeforeLambdaBody: false      # Don't break before lambda body
+  BeforeWhile:     false       # Don't put while on new line (do-while loops)
+  IndentBraces:    false       # Don't indent the braces themselves
+  SplitEmptyFunction: false    # Don't split empty functions across lines
+  SplitEmptyRecord: false      # Don't split empty classes/structs across lines
+  SplitEmptyNamespace: false   # Don't split empty namespaces across lines
+
+# Line length
+ColumnLimit:     120  # Maximum line length of 120 characters
+
+# Pointer and reference alignment
+# Force pointers and references to align with the type (e.g., `int* ptr` not `int *ptr`)
 DerivePointerAlignment: false
 PointerAlignment: Left
-# Control the spaces around conditionals
-SpacesInConditionalStatement: false
-SpaceBeforeParens: false
+
+# Spacing in control statements
+SpacesInConditionalStatement: false  # No extra spaces inside conditionals: `if(condition)` not `if( condition )`
+SpaceBeforeParens: false  # No space before parentheses: `if(` not `if (`
+
+# Include directive handling
+SortIncludes:    Never  # Preserve the original order of #include statements (don't sort them)
+
+# Preprocessor directive formatting
+IndentPPDirectives: None  # Don't indent preprocessor directives (#ifdef, #include, etc.)
+
+# Blank line handling
+MaxEmptyLinesToKeep: 2  # Keep up to 2 consecutive blank lines
 ...

Arrangement_on_surface_2/include/CGAL/Arr_circle_segment_traits_2.h

@@ -30,7 +30,7 @@
 
 #include <CGAL/tags.h>
 #include <CGAL/Arr_tags.h>
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Arr_geometry_traits/Circle_segment_2.h>
 
 namespace CGAL {
@@ -41,31 +41,31 @@ namespace CGAL {
 template <typename Kernel_, bool Filter = true>
 class Arr_circle_segment_traits_2 {
 public:
-  typedef Kernel_                                        Kernel;
-  typedef typename Kernel::FT                            NT;
-  typedef typename Kernel::Point_2                       Rational_point_2;
-  typedef typename Kernel::Segment_2                     Rational_segment_2;
-  typedef typename Kernel::Circle_2                      Rational_circle_2;
-  typedef _One_root_point_2<NT, Filter>                  Point_2;
-  typedef typename Point_2::CoordNT                      CoordNT;
-  typedef _Circle_segment_2<Kernel, Filter>              Curve_2;
-  typedef _X_monotone_circle_segment_2<Kernel, Filter>   X_monotone_curve_2;
-  typedef unsigned int                                   Multiplicity;
-  typedef Arr_circle_segment_traits_2<Kernel, Filter>    Self;
+  using Kernel = Kernel_;
+  using NT = typename Kernel::FT;
+  using Rational_point_2 = typename Kernel::Point_2;
+  using Rational_segment_2 = typename Kernel::Segment_2;
+  using Rational_circle_2 = typename Kernel::Circle_2;
+  using Point_2 = _One_root_point_2<NT, Filter>;
+  using CoordNT = typename Point_2::CoordNT;
+  using Curve_2 = _Circle_segment_2<Kernel, Filter>;
+  using X_monotone_curve_2 = _X_monotone_circle_segment_2<Kernel, Filter>;
+  using Multiplicity = std::size_t;
+  using Self = Arr_circle_segment_traits_2<Kernel, Filter>;
 
   // Category tags:
-  typedef Tag_true                                   Has_left_category;
-  typedef Tag_true                                   Has_merge_category;
-  typedef Tag_false                                  Has_do_intersect_category;
+  using Has_left_category = Tag_true;
+  using Has_merge_category = Tag_true;
+  using Has_do_intersect_category = Tag_false;
 
-  typedef Arr_oblivious_side_tag                     Left_side_category;
-  typedef Arr_oblivious_side_tag                     Bottom_side_category;
-  typedef Arr_oblivious_side_tag                     Top_side_category;
-  typedef Arr_oblivious_side_tag                     Right_side_category;
+  using Left_side_category = Arr_oblivious_side_tag;
+  using Bottom_side_category = Arr_oblivious_side_tag;
+  using Top_side_category = Arr_oblivious_side_tag;
+  using Right_side_category = Arr_oblivious_side_tag;
 
 protected:
   // Type definition for the intersection points mapping.
-  typedef typename X_monotone_curve_2::Intersection_map   Intersection_map;
+  using Intersection_map = typename X_monotone_curve_2::Intersection_map;
 
   mutable Intersection_map inter_map;   // Mapping pairs of curve IDs to their
                                         // intersection points.
@@ -78,8 +78,7 @@ public:
   {}
 
   /*! obtains the next curve index. */
-  static unsigned int get_index ()
-  {
+  static unsigned int get_index() {
 #ifdef CGAL_NO_ATOMIC
     static unsigned int index;
 #else
@@ -91,8 +90,7 @@ public:
   /// \name Basic functor definitions.
   //@{
 
-  class Compare_x_2
-  {
+  class Compare_x_2 {
   public:
     /*! compares the \f$x\f$-coordinates of two points.
      * \param p1 The first point.
@@ -101,23 +99,17 @@ public:
      *         SMALLER if x(p1) < x(p2);
      *         EQUAL if x(p1) = x(p2).
      */
-    Comparison_result operator() (const Point_2& p1, const Point_2& p2) const
-    {
-      if (p1.identical (p2))
-        return (EQUAL);
+    Comparison_result operator() (const Point_2& p1, const Point_2& p2) const {
+      if (p1.identical (p2)) return (EQUAL);
 
       return (CGAL::compare (p1.x(), p2.x()));
     }
   };
 
   /*! obtains a `Compare_x_2` functor object. */
-  Compare_x_2 compare_x_2_object () const
-  {
-    return Compare_x_2();
-  }
+  Compare_x_2 compare_x_2_object () const { return Compare_x_2(); }
 
-  class Compare_xy_2
-  {
+  class Compare_xy_2 {
   public:
     /*! compares two points lexigoraphically: by x, then by y.
      * \param p1 The first point.
@@ -126,15 +118,11 @@ public:
      *         SMALLER if x(p1) < x(p2), or if x(p1) = x(p2) and y(p1) < y(p2);
      *         EQUAL if the two points are equal.
      */
-    Comparison_result operator() (const Point_2& p1, const Point_2& p2) const
-    {
-      if (p1.identical (p2))
-        return (EQUAL);
+    Comparison_result operator() (const Point_2& p1, const Point_2& p2) const {
+      if (p1.identical (p2)) return (EQUAL);
 
-      Comparison_result  res = CGAL::compare (p1.x(), p2.x());
-
-      if (res != EQUAL)
-        return (res);
+      Comparison_result res = CGAL::compare(p1.x(), p2.x());
+      if (res != EQUAL) return (res);
 
       return (CGAL::compare (p1.y(), p2.y()));
     }
@@ -142,69 +130,51 @@ public:
 
   /*! obtains a Compare_xy_2 functor object. */
   Compare_xy_2 compare_xy_2_object () const
-  {
-    return Compare_xy_2();
-  }
+  { return Compare_xy_2(); }
 
-  class Construct_min_vertex_2
-  {
+  class Construct_min_vertex_2 {
   public:
     /*! obtains the left endpoint of the \f$x\f$-monotone curve (segment).
      * \param cv The curve.
      * \return The left endpoint.
      */
     const Point_2& operator() (const X_monotone_curve_2 & cv) const
-    {
-      return (cv.left());
-    }
+    { return (cv.left()); }
   };
 
   /*! obtains a `Construct_min_vertex_2` functor object. */
   Construct_min_vertex_2 construct_min_vertex_2_object () const
-  {
-    return Construct_min_vertex_2();
-  }
+  { return Construct_min_vertex_2(); }
 
-  class Construct_max_vertex_2
-  {
+  class Construct_max_vertex_2 {
   public:
     /*! obtains the right endpoint of the \f$x\f$-monotone curve (segment).
      * \param cv The curve.
      * \return The right endpoint.
      */
     const Point_2& operator() (const X_monotone_curve_2 & cv) const
-    {
-      return (cv.right());
-    }
+    { return (cv.right()); }
   };
 
   /*! obtains a Construct_max_vertex_2 functor object. */
   Construct_max_vertex_2 construct_max_vertex_2_object () const
-  {
-    return Construct_max_vertex_2();
-  }
+  { return Construct_max_vertex_2(); }
 
-  class Is_vertical_2
-  {
+  class Is_vertical_2 {
   public:
     /*! checks whether the given \f$x\f$-monotone curve is a vertical segment.
      * \param cv The curve.
      * \return (true) if the curve is a vertical segment; (false) otherwise.
      */
     bool operator() (const X_monotone_curve_2& cv) const
-    {
-      return (cv.is_vertical());
-    }
+    { return (cv.is_vertical()); }
   };
 
   /*! obtains an `Is_vertical_2` functor object. */
   Is_vertical_2 is_vertical_2_object () const
-  {
-    return Is_vertical_2();
-  }
+  { return Is_vertical_2(); }
 
-  class Compare_y_at_x_2
-  {
+  class Compare_y_at_x_2 {
   public:
     /*! returns the location of the given point with respect to the input curve.
      * \param cv The curve.
@@ -214,23 +184,19 @@ public:
      *         LARGER if y(p) > cv(x(p)), i.e. the point is above the curve;
      *         EQUAL if p lies on the curve.
      */
-    Comparison_result operator() (const Point_2& p,
-                                  const X_monotone_curve_2& cv) const
-    {
-      CGAL_precondition (cv.is_in_x_range (p));
+    Comparison_result operator()(const Point_2& p,
+                                 const X_monotone_curve_2& cv) const {
+      CGAL_precondition (cv.is_in_x_range(p));
 
-      return (cv.point_position (p));
+      return (cv.point_position(p));
     }
   };
 
   /*! obtains a `Compare_y_at_x_2` functor object. */
   Compare_y_at_x_2 compare_y_at_x_2_object () const
-  {
-    return Compare_y_at_x_2();
-  }
+  { return Compare_y_at_x_2(); }
 
-  class Compare_y_at_x_right_2
-  {
+  class Compare_y_at_x_right_2 {
   public:
     /*! compares the y value of two \f$x\f$-monotone curves immediately to the
      * right of their intersection point.
@@ -244,30 +210,29 @@ public:
      */
     Comparison_result operator() (const X_monotone_curve_2& cv1,
                                   const X_monotone_curve_2& cv2,
-                                  const Point_2& p) const
-    {
+                                  const Point_2& p) const {
       // Make sure that p lies on both curves, and that both are defined to its
       // right (so their right endpoint is lexicographically larger than p).
       CGAL_precondition (cv1.point_position (p) == EQUAL &&
                          cv2.point_position (p) == EQUAL);
 
       if ((CGAL::compare (cv1.left().x(),cv1.right().x()) == EQUAL) &&
-          (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL))
-      { //both cv1 and cv2 are vertical
+          (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL)) {
+        //both cv1 and cv2 are vertical
         CGAL_precondition (!(cv1.right()).equals(p) && !(cv2.right()).equals(p));
       }
       else if ((CGAL::compare (cv1.left().x(),cv1.right().x()) != EQUAL) &&
-               (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL))
-      { //only cv1 is vertical
+               (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL)) {
+        //only cv1 is vertical
         CGAL_precondition (!(cv1.right()).equals(p));
       }
       else if ((CGAL::compare (cv1.left().x(),cv1.right().x()) == EQUAL) &&
-               (CGAL::compare (cv2.left().x(),cv2.right().x()) != EQUAL))
-      { //only cv2 is vertical
+               (CGAL::compare (cv2.left().x(),cv2.right().x()) != EQUAL)) {
+        //only cv2 is vertical
         CGAL_precondition (!(cv2.right()).equals(p));
       }
-      else
-      { //both cv1 and cv2 are non vertical
+      else {
+        //both cv1 and cv2 are non vertical
         CGAL_precondition (CGAL::compare (cv1.right().x(),p.x()) == LARGER &&
                            CGAL::compare (cv2.right().x(),p.x()) == LARGER);
       }
@@ -278,12 +243,9 @@ public:
 
   /*! obtains a `Compare_y_at_x_right_2` functor object. */
   Compare_y_at_x_right_2 compare_y_at_x_right_2_object () const
-  {
-    return Compare_y_at_x_right_2();
-  }
+  { return Compare_y_at_x_right_2(); }
 
-  class Compare_y_at_x_left_2
-  {
+  class Compare_y_at_x_left_2 {
   public:
     /*! compares the \f$y\f$-value of two \f$x\f$-monotone curves immediately to
      * the left of their intersection point.
@@ -297,8 +259,7 @@ public:
      */
     Comparison_result operator() (const X_monotone_curve_2& cv1,
                                   const X_monotone_curve_2& cv2,
-                                  const Point_2& p) const
-    {
+                                  const Point_2& p) const {
       // Make sure that p lies on both curves, and that both are defined to its
       // left (so their left endpoint is lexicographically smaller than p).
 
@@ -306,25 +267,25 @@ public:
                          cv2.point_position (p) == EQUAL);
 
       if ((CGAL::compare (cv1.left().x(),cv1.right().x()) == EQUAL) &&
-          (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL))
-          { //both cv1 and cv2 are vertical
-         CGAL_precondition (!(cv1.left()).equals(p) && !(cv2.left()).equals(p));
-          }
-          else if ((CGAL::compare (cv1.left().x(),cv1.right().x()) != EQUAL) &&
-                   (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL))
-          { //only cv1 is vertical
-         CGAL_precondition (!(cv1.left()).equals(p));
-          }
-          else if ((CGAL::compare (cv1.left().x(),cv1.right().x()) == EQUAL) &&
-                   (CGAL::compare (cv2.left().x(),cv2.right().x()) != EQUAL))
-          { //only cv2 is vertical
-         CGAL_precondition (!(cv2.left()).equals(p));
-          }
-          else
-          { //both cv1 and cv2 are non vertical
+          (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL)) {
+        //both cv1 and cv2 are vertical
+        CGAL_precondition (!(cv1.left()).equals(p) && !(cv2.left()).equals(p));
+      }
+      else if ((CGAL::compare (cv1.left().x(),cv1.right().x()) != EQUAL) &&
+               (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL)) {
+        //only cv1 is vertical
+        CGAL_precondition (!(cv1.left()).equals(p));
+      }
+      else if ((CGAL::compare (cv1.left().x(),cv1.right().x()) == EQUAL) &&
+               (CGAL::compare (cv2.left().x(),cv2.right().x()) != EQUAL)) {
+        //only cv2 is vertical
+        CGAL_precondition (!(cv2.left()).equals(p));
+      }
+      else {
+        //both cv1 and cv2 are non vertical
         CGAL_precondition (CGAL::compare (cv1.left().x(),p.x()) == SMALLER &&
                            CGAL::compare (cv2.left().x(),p.x()) == SMALLER);
-          }
+      }
       // Compare the two curves immediately to the left of p:
       return (cv1.compare_to_left (cv2, p));
     }
@@ -332,12 +293,9 @@ public:
 
   /*! obtains a `Compare_y_at_x_left_2` functor object. */
   Compare_y_at_x_left_2 compare_y_at_x_left_2_object () const
-  {
-    return Compare_y_at_x_left_2();
-  }
+  { return Compare_y_at_x_left_2(); }
 
-  class Equal_2
-  {
+  class Equal_2 {
   public:
     /*! checks if the two \f$x\f$-monotone curves are the same (have the same
      * graph).
@@ -346,10 +304,8 @@ public:
      * \return (true) if the two curves are the same; (false) otherwise.
      */
     bool operator() (const X_monotone_curve_2& cv1,
-                     const X_monotone_curve_2& cv2) const
-    {
-      if (&cv1 == &cv2)
-        return (true);
+                     const X_monotone_curve_2& cv2) const {
+      if (&cv1 == &cv2) return (true);
 
       return (cv1.equals (cv2));
     }
@@ -360,24 +316,20 @@ public:
      * \return (true) if the two point are the same; (false) otherwise.
      */
     bool operator() (const Point_2& p1, const Point_2& p2) const
-    {
-      return (p1.equals (p2));
-    }
+    { return (p1.equals (p2)); }
   };
 
   /*! obtains an `Equal_2` functor object. */
   Equal_2 equal_2_object () const
-  {
-    return Equal_2();
-  }
+  { return Equal_2(); }
   //@}
 
   /// \name Functor definitions for approximations. Used by the landmarks
   // point-location strategy and the drawing procedure.
   //@{
-  typedef double                                        Approximate_number_type;
-  typedef CGAL::Cartesian<Approximate_number_type>      Approximate_kernel;
-  typedef Approximate_kernel::Point_2                   Approximate_point_2;
+  using Approximate_number_type = double;
+  using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
+  using Approximate_point_2 = Approximate_kernel::Point_2;
 
   class Approximate_2 {
   protected:
@@ -557,7 +509,7 @@ public:
    */
   class Make_x_monotone_2 {
   private:
-    typedef Arr_circle_segment_traits_2<Kernel_, Filter> Self;
+    using Self = Arr_circle_segment_traits_2<Kernel_, Filter>;
 
     bool m_use_cache;
 
@@ -573,8 +525,7 @@ public:
      * \return the past-the-end iterator.
      */
     template <typename OutputIterator>
-    OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const
-    {
+    OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const {
       // Increment the serial number of the curve cv, which will serve as its
       // unique identifier.
       unsigned int index = 0;
@@ -591,7 +542,7 @@ public:
 
       // Check the case of a degenerate circle (a point).
       const typename Kernel::Circle_2&  circ = cv.supporting_circle();
-      CGAL::Sign   sign_rad = CGAL::sign (circ.squared_radius());
+      CGAL::Sign sign_rad = CGAL::sign (circ.squared_radius());
       CGAL_precondition (sign_rad != NEGATIVE);
 
       if (sign_rad == ZERO) {
@@ -603,8 +554,8 @@ public:
 
       // The curve is circular: compute the to vertical tangency points
       // of the supporting circle.
-      Point_2         vpts[2];
-      unsigned int    n_vpts = cv.vertical_tangency_points (vpts);
+      Point_2 vpts[2];
+      unsigned int n_vpts = cv.vertical_tangency_points (vpts);
 
       if (cv.is_full()) {
         CGAL_assertion (n_vpts == 2);
@@ -674,8 +625,7 @@ public:
   Make_x_monotone_2 make_x_monotone_2_object() const
   { return Make_x_monotone_2(m_use_cache); }
 
-  class Split_2
-  {
+  class Split_2 {
   public:
 
     /*! splits a given \f$x\f$-monotone curve at a given point into two
@@ -687,8 +637,7 @@ public:
      * \pre `p` lies on cv but is not one of its end-points.
      */
     void operator() (const X_monotone_curve_2& cv, const Point_2& p,
-                     X_monotone_curve_2& c1, X_monotone_curve_2& c2) const
-    {
+                     X_monotone_curve_2& c1, X_monotone_curve_2& c2) const {
       CGAL_precondition (cv.point_position(p)==EQUAL &&
       ! p.equals (cv.source()) &&
       ! p.equals (cv.target()));
@@ -699,10 +648,7 @@ public:
   };
 
   /*! obtains a `Split_2` functor object. */
-  Split_2 split_2_object () const
-  {
-    return Split_2();
-  }
+  Split_2 split_2_object () const { return Split_2(); }
 
   class Intersect_2 {
   private:
@@ -730,8 +676,7 @@ public:
   /*! obtains an `Intersect_2` functor object. */
   Intersect_2 intersect_2_object() const { return (Intersect_2(inter_map)); }
 
-  class Are_mergeable_2
-  {
+  class Are_mergeable_2 {
   public:
     /*! checks whether it is possible to merge two given \f$x\f$-monotone curves.
      * \param cv1 The first curve.
@@ -742,24 +687,19 @@ public:
      */
     bool operator() (const X_monotone_curve_2& cv1,
                      const X_monotone_curve_2& cv2) const
-    {
-      return (cv1.can_merge_with (cv2));
-    }
+    { return (cv1.can_merge_with (cv2)); }
   };
 
   /*! obtains an `Are_mergeable_2` functor object. */
   Are_mergeable_2 are_mergeable_2_object () const
-  {
-    return Are_mergeable_2();
-  }
+  { return Are_mergeable_2(); }
 
   /*! \class Merge_2
    * A functor that merges two \f$x\f$-monotone arcs into one.
    */
-  class Merge_2
-  {
+  class Merge_2 {
   protected:
-    typedef Arr_circle_segment_traits_2<Kernel, Filter> Traits;
+    using Traits = Arr_circle_segment_traits_2<Kernel, Filter>;
 
     /*! The traits (in case it has state) */
     const Traits* m_traits;
@@ -780,8 +720,7 @@ public:
      */
     void operator() (const X_monotone_curve_2& cv1,
                      const X_monotone_curve_2& cv2,
-                     X_monotone_curve_2& c) const
-    {
+                     X_monotone_curve_2& c) const {
       CGAL_precondition(m_traits->are_mergeable_2_object()(cv2, cv1));
 
       c = cv1;
@@ -790,20 +729,15 @@ public:
   };
 
   /*! obtains a `Merge_2` functor object. */
-  Merge_2 merge_2_object () const
-  {
-    return Merge_2(this);
-  }
+  Merge_2 merge_2_object () const { return Merge_2(this); }
 
-  class Compare_endpoints_xy_2
-  {
+  class Compare_endpoints_xy_2 {
   public:
     /*! compares lexicogrphic the endpoints of a \f$x\f$-monotone curve.
      * \param cv the curve
      * \return `SMALLER` if the curve is directed right, else return `LARGER`.
      */
-    Comparison_result operator()(const X_monotone_curve_2& cv) const
-    {
+    Comparison_result operator()(const X_monotone_curve_2& cv) const {
       if(cv.is_directed_right())
         return(SMALLER);
       return (LARGER);
@@ -812,32 +746,25 @@ public:
 
   /*! obtains a `Compare_endpoints_xy_2` functor object. */
   Compare_endpoints_xy_2 compare_endpoints_xy_2_object() const
-  {
-    return Compare_endpoints_xy_2();
-  }
+  { return Compare_endpoints_xy_2(); }
 
-  class Construct_opposite_2
-  {
+  class Construct_opposite_2 {
   public:
     /*! constructs an opposite \f$x\f$-monotone curve.
      * \param cv the curve
      * \return an opposite \f$x\f$-monotone curve.
      */
     X_monotone_curve_2 operator()(const X_monotone_curve_2& cv) const
-    {
-      return cv.construct_opposite();
-    }
+    { return cv.construct_opposite(); }
   };
 
   /*! obtains a `Construct_opposite_2` functor object. */
   Construct_opposite_2 construct_opposite_2_object() const
-  {
-    return Construct_opposite_2();
-  }
+  { return Construct_opposite_2(); }
 
   class Trim_2 {
   protected:
-    typedef Arr_circle_segment_traits_2<Kernel, Filter> Traits;
+    using Traits = Arr_circle_segment_traits_2<Kernel, Filter>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -860,8 +787,7 @@ public:
      */
     X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv,
                                   const Point_2& src,
-                                  const Point_2& tgt)const
-    {
+                                  const Point_2& tgt)const {
       // make functor objects
       CGAL_precondition_code(Compare_y_at_x_2 compare_y_at_x_2 =
                              m_traits.compare_y_at_x_2_object());
@@ -885,7 +811,6 @@ public:
   Trim_2 trim_2_object() const { return Trim_2(*this); }
 
   // @}
-
 };
 
 } // namespace CGAL

Arrangement_on_surface_2/include/CGAL/Arr_circular_arc_traits_2.h

@@ -40,55 +40,54 @@
 namespace CGAL {
 
 namespace internal{
-template <class CircularKernel>
-class Non_x_monotonic_Circular_arc_2
-  : public CircularKernel::Circular_arc_2
-{
-  typedef typename CircularKernel::FT             FT;
-  typedef typename CircularKernel::Point_2        Point_2;
-  typedef typename CircularKernel::Line_2         Line_2;
-  typedef typename CircularKernel::Circle_2       Circle_2;
-  typedef typename CircularKernel::Circular_arc_point_2
-                                                Circular_arc_point_2;
 
-  typedef typename CircularKernel::Circular_arc_2 Base;
+template <typename CircularKernel>
+class Non_x_monotonic_Circular_arc_2 :
+    public CircularKernel::Circular_arc_2 {
+  using FT = typename CircularKernel::FT;
+  using Point_2 = typename CircularKernel::Point_2;
+  using Line_2 = typename CircularKernel::Line_2;
+  using Circle_2 = typename CircularKernel::Circle_2;
+  using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
+
+  using Base = typename CircularKernel::Circular_arc_2;
 
 public:
   Non_x_monotonic_Circular_arc_2(): Base(){}
 
-  Non_x_monotonic_Circular_arc_2(const Circle_2 &c): Base(c){}
+  Non_x_monotonic_Circular_arc_2(const Circle_2& c): Base(c){}
   // Not Documented
-  Non_x_monotonic_Circular_arc_2(const Circle_2 &support,
-                                 const Line_2 &l1, const bool b_l1,
-                                 const Line_2 &l2, const bool b_l2)
-    : Base(support,l1,b_l1,l2,b_l2){}
+  Non_x_monotonic_Circular_arc_2(const Circle_2& support,
+                                 const Line_2& l1, const bool b_l1,
+                                 const Line_2& l2, const bool b_l2) :
+    Base(support,l1,b_l1,l2,b_l2){}
 
   // Not Documented
-  Non_x_monotonic_Circular_arc_2(const Circle_2 &c,
-                                 const Circle_2 &c1, const bool b_1,
-                                 const Circle_2 &c2, const bool b_2)
-    : Base(c,c1,b_1,c2,b_2)
+  Non_x_monotonic_Circular_arc_2(const Circle_2& c,
+                                 const Circle_2& c1, const bool b_1,
+                                 const Circle_2& c2, const bool b_2) :
+    Base(c,c1,b_1,c2,b_2)
   {}
 
-  Non_x_monotonic_Circular_arc_2(const Point_2 &start,
-                                 const Point_2 &middle,
-                                 const Point_2 &end)
-    : Base(start,middle,end)
+  Non_x_monotonic_Circular_arc_2(const Point_2& start,
+                                 const Point_2& middle,
+                                 const Point_2& end) :
+    Base(start,middle,end)
   {}
 
-  Non_x_monotonic_Circular_arc_2(const Circle_2 &support,
-                                 const Circular_arc_point_2 &begin,
-                                 const Circular_arc_point_2 &end)
-    : Base(support,begin,end)
+  Non_x_monotonic_Circular_arc_2(const Circle_2& support,
+                                 const Circular_arc_point_2& begin,
+                                 const Circular_arc_point_2& end) :
+    Base(support,begin,end)
   {}
 
-  Non_x_monotonic_Circular_arc_2(const Point_2 &start,
-                                 const Point_2 &end,
-                                 const FT &bulge)
-    : Base(start,end,bulge)
+  Non_x_monotonic_Circular_arc_2(const Point_2& start,
+                                 const Point_2& end,
+                                 const FT& bulge) :
+    Base(start,end,bulge)
   {}
 
- Non_x_monotonic_Circular_arc_2(const Base& a) : Base(a) {}
+  Non_x_monotonic_Circular_arc_2(const Base& a) : Base(a) {}
 };
 
 } //namespace internal
@@ -98,45 +97,40 @@ public:
 
 template < typename CircularKernel >
 class Arr_circular_arc_traits_2 {
-
   CircularKernel ck;
 
 public:
+  using Kernel = CircularKernel;
+  using Curve_2 = internal::Non_x_monotonic_Circular_arc_2<CircularKernel>;
+  using X_monotone_curve_2 = typename CircularKernel::Circular_arc_2;
 
-  typedef CircularKernel Kernel;
-  typedef internal::Non_x_monotonic_Circular_arc_2<CircularKernel>  Curve_2;
-  typedef typename CircularKernel::Circular_arc_2                   X_monotone_curve_2;
+  using Point = typename CircularKernel::Circular_arc_point_2;
+  using Point_2 = typename CircularKernel::Circular_arc_point_2;
 
-  typedef typename CircularKernel::Circular_arc_point_2 Point;
-  typedef typename CircularKernel::Circular_arc_point_2 Point_2;
+  using Multiplicity = std::size_t;
 
-  typedef unsigned int                           Multiplicity;
+  using Has_left_category = CGAL::Tag_false;
+  using Has_merge_category = CGAL::Tag_false;
+  using Has_do_intersect_category = CGAL::Tag_false;
 
-  typedef CGAL::Tag_false                        Has_left_category;
-  typedef CGAL::Tag_false                        Has_merge_category;
-  typedef CGAL::Tag_false                        Has_do_intersect_category;
+  using Left_side_category = Arr_oblivious_side_tag;
+  using Bottom_side_category = Arr_oblivious_side_tag;
+  using Top_side_category = Arr_oblivious_side_tag;
+  using Right_side_category = Arr_oblivious_side_tag;
 
-  typedef Arr_oblivious_side_tag                 Left_side_category;
-  typedef Arr_oblivious_side_tag                 Bottom_side_category;
-  typedef Arr_oblivious_side_tag                 Top_side_category;
-  typedef Arr_oblivious_side_tag                 Right_side_category;
+  Arr_circular_arc_traits_2(const CircularKernel& k = CircularKernel()) : ck(k) {}
 
-  Arr_circular_arc_traits_2(const CircularKernel &k = CircularKernel())
-    : ck(k) {}
-
-  typedef typename CircularKernel::Compare_x_2          Compare_x_2;
-  typedef typename CircularKernel::Compare_xy_2         Compare_xy_2;
-  typedef typename CircularKernel::Compare_y_at_x_2     Compare_y_at_x_2;
-  typedef typename CircularKernel::Compare_y_to_right_2 Compare_y_at_x_right_2;
-  typedef typename CircularKernel::Construct_circular_max_vertex_2
-                                                        Construct_max_vertex_2;
-  typedef typename CircularKernel::Construct_circular_min_vertex_2
-                                                        Construct_min_vertex_2;
-  typedef typename CircularKernel::Equal_2              Equal_2;
+  using Compare_x_2 = typename CircularKernel::Compare_x_2;
+  using Compare_xy_2 = typename CircularKernel::Compare_xy_2;
+  using Compare_y_at_x_2 = typename CircularKernel::Compare_y_at_x_2;
+  using Compare_y_at_x_right_2 = typename CircularKernel::Compare_y_to_right_2;
+  using Construct_max_vertex_2 = typename CircularKernel::Construct_circular_max_vertex_2;
+  using Construct_min_vertex_2 = typename CircularKernel::Construct_circular_min_vertex_2;
+  using Equal_2 = typename CircularKernel::Equal_2;
   // typedef typename CircularKernel::Make_x_monotone_2    Make_x_monotone_2;
-  typedef typename CircularKernel::Split_2              Split_2;
-  typedef typename CircularKernel::Intersect_2          Intersect_2;
-  typedef typename CircularKernel::Is_vertical_2        Is_vertical_2;
+  using Split_2 = typename CircularKernel::Split_2;
+  using Intersect_2 = typename CircularKernel::Intersect_2;
+  using Is_vertical_2 = typename CircularKernel::Is_vertical_2;
 
   Compare_x_2 compare_x_2_object() const
   { return ck.compare_x_2_object(); }
@@ -160,26 +154,23 @@ public:
   { return ck.split_2_object(); }
 
   Intersect_2 intersect_2_object() const
-    { return ck.intersect_2_object(); }
+  { return ck.intersect_2_object(); }
 
   Construct_max_vertex_2 construct_max_vertex_2_object() const
-    { return ck.construct_circular_max_vertex_2_object(); }
+  { return ck.construct_circular_max_vertex_2_object(); }
 
   Construct_min_vertex_2 construct_min_vertex_2_object() const
-    { return ck.construct_circular_min_vertex_2_object(); }
+  { return ck.construct_circular_min_vertex_2_object(); }
 
   Is_vertical_2 is_vertical_2_object() const
-    { return ck.is_vertical_2_object();  }
-
+  { return ck.is_vertical_2_object();  }
 
   //! A functor for subdividing curves into x-monotone curves.
   class Make_x_monotone_2 {
   public:
     template <typename OutputIterator>
-    OutputIterator operator()(const Curve_2& arc, OutputIterator oi) const
-    {
-      typedef std::variant<Point_2, X_monotone_curve_2>
-        Make_x_monotone_result;
+    OutputIterator operator()(const Curve_2& arc, OutputIterator oi) const {
+      using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
 
       std::vector<Make_x_monotone_result> objs;
       CircularKernel().make_x_monotone_2_object()(arc, std::back_inserter(objs));

Arrangement_on_surface_2/include/CGAL/Arr_circular_line_arc_traits_2.h

@@ -41,515 +41,395 @@
 #include <CGAL/Arr_tags.h>
 
 namespace CGAL {
-  namespace VariantFunctors{
 
-    // Takes an iterator range of Object(Line/Circular_arc/Point),
-    // returns a variant of Line, Circular_arc, and Point_2.
-    template <class CK, class Arc1, class Arc2, class OutputIterator>
-    OutputIterator
-    object_to_object_variant(const std::vector<CGAL::Object>& res1,
-                             OutputIterator res2)
-    {
-      typedef typename CK::Circular_arc_point_2         Point_2;
-      typedef std::variant<Arc1, Arc2>                X_monotone_curve_2;
-      typedef std::variant<Point_2, X_monotone_curve_2>
-        Make_x_monotone_result;
+namespace VariantFunctors {
 
-      for (auto it = res1.begin(); it != res1.end(); ++it) {
-        if (const Arc1* arc = CGAL::object_cast<Arc1>(&*it)) {
-          std::variant<Arc1, Arc2> v =  *arc;
-          *res2++ = Make_x_monotone_result(v);
-        }
-        else if (const Arc2* line = CGAL::object_cast<Arc2>(&*it)) {
-          std::variant<Arc1, Arc2> v =  *line;
-          *res2++ = Make_x_monotone_result(v);
-        }
-        else if (const Point_2* p = CGAL::object_cast<Point_2>(&*it)) {
-          *res2++ = Make_x_monotone_result(*p);
-        }
-        else CGAL_error();
+// Takes an iterator range of Object(Line/Circular_arc/Point),
+// returns a variant of Line, Circular_arc, and Point_2.
+template <typename CK, typename Arc1, typename Arc2, typename OutputIterator>
+OutputIterator object_to_object_variant(const std::vector<CGAL::Object>& res1,
+                                        OutputIterator res2) {
+  using Point_2 = typename CK::Circular_arc_point_2;
+  using X_monotone_curve_2 = std::variant<Arc1, Arc2>;
+  using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
+
+  for (auto it = res1.begin(); it != res1.end(); ++it) {
+    if (const Arc1* arc = CGAL::object_cast<Arc1>(&*it)) {
+      std::variant<Arc1, Arc2> v = *arc;
+      *res2++ = Make_x_monotone_result(v);
+    }
+    else if (const Arc2* line = CGAL::object_cast<Arc2>(&*it)) {
+      std::variant<Arc1, Arc2> v = *line;
+      *res2++ = Make_x_monotone_result(v);
+    }
+    else if (const Point_2* p = CGAL::object_cast<Point_2>(&*it)) {
+      *res2++ = Make_x_monotone_result(*p);
+    }
+    else CGAL_error();
+  }
+  return res2;
+}
+
+template <typename CircularKernel, typename Arc1, typename Arc2>
+class Compare_y_to_right_2 {
+public:
+  using result_type = CGAL::Comparison_result;
+  using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
+
+  result_type operator()(const std::variant<Arc1, Arc2>& a1,
+                         const std::variant<Arc1, Arc2>& a2,
+                         const Circular_arc_point_2& p) const {
+    if (const Arc1* arc1 = std::get_if<Arc1>(&a1)) {
+      if (const Arc1* arc2 = std::get_if<Arc1>(&a2)) {
+        return CircularKernel().compare_y_to_right_2_object()(*arc1, *arc2, p);
       }
-      return res2;
+      else {
+        const Arc2* arc2e = std::get_if<Arc2>(&a2);
+        return CircularKernel().compare_y_to_right_2_object()(*arc1, *arc2e, p);
+      }
+    }
+    const Arc2* arc1 = std::get_if<Arc2>(&a1);
+    if (const Arc1* arc2 = std::get_if<Arc1>(&a2)) {
+      return CircularKernel().compare_y_to_right_2_object()(*arc1, *arc2, p);
+    }
+    const Arc2* arc2e = std::get_if<Arc2>(&a2);
+    return CircularKernel().compare_y_to_right_2_object()(*arc1, *arc2e, p);
+  }
+};
+
+template <typename CircularKernel>
+class Variant_Equal_2 {
+public:
+  template <typename T>
+  bool operator()(const T& a0, const T& a1) const
+  { return CircularKernel().equal_2_object()(a0,a1); }
+
+  template <typename T1, typename T2>
+  bool operator()(const T1& , const T2&) const
+  { return false; }
+};
+
+template <typename CircularKernel, class Arc1, class Arc2>
+class Equal_2 : public CircularKernel::Equal_2 {
+public:
+  using Curve_2 = std::variant< Arc1, Arc2>;
+  using result_type = bool;
+  using CircularKernel::Equal_2::operator();
+  using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
+  using Line_arc_2 = typename CircularKernel::Line_arc_2;
+  using Circular_arc_2 = typename CircularKernel::Circular_arc_2;
+  using CK_Equal_2 = typename CircularKernel::Equal_2;
+
+  result_type operator()(const Circular_arc_point_2& p0,
+                         const Circular_arc_point_2& p1) const
+  { return CK_Equal_2()(p0, p1); }
+
+  result_type operator()(const Circular_arc_2& a0, const Circular_arc_2& a1) const
+  { return CK_Equal_2()(a0, a1); }
+
+  result_type operator()(const Line_arc_2& a0, const Line_arc_2& a1) const
+  { return CK_Equal_2()(a0, a1); }
+
+  result_type operator()(const Line_arc_2& /*a0*/, const Circular_arc_2& /*a1*/) const
+  { return false; }
+
+  result_type operator()(const Circular_arc_2& /*a0*/, const Line_arc_2& /*a1*/) const
+  { return false; }
+
+  result_type operator()(const Curve_2& a0, const Curve_2& a1) const
+  { return std::visit(Variant_Equal_2<CircularKernel>(), a0, a1); }
+};
+
+template <typename CircularKernel, typename Arc1, typename Arc2>
+class Compare_y_at_x_2 {
+public:
+  using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
+  using result_type = CGAL::Comparison_result;
+
+  result_type operator()(const Circular_arc_point_2& p,
+                         const std::variant< Arc1, Arc2>& A1) const {
+    if (const Arc1* arc1 = std::get_if<Arc1>(&A1)){
+      return CircularKernel().compare_y_at_x_2_object()(p, *arc1);
+    }
+    else {
+      const Arc2* arc2 = std::get_if<Arc2>(&A1);
+      return CircularKernel().compare_y_at_x_2_object()(p, *arc2);
+    }
+  }
+};
+
+template <typename CircularKernel>
+class Variant_Do_overlap_2 {
+public:
+  template <typename T>
+  bool operator()(const T& a0, const T& a1) const
+  { return CircularKernel().do_overlap_2_object()(a0, a1); }
+
+  template <typename T1, typename T2>
+  bool operator()(const T1&, const T2&) const
+  { return false; }
+};
+
+template <typename CircularKernel, typename Arc1, typename Arc2>
+class Do_overlap_2 {
+public:
+  using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
+  using result_type = bool;
+
+  result_type operator()(const std::variant< Arc1, Arc2>& A0,
+                         const std::variant< Arc1, Arc2>& A1) const
+  { return std::visit(Variant_Do_overlap_2<CircularKernel>(), A0, A1); }
+};
+
+//! A functor for subdividing curves into x-monotone curves.
+template <typename CircularKernel, typename Arc1, typename Arc2>
+class Make_x_monotone_2 {
+public:
+  using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
+
+  template <typename OutputIterator, typename Not_X_Monotone>
+  OutputIterator operator()(const std::variant<Arc1, Arc2, Not_X_Monotone>& A,
+                            OutputIterator res) const {
+    if ( const Arc1* arc1 = std::get_if<Arc1>(&A)) {
+      return CircularKernel().make_x_monotone_2_object()(*arc1, res);
+    }
+    else {
+      const Arc2* arc2 = std::get_if<Arc2>(&A);
+      return CircularKernel().make_x_monotone_2_object()(*arc2, res);
+    }
+  }
+};
+
+template <typename CircularKernel, typename Arc1, typename Arc2>
+class Intersect_2 {
+public:
+  using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
+
+  template <typename OutputIterator>
+  OutputIterator operator()(const std::variant< Arc1, Arc2>& c1,
+                            const std::variant< Arc1, Arc2>& c2,
+                            OutputIterator oi) const {
+    if (const Arc1* arc1 = std::get_if<Arc1>(&c1)) {
+      if ( const Arc1* arc2 = std::get_if<Arc1>(&c2)) {
+        return CircularKernel().intersect_2_object()(*arc1, *arc2, oi);
+      }
+      const Arc2* arc2 = std::get_if<Arc2>(&c2);
+      return CircularKernel().intersect_2_object()(*arc1, *arc2, oi);
     }
 
-    template <class CircularKernel, class Arc1, class Arc2>
-    class Compare_y_to_right_2
-    {
-    public:
-      typedef CGAL::Comparison_result result_type;
-      typedef typename CircularKernel::Circular_arc_point_2
-                                                  Circular_arc_point_2;
-
-      result_type
-        operator()(const std::variant< Arc1, Arc2 > &a1,
-                   const std::variant< Arc1, Arc2 > &a2,
-                   const Circular_arc_point_2 &p) const
-      {
-        if ( const Arc1* arc1 = std::get_if<Arc1>( &a1 ) ){
-          if ( const Arc1* arc2 = std::get_if<Arc1>( &a2 ) ){
-            return CircularKernel()
-              .compare_y_to_right_2_object()(*arc1, *arc2, p);
-          }
-          else {
-            const Arc2* arc2e = std::get_if<Arc2>( &a2 );
-            return CircularKernel()
-              .compare_y_to_right_2_object()(*arc1, *arc2e, p);
-          }
-        }
-        const Arc2* arc1 = std::get_if<Arc2>( &a1 );
-        if ( const Arc1* arc2 = std::get_if<Arc1>( &a2 ) ){
-          return CircularKernel()
-            .compare_y_to_right_2_object()(*arc1, *arc2, p);
-        }
-        const Arc2* arc2e = std::get_if<Arc2>( &a2 );
-        return CircularKernel()
-          .compare_y_to_right_2_object()(*arc1, *arc2e, p);
-      }
-    };
-
-
-    template <class CircularKernel>
-    class Variant_Equal_2
-    {
-    public :
-
-      template < typename T >
-      bool
-      operator()(const T &a0, const T &a1) const
-      {
-        return CircularKernel().equal_2_object()(a0,a1);
-      }
-
-      template < typename T1, typename T2 >
-      bool
-      operator()(const T1 &, const T2 &) const
-      {
-        return false;
-      }
-    };
-
-
-
-    template <class CircularKernel, class Arc1, class Arc2>
-    class Equal_2
-      : public CircularKernel::Equal_2
-    {
-    public:
-      typedef std::variant< Arc1, Arc2 >  Curve_2;
-      typedef bool result_type;
-      using CircularKernel::Equal_2::operator();
-      typedef typename CircularKernel::Circular_arc_point_2
-                                                  Circular_arc_point_2;
-      typedef typename CircularKernel::Line_arc_2     Line_arc_2;
-      typedef typename CircularKernel::Circular_arc_2 Circular_arc_2;
-      typedef typename CircularKernel::Equal_2        CK_Equal_2;
-
-    result_type
-    operator() (const Circular_arc_point_2 &p0,
-                const Circular_arc_point_2 &p1) const
-    { return CK_Equal_2()(p0, p1); }
-
-    result_type
-    operator() (const Circular_arc_2 &a0, const Circular_arc_2 &a1) const
-    { return CK_Equal_2()(a0, a1); }
-
-    result_type
-    operator() (const Line_arc_2 &a0, const Line_arc_2 &a1) const
-    { return CK_Equal_2()(a0, a1); }
-
-    result_type
-    operator() ( const Line_arc_2 &/*a0*/, const Circular_arc_2 &/*a1*/) const
-    { return false; }
-
-    result_type
-    operator() ( const Circular_arc_2 &/*a0*/, const Line_arc_2 &/*a1*/) const
-    { return false; }
-
-      result_type
-      operator()(const Curve_2 &a0, const Curve_2 &a1) const
-      {
-        return std::visit
-          ( Variant_Equal_2<CircularKernel>(), a0, a1 );
-      }
-
-    };
-
-
-
-
-    template <class CircularKernel, class Arc1, class Arc2>
-    class Compare_y_at_x_2
-    {
-    public:
-      typedef typename CircularKernel::Circular_arc_point_2
-                                                  Circular_arc_point_2;
-      typedef CGAL::Comparison_result result_type;
-
-      result_type
-      operator() (const Circular_arc_point_2 &p,
-                  const std::variant< Arc1, Arc2 > &A1) const
-      {
-        if ( const Arc1* arc1 = std::get_if<Arc1>( &A1 ) ){
-          return CircularKernel().compare_y_at_x_2_object()(p, *arc1);
-        }
-        else {
-          const Arc2* arc2 = std::get_if<Arc2>( &A1 );
-          return CircularKernel().compare_y_at_x_2_object()(p, *arc2);
-        }
-      }
-    };
-
-    template <class CircularKernel>
-    class Variant_Do_overlap_2
-    {
-    public:
-      template < typename T >
-      bool
-      operator()(const T &a0, const T &a1) const
-      {
-        return CircularKernel().do_overlap_2_object()(a0, a1);
-      }
-
-      template < typename T1, typename T2 >
-      bool
-      operator()(const T1 &, const T2 &) const
-      {
-        return false;
-      }
-    };
-
-
-    template <class CircularKernel, class Arc1, class Arc2>
-    class Do_overlap_2
-    {
-    public:
-      typedef typename CircularKernel::Circular_arc_point_2
-                                                  Circular_arc_point_2;
-      typedef bool result_type;
-
-      result_type
-      operator()(const std::variant< Arc1, Arc2 > &A0,
-                 const std::variant< Arc1, Arc2 > &A1) const
-      {
-        return std::visit
-          ( Variant_Do_overlap_2<CircularKernel>(), A0, A1 );
-      }
-    };
-
-
-    //! A functor for subdividing curves into x-monotone curves.
-    template <class CircularKernel, class Arc1, class Arc2>
-    class Make_x_monotone_2
-    {
-    public:
-      typedef typename CircularKernel::Circular_arc_point_2
-                                                  Circular_arc_point_2;
-
-      template < class OutputIterator,class Not_X_Monotone >
-      OutputIterator
-      operator()(const std::variant<Arc1, Arc2, Not_X_Monotone> &A,
-                 OutputIterator res) const
-      {
-        if ( const Arc1* arc1 = std::get_if<Arc1>( &A ) ) {
-          return CircularKernel().
-            make_x_monotone_2_object()(*arc1, res);
-        }
-        else {
-          const Arc2* arc2 = std::get_if<Arc2>( &A );
-            return CircularKernel().
-              make_x_monotone_2_object()(*arc2, res);
-        }
-      }
-    };
-
-    template <class CircularKernel, class Arc1, class Arc2>
-    class Intersect_2
-    {
-    public:
-      typedef typename CircularKernel::Circular_arc_point_2
-                                                        Circular_arc_point_2;
-
-      template < class OutputIterator >
-        OutputIterator
-        operator()(const std::variant< Arc1, Arc2 > &c1,
-                   const std::variant< Arc1, Arc2 > &c2,
-                   OutputIterator oi) const
-      {
-        if ( const Arc1* arc1 = std::get_if<Arc1>( &c1 ) ){
-          if ( const Arc1* arc2 = std::get_if<Arc1>( &c2 ) ){
-            return CircularKernel().intersect_2_object()(*arc1, *arc2, oi);
-          }
-          const Arc2* arc2 = std::get_if<Arc2>( &c2 );
-          return CircularKernel().intersect_2_object()(*arc1, *arc2, oi);
-        }
-
-        const Arc2* arc1e = std::get_if<Arc2>( &c1 );
-        if ( const Arc1* arc2 = std::get_if<Arc1>( &c2 ) ){
-          return CircularKernel().intersect_2_object()(*arc1e, *arc2, oi);
-        }
-        const Arc2* arc2 = std::get_if<Arc2>( &c2 );
-        return CircularKernel().intersect_2_object()(*arc1e, *arc2, oi);
-      }
-
-    };
-
-    template <class CircularKernel, class Arc1, class Arc2>
-    class Split_2
-    {
-
-    public:
-    typedef typename CircularKernel::Circular_arc_point_2
-                                                Circular_arc_point_2;
-      typedef void result_type;
-      result_type
-        operator()(const std::variant< Arc1, Arc2 > &A,
-                   const Circular_arc_point_2 &p,
-                   std::variant< Arc1, Arc2 > &ca1,
-                   std::variant< Arc1, Arc2 > &ca2) const
-      {
-        // TODO : optimize by extracting the references from the variants ?
-        if ( const Arc1* arc1 = std::get_if<Arc1>( &A ) ){
-          Arc1 carc1;
-          Arc1 carc2;
-          CircularKernel().split_2_object()(*arc1, p, carc1, carc2);
-          ca1 = carc1;
-          ca2 = carc2;
-          return ;
-
-        }
-        else{
-          const Arc2* arc2 = std::get_if<Arc2>( &A );
-          Arc2 cline1;
-          Arc2 cline2;
-          CircularKernel().split_2_object()(*arc2, p, cline1, cline2);
-          ca1 = cline1;
-          ca2 = cline2;
-          return ;
-
-        }
-      }
-    };
-
-
-     template <class CircularKernel>
-    class Variant_Construct_min_vertex_2
-    {
-      typedef typename CircularKernel::Circular_arc_point_2
-                                                  Circular_arc_point_2;
-
-    public :
-
-      typedef Circular_arc_point_2  result_type;
-      //typedef const result_type&       qualified_result_type;
-
-      template < typename T >
-      //std::remove_reference_t<qualified_result_type>
-        Circular_arc_point_2
-      operator()(const T &a) const
-      {
-        //CGAL_kernel_precondition(CircularKernel().compare_xy_2_object()(a.left(), a.right())==CGAL::SMALLER);
-        return CircularKernel().construct_circular_min_vertex_2_object()(a);
-      }
-    };
-
-    template <class CircularKernel, class Arc1, class Arc2>
-    class Construct_min_vertex_2//: public Has_qrt
-    {
-      typedef typename CircularKernel::Circular_arc_point_2      Point_2;
-    public:
-
-      typedef Point_2                  result_type;
-      //typedef const result_type&       qualified_result_type;
-
-      //std::remove_reference_t<qualified_result_type>
-      result_type
-      operator() (const std::variant< Arc1, Arc2 > & cv) const
-      {
-        return std::visit
-          ( Variant_Construct_min_vertex_2<CircularKernel>(), cv );
-      }
-    };
-
-
-
-
-
-     template <class CircularKernel>
-    class Variant_Construct_max_vertex_2
-    {
-      typedef typename CircularKernel::Circular_arc_point_2
-                                                  Circular_arc_point_2;
-
-    public:
-      typedef Circular_arc_point_2  result_type;
-      //typedef const result_type&       qualified_result_type;
-
-      template < typename T >
-      //std::remove_reference_t<qualified_result_type>
-        Circular_arc_point_2
-      operator()(const T &a) const
-      {
-        //CGAL_kernel_precondition(CircularKernel().compare_xy_2_object()(a.left(), a.right())==CGAL::SMALLER);
-        return (CircularKernel().construct_circular_max_vertex_2_object()(a));
-      }
-    };
-
-    template <class CircularKernel, class Arc1, class Arc2>
-    class Construct_max_vertex_2//: public Has_qrt
-    {
-      typedef typename CircularKernel::Circular_arc_point_2      Point_2;
-
-    public:
-      /*! obtains the right endpoint of the x-monotone curve (segment).
-       * \param cv The curve.
-       * \return The right endpoint.
-       */
-      typedef Point_2                  result_type;
-      //typedef const result_type&       qualified_result_type;
-
-       //std::remove_reference<qualified_result_type>
-      result_type
-       operator() (const std::variant< Arc1, Arc2 > & cv) const
-      {
-        return std::visit
-          ( Variant_Construct_max_vertex_2<CircularKernel>(), cv );
-      }
-    };
-
-    template <class CircularKernel>
-    class Variant_Is_vertical_2
-    {
-    public:
-
-      template < typename T >
-      bool
-      operator()(const T &a) const
-      {
-        return CircularKernel().is_vertical_2_object()(a);
-      }
-    };
-
-    template <class CircularKernel, class Arc1, class Arc2>
-    class Is_vertical_2
-    {
-    public:
-      typedef bool result_type;
-
-      bool operator() (const std::variant< Arc1, Arc2 >& cv) const
-      {
-        return std::visit
-          ( Variant_Is_vertical_2<CircularKernel>(), cv );
-      }
-    };
-
+    const Arc2* arc1e = std::get_if<Arc2>(&c1);
+    if ( const Arc1* arc2 = std::get_if<Arc1>(&c2)) {
+      return CircularKernel().intersect_2_object()(*arc1e, *arc2, oi);
+    }
+    const Arc2* arc2 = std::get_if<Arc2>(&c2);
+    return CircularKernel().intersect_2_object()(*arc1e, *arc2, oi);
   }
+};
 
+template <typename CircularKernel, typename Arc1, typename Arc2>
+class Split_2 {
+public:
+  using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
+  using result_type = void;
 
-  // an empty class used to have different types between Curve_2 and X_monotone_curve_2
-  // in Arr_circular_line_arc_traits_2.
-  namespace internal_Argt_traits {
-    struct Not_X_Monotone{};
-    inline std::ostream& operator << (std::ostream& os, const Not_X_Monotone&)
-    {return os;}
+  result_type operator()(const std::variant< Arc1, Arc2>& A,
+                         const Circular_arc_point_2& p,
+                         std::variant< Arc1, Arc2>& ca1,
+                         std::variant< Arc1, Arc2>& ca2) const {
+    // TODO : optimize by extracting the references from the variants ?
+    if (const Arc1* arc1 = std::get_if<Arc1>(&A)) {
+      Arc1 carc1;
+      Arc1 carc2;
+      CircularKernel().split_2_object()(*arc1, p, carc1, carc2);
+      ca1 = carc1;
+      ca2 = carc2;
+      return ;
+    }
+    else {
+      const Arc2* arc2 = std::get_if<Arc2>(&A);
+      Arc2 cline1;
+      Arc2 cline2;
+      CircularKernel().split_2_object()(*arc2, p, cline1, cline2);
+      ca1 = cline1;
+      ca2 = cline2;
+      return ;
+    }
   }
+};
 
-  /// Traits class for CGAL::Arrangement_2 (and similar) based on a CircularKernel.
+template <typename CircularKernel>
+class Variant_Construct_min_vertex_2 {
+  using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
+public:
+  using result_type = Circular_arc_point_2;
+  // using qualified_result_type = const result_type& ;
 
-  template < typename CircularKernel>
-  class Arr_circular_line_arc_traits_2 {
+  template <typename T>
+  //std::remove_reference_t<qualified_result_type>
+  Circular_arc_point_2 operator()(const T& a) const {
+    //CGAL_kernel_precondition(CircularKernel().compare_xy_2_object()(a.left(), a.right())==CGAL::SMALLER);
+    return CircularKernel().construct_circular_min_vertex_2_object()(a);
+  }
+};
 
-    typedef Arr_circular_line_arc_traits_2< CircularKernel >   Self;
+template <typename CircularKernel, typename Arc1, typename Arc2>
+class Construct_min_vertex_2 {
+  //: public Has_qrt
+  using Point_2 = typename CircularKernel::Circular_arc_point_2;
 
-    typedef typename CircularKernel::Line_arc_2                Arc1;
-    typedef typename CircularKernel::Circular_arc_2            Arc2;
+public:
+  using result_type = Point_2;
+  // using qualified_result_type = const result_type&;
 
-  public:
+  //std::remove_reference_t<qualified_result_type>
+  result_type operator() (const std::variant< Arc1, Arc2>& cv) const
+  { return std::visit(Variant_Construct_min_vertex_2<CircularKernel>(), cv); }
+};
 
-    typedef CircularKernel Kernel;
-    typedef typename CircularKernel::Circular_arc_point_2
-                                                Circular_arc_point_2;
+template <typename CircularKernel>
+class Variant_Construct_max_vertex_2 {
+  using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
+public:
+  using result_type = Circular_arc_point_2;
+  // using qualified_result_type = const result_type&;
 
-    typedef typename CircularKernel::Circular_arc_point_2      Point;
-    typedef typename CircularKernel::Circular_arc_point_2      Point_2;
+  template <typename T>
+    //std::remove_reference_t<qualified_result_type>
+  Circular_arc_point_2 operator()(const T& a) const {
+    //CGAL_kernel_precondition(CircularKernel().compare_xy_2_object()(a.left(), a.right())==CGAL::SMALLER);
+    return (CircularKernel().construct_circular_max_vertex_2_object()(a));
+  }
+};
 
-    typedef unsigned int                           Multiplicity;
+template <typename CircularKernel, typename Arc1, typename Arc2>
+class Construct_max_vertex_2 {
+  //: public Has_qrt
+  using Point_2 = typename CircularKernel::Circular_arc_point_2;
 
-    typedef CGAL::Tag_false                        Has_left_category;
-    typedef CGAL::Tag_false                        Has_merge_category;
-    typedef CGAL::Tag_false                        Has_do_intersect_category;
+public:
+  /*! obtains the right endpoint of the x-monotone curve (segment).
+   * \param cv The curve.
+   * \return The right endpoint.
+   */
+  using result_type = Point_2;
+  // using qualified_result_type = const result_type&;
 
-    typedef Arr_oblivious_side_tag                 Left_side_category;
-    typedef Arr_oblivious_side_tag                 Bottom_side_category;
-    typedef Arr_oblivious_side_tag                 Top_side_category;
-    typedef Arr_oblivious_side_tag                 Right_side_category;
+  //std::remove_reference<qualified_result_type>
+  result_type operator() (const std::variant<Arc1, Arc2>& cv) const
+  { return std::visit(Variant_Construct_max_vertex_2<CircularKernel>(), cv); }
+};
 
-    typedef internal_Argt_traits::Not_X_Monotone                Not_X_Monotone;
+template <typename CircularKernel>
+class Variant_Is_vertical_2 {
+public:
+  template <typename T>
+  bool operator()(const T& a) const
+  { return CircularKernel().is_vertical_2_object()(a); }
+};
 
-    typedef std::variant< Arc1, Arc2, Not_X_Monotone >        Curve_2;
-    typedef std::variant< Arc1, Arc2 >                        X_monotone_curve_2;
+template <typename CircularKernel, typename Arc1, typename Arc2>
+class Is_vertical_2 {
+public:
+  using result_type = bool;
 
-  private:
-    CircularKernel ck;
-  public:
+  bool operator() (const std::variant<Arc1, Arc2>& cv) const
+  { return std::visit(Variant_Is_vertical_2<CircularKernel>(), cv); }
+};
 
-    Arr_circular_line_arc_traits_2(const CircularKernel &k = CircularKernel())
-      : ck(k) {}
+}
 
-    typedef typename CircularKernel::Compare_x_2           Compare_x_2;
-    typedef typename CircularKernel::Compare_xy_2          Compare_xy_2;
-    typedef typename
-    VariantFunctors::Construct_min_vertex_2<CircularKernel, Arc1, Arc2>
-                                                  Construct_min_vertex_2;
-    typedef
-    VariantFunctors::Construct_max_vertex_2<CircularKernel, Arc1, Arc2>
-                                                  Construct_max_vertex_2;
-    typedef VariantFunctors::Is_vertical_2<CircularKernel, Arc1, Arc2>
-                                                  Is_vertical_2;
-    typedef VariantFunctors::Compare_y_at_x_2<CircularKernel, Arc1, Arc2>
-                                                  Compare_y_at_x_2;
-    typedef VariantFunctors::Compare_y_to_right_2<CircularKernel, Arc1, Arc2>
-                                                  Compare_y_at_x_right_2;
-    typedef VariantFunctors::Equal_2<CircularKernel, Arc1, Arc2>
-                                                  Equal_2;
-    typedef VariantFunctors::Make_x_monotone_2<CircularKernel, Arc1, Arc2>
-                                                  Make_x_monotone_2;
-    typedef VariantFunctors::Split_2<CircularKernel, Arc1, Arc2>
-                                                  Split_2;
-    typedef VariantFunctors::Intersect_2<CircularKernel, Arc1, Arc2>
-                                                  Intersect_2;
+// an empty class used to have different types between Curve_2 and X_monotone_curve_2
+// in Arr_circular_line_arc_traits_2.
+namespace internal_Argt_traits {
 
-    Compare_x_2 compare_x_2_object() const
-    { return ck.compare_x_2_object(); }
+struct Not_X_Monotone{};
 
-    Compare_xy_2 compare_xy_2_object() const
-    { return ck.compare_xy_2_object(); }
+inline std::ostream& operator << (std::ostream& os, const Not_X_Monotone&) { return os; }
 
-    Compare_y_at_x_2 compare_y_at_x_2_object() const
-    { return Compare_y_at_x_2(); }
+}
 
-    Compare_y_at_x_right_2 compare_y_at_x_right_2_object() const
-    { return Compare_y_at_x_right_2(); }
+/// Traits class for CGAL::Arrangement_2 (and similar) based on a CircularKernel.
 
-    Equal_2 equal_2_object() const
-    { return Equal_2(); }
+template <typename CircularKernel>
+class Arr_circular_line_arc_traits_2 {
+  using Self = Arr_circular_line_arc_traits_2<CircularKernel>;
 
-    Make_x_monotone_2 make_x_monotone_2_object() const
-    { return Make_x_monotone_2(); }
+  using Arc1 = typename CircularKernel::Line_arc_2;
+  using Arc2 = typename CircularKernel::Circular_arc_2;
 
-    Split_2 split_2_object() const
-    { return Split_2(); }
+public:
+  using Kernel = CircularKernel;
+  using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
 
-    Intersect_2 intersect_2_object() const
-    { return Intersect_2(); }
+  using Point = typename CircularKernel::Circular_arc_point_2;
+  using Point_2 = typename CircularKernel::Circular_arc_point_2;
 
-    Construct_min_vertex_2 construct_min_vertex_2_object() const
-    { return Construct_min_vertex_2(); }
+  using Multiplicity = std::size_t;
 
-    Construct_max_vertex_2 construct_max_vertex_2_object() const
-    { return Construct_max_vertex_2(); }
+  using Has_left_category = CGAL::Tag_false;
+  using Has_merge_category = CGAL::Tag_false;
+  using Has_do_intersect_category = CGAL::Tag_false;
 
-    Is_vertical_2 is_vertical_2_object() const
-    { return Is_vertical_2();}
+  using Left_side_category = Arr_oblivious_side_tag;
+  using Bottom_side_category = Arr_oblivious_side_tag;
+  using Top_side_category = Arr_oblivious_side_tag;
+  using Right_side_category = Arr_oblivious_side_tag;
+
+  using Not_X_Monotone = internal_Argt_traits::Not_X_Monotone;
+
+  using Curve_2 = std::variant<Arc1, Arc2, Not_X_Monotone>;
+  using X_monotone_curve_2 = std::variant<Arc1, Arc2>;
+
+private:
+  CircularKernel ck;
+
+public:
+  Arr_circular_line_arc_traits_2(const CircularKernel& k = CircularKernel()) : ck(k) {}
+
+  using Compare_x_2 = typename CircularKernel::Compare_x_2;
+  using Compare_xy_2 = typename CircularKernel::Compare_xy_2;
+  using Construct_min_vertex_2 = typename  VariantFunctors::Construct_min_vertex_2<CircularKernel, Arc1, Arc2>;
+  using Construct_max_vertex_2 = VariantFunctors::Construct_max_vertex_2<CircularKernel, Arc1, Arc2>;
+  using Is_vertical_2 = VariantFunctors::Is_vertical_2<CircularKernel, Arc1, Arc2>;
+  using Compare_y_at_x_2 = VariantFunctors::Compare_y_at_x_2<CircularKernel, Arc1, Arc2>;
+  using Compare_y_at_x_right_2 = VariantFunctors::Compare_y_to_right_2<CircularKernel, Arc1, Arc2>;
+  using Equal_2 = VariantFunctors::Equal_2<CircularKernel, Arc1, Arc2>;
+  using Make_x_monotone_2 = VariantFunctors::Make_x_monotone_2<CircularKernel, Arc1, Arc2>;
+  using Split_2 = VariantFunctors::Split_2<CircularKernel, Arc1, Arc2>;
+  using Intersect_2 = VariantFunctors::Intersect_2<CircularKernel, Arc1, Arc2>;
+
+  Compare_x_2 compare_x_2_object() const
+  { return ck.compare_x_2_object(); }
+
+  Compare_xy_2 compare_xy_2_object() const
+  { return ck.compare_xy_2_object(); }
+
+  Compare_y_at_x_2 compare_y_at_x_2_object() const
+  { return Compare_y_at_x_2(); }
+
+  Compare_y_at_x_right_2 compare_y_at_x_right_2_object() const
+  { return Compare_y_at_x_right_2(); }
+
+  Equal_2 equal_2_object() const
+  { return Equal_2(); }
+
+  Make_x_monotone_2 make_x_monotone_2_object() const
+  { return Make_x_monotone_2(); }
+
+  Split_2 split_2_object() const
+  { return Split_2(); }
+
+  Intersect_2 intersect_2_object() const
+  { return Intersect_2(); }
+
+  Construct_min_vertex_2 construct_min_vertex_2_object() const
+  { return Construct_min_vertex_2(); }
+
+  Construct_max_vertex_2 construct_max_vertex_2_object() const
+  { return Construct_max_vertex_2(); }
+
+  Is_vertical_2 is_vertical_2_object() const
+  { return Is_vertical_2();}
 };
 
 } // namespace CGAL

Arrangement_on_surface_2/include/CGAL/Arr_conic_traits_2.h

@@ -32,7 +32,7 @@
 
 #include <boost/math/constants/constants.hpp>
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/tags.h>
 #include <CGAL/Arr_tags.h>
 #include <CGAL/Arr_enums.h>
@@ -59,37 +59,37 @@ namespace CGAL {
 template <typename RatKernel, typename AlgKernel, typename NtTraits>
 class Arr_conic_traits_2 {
 public:
-  typedef RatKernel                       Rat_kernel;
-  typedef AlgKernel                       Alg_kernel;
-  typedef NtTraits                        Nt_traits;
+  using Rat_kernel = RatKernel;
+  using Alg_kernel = AlgKernel;
+  using Nt_traits = NtTraits;
 
-  typedef typename Rat_kernel::FT         Rational;
-  typedef typename Rat_kernel::Point_2    Rat_point_2;
-  typedef typename Rat_kernel::Segment_2  Rat_segment_2;
-  typedef typename Rat_kernel::Line_2     Rat_line_2;
-  typedef typename Rat_kernel::Circle_2   Rat_circle_2;
+  using Rational = typename Rat_kernel::FT;
+  using Rat_point_2 = typename Rat_kernel::Point_2;
+  using Rat_segment_2 = typename Rat_kernel::Segment_2;
+  using Rat_line_2 = typename Rat_kernel::Line_2;
+  using Rat_circle_2 = typename Rat_kernel::Circle_2;
 
-  typedef typename Alg_kernel::FT         Algebraic;
-  typedef typename Alg_kernel::Point_2    Alg_point_2;
+  using Algebraic = typename Alg_kernel::FT;
+  using Alg_point_2 = typename Alg_kernel::Point_2;
 
-  typedef typename Nt_traits::Integer     Integer;
+  using Integer = typename Nt_traits::Integer;
 
   // Category tags:
-  typedef Tag_true                        Has_left_category;
-  typedef Tag_true                        Has_merge_category;
-  typedef Tag_false                       Has_do_intersect_category;
+  using Has_left_category = Tag_true;
+  using Has_merge_category = Tag_true;
+  using Has_do_intersect_category = Tag_false;
   //typedef std::true_type                Has_line_segment_constructor;
 
-  typedef Arr_oblivious_side_tag          Left_side_category;
-  typedef Arr_oblivious_side_tag          Bottom_side_category;
-  typedef Arr_oblivious_side_tag          Top_side_category;
-  typedef Arr_oblivious_side_tag          Right_side_category;
+  using Left_side_category = Arr_oblivious_side_tag;
+  using Bottom_side_category = Arr_oblivious_side_tag;
+  using Top_side_category = Arr_oblivious_side_tag;
+  using Right_side_category = Arr_oblivious_side_tag;
 
   // Traits objects:
-  typedef Conic_arc_2<Rat_kernel, Alg_kernel, Nt_traits>  Curve_2;
-  typedef Conic_x_monotone_arc_2<Curve_2>                 X_monotone_curve_2;
-  typedef Conic_point_2<Alg_kernel>                       Point_2;
-  typedef size_t                                          Multiplicity;
+  using Curve_2 = Conic_arc_2<Rat_kernel, Alg_kernel, Nt_traits>;
+  using X_monotone_curve_2 = Conic_x_monotone_arc_2<Curve_2>;
+  using Point_2 = Conic_point_2<Alg_kernel>;
+  using Multiplicity = std::size_t;
 
 private:
   // Type definition for the intersection points mapping.
@@ -106,16 +106,14 @@ private:
     }
   };
 
-  typedef std::pair<Point_2, Multiplicity>          Intersection_point;
-  typedef std::list<Intersection_point>             Intersection_list;
-  typedef std::map<Conic_pair, Intersection_list, Less_conic_pair>
-                                                    Intersection_map;
-  typedef typename Intersection_map::iterator       Intersection_map_iterator;
+  using Intersection_point = std::pair<Point_2, Multiplicity>;
+  using Intersection_list = std::list<Intersection_point>;
+  using Intersection_map = std::map<Conic_pair, Intersection_list, Less_conic_pair>;
+  using Intersection_map_iterator = typename Intersection_map::iterator;
 
-
-  typedef std::shared_ptr<Rat_kernel>               Shared_rat_kernel;
-  typedef std::shared_ptr<Alg_kernel>               Shared_alg_kernel;
-  typedef std::shared_ptr<Nt_traits>                Shared_nt_traits;
+  using Shared_rat_kernel = std::shared_ptr<Rat_kernel>;
+  using Shared_alg_kernel = std::shared_ptr<Alg_kernel>;
+  using Shared_nt_traits = std::shared_ptr<Nt_traits>;
 
   const Shared_rat_kernel m_rat_kernel;
   const Shared_alg_kernel m_alg_kernel;
@@ -127,10 +125,10 @@ private:
 public:
   /*! constructs default.
    */
-  Arr_conic_traits_2()
-   : m_rat_kernel(std::make_shared<Rat_kernel>()),
-     m_alg_kernel(std::make_shared<Alg_kernel>()),
-     m_nt_traits(std::make_shared<Nt_traits>())
+  Arr_conic_traits_2() :
+    m_rat_kernel(std::make_shared<Rat_kernel>()),
+    m_alg_kernel(std::make_shared<Alg_kernel>()),
+    m_nt_traits(std::make_shared<Nt_traits>())
   {}
 
   /*! constructs from resources.
@@ -360,8 +358,7 @@ public:
      */
     Comparison_result operator()(const X_monotone_curve_2& xcv1,
                                  const X_monotone_curve_2& xcv2,
-                                 const Point_2& p) const
-    {
+                                 const Point_2& p) const {
       // Make sure that p lies on both curves, and that both are defined to its
       // left (so their left endpoint is lexicographically smaller than p).
       CGAL_precondition(m_traits.contains_point(xcv1, p) &&
@@ -538,8 +535,7 @@ public:
      */
     Comparison_result operator()(const X_monotone_curve_2& xcv1,
                                  const X_monotone_curve_2& xcv2,
-                                 const Point_2& p) const
-    {
+                                 const Point_2& p) const {
       // Make sure that p lies on both curves, and that both are defined to its
       // left (so their left endpoint is lexicographically smaller than p).
       CGAL_precondition(m_traits.contains_point(xcv1, p) &&
@@ -703,8 +699,7 @@ public:
      * \return `true` if the two curves are the same; `false` otherwise.
      */
     bool operator()(const X_monotone_curve_2& xcv1,
-                    const X_monotone_curve_2& xcv2) const
-    {
+                    const X_monotone_curve_2& xcv2) const {
       if (&xcv1 == &xcv2) return true;
       return equals(xcv1, xcv2);
     }
@@ -924,8 +919,7 @@ public:
 
           if (((cv.orientation() == COUNTERCLOCKWISE) &&
                (start_pos == order_vpts)) ||
-              ((cv.orientation() == CLOCKWISE) && (start_pos != order_vpts)))
-          {
+              ((cv.orientation() == CLOCKWISE) && (start_pos != order_vpts))) {
             ind_first = 1;
             ind_second = 0;
           }
@@ -1101,8 +1095,7 @@ public:
       else if (m_traits.is_between_endpoints(xcv2, xcv1.source()) &&
                m_traits.is_between_endpoints(xcv2, xcv1.target()) &&
                (m_traits.is_strictly_between_endpoints(xcv2, xcv1.source()) ||
-                m_traits.is_strictly_between_endpoints(xcv2, xcv1.target())))
-      {
+                m_traits.is_strictly_between_endpoints(xcv2, xcv1.target()))) {
         // Case 4 - *this:     +----------->
         //            arc:   +================>
         overlap = xcv1;
@@ -1285,8 +1278,7 @@ public:
       for (i = 0; i < n_xs; ++i) {
         for (j = 0; j < n_ys; ++j) {
           if (xcv1.is_on_supporting_conic(xs[i], ys[j]) &&
-              xcv2.is_on_supporting_conic(xs[i], ys[j]))
-          {
+              xcv2.is_on_supporting_conic(xs[i], ys[j])) {
             // Create the intersection point and set its generating conics.
             Point_2 ip(xs[i], ys[j]);
 
@@ -1314,8 +1306,7 @@ public:
     OutputIterator intersect(const X_monotone_curve_2& xcv1,
                              const X_monotone_curve_2& xcv2,
                              Intersection_map& inter_map,
-                             OutputIterator oi) const
-    {
+                             OutputIterator oi) const {
       if (m_traits.has_same_supporting_conic(xcv1, xcv2)) {
         // Check for overlaps between the two arcs.
         X_monotone_curve_2 overlap;
@@ -1392,8 +1383,7 @@ public:
       // both \f$x\f$-monotone arcs.
       for (auto iter = inter_list.begin(); iter != inter_list.end(); ++iter) {
         if (m_traits.is_between_endpoints(xcv1, (*iter).first) &&
-            m_traits.is_between_endpoints(xcv2, (*iter).first))
-        {
+            m_traits.is_between_endpoints(xcv2, (*iter).first)) {
           *oi++ = *iter;
         }
       }
@@ -1481,8 +1471,7 @@ public:
      */
     void operator()(const X_monotone_curve_2& xcv1,
                     const X_monotone_curve_2& xcv2,
-                    X_monotone_curve_2& xcv) const
-    {
+                    X_monotone_curve_2& xcv) const {
       CGAL_precondition(m_traits.are_mergeable_2_object()(xcv2, xcv1));
       xcv = xcv1;
       merge(xcv, xcv2);
@@ -1523,11 +1512,11 @@ public:
    * point-location strategy and the drawing function.
    */
   //@{
-  typedef double                                        Approximate_number_type;
-  typedef CGAL::Cartesian<Approximate_number_type>      Approximate_kernel;
-  typedef Approximate_kernel::Point_2                   Approximate_point_2;
+  using Approximate_number_type = double;
+  using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
+  using Approximate_point_2 = Approximate_kernel::Point_2;
 
-  class Approximate_curve_length_2 {
+  class Approximate_length_2 {
   protected:
     using Traits = Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits>;
 
@@ -1537,7 +1526,7 @@ public:
     /*! constructs
      * \param traits the traits.
      */
-    Approximate_curve_length_2(const Traits& traits) : m_traits(traits) {}
+    Approximate_length_2(const Traits& traits) : m_traits(traits) {}
 
     friend class Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits>;
 
@@ -1557,7 +1546,7 @@ public:
   private:
     /*! obtains the segment length.
      */
-    double segment_length(const X_monotone_curve_2& xcv) {
+    double segment_length(const X_monotone_curve_2& xcv) const {
       auto min_vertex = m_traits.construct_min_vertex_2_object();
       auto max_vertex = m_traits.construct_max_vertex_2_object();
       const auto& minv = min_vertex(xcv);
@@ -1597,7 +1586,7 @@ public:
 
     /*! obtains the parabolic arc length.
      */
-    double parabola_length(const X_monotone_curve_2& xcv) {
+    double parabola_length(const X_monotone_curve_2& xcv) const {
       double r_m, t_m, s_m, u_m, v_m, w_m;
       double cost, sint;
       double xs_t, ys_t, xt_t, yt_t;
@@ -1617,7 +1606,7 @@ public:
       return d;
     }
 
-    double ellipse_length(const X_monotone_curve_2& xcv) {
+    double ellipse_length(const X_monotone_curve_2& xcv) const {
       double r_m, t_m, s_m, u_m, v_m, w_m;
       double cost, sint;
       double xs_t, ys_t, xt_t, yt_t;
@@ -1638,7 +1627,7 @@ public:
       return d;
     }
 
-    double hyperbola_length(const X_monotone_curve_2& /* xcv */) {
+    double hyperbola_length(const X_monotone_curve_2& /* xcv */) const {
       CGAL_error_msg("Not implemented yet!");
       double l(0.0);
       return l;
@@ -1901,8 +1890,7 @@ public:
     template <typename OutputIterator>
     OutputIterator approximate_parabola(const X_monotone_curve_2& xcv,
                                         double error, OutputIterator oi,
-                                        bool l2r = true)
-      const {
+                                        bool l2r = true) const {
       // std::cout << "PARABOLA\n";
       auto min_vertex = m_traits.construct_min_vertex_2_object();
       auto max_vertex = m_traits.construct_max_vertex_2_object();
@@ -2104,8 +2092,7 @@ public:
      */
     X_monotone_curve_2 operator()(const Curve_2& cv,
                                   const Point_2& source, const Point_2& target,
-                                  const Conic_id& id) const
-    {
+                                  const Conic_id& id) const {
       // Set the two endpoints.
       X_monotone_curve_2 xcv(cv, id);
       xcv.set_source(source);
@@ -2122,8 +2109,7 @@ public:
      * \return A segment connecting `source` and `target`.
      */
     X_monotone_curve_2 operator()(const Point_2& source, const Point_2& target)
-      const
-    {
+      const {
       X_monotone_curve_2 xcv;
 
       // Set the basic properties.
@@ -2157,8 +2143,7 @@ public:
     X_monotone_curve_2 operator()(const Algebraic& a, const Algebraic& b,
                                   const Algebraic& c,
                                   const Point_2& source, const Point_2& target)
-      const
-    {
+      const {
       auto cmp_xy = m_traits.m_alg_kernel->compare_xy_2_object();
       Comparison_result res = cmp_xy(source, target);
       CGAL_precondition(res != EQUAL);
@@ -2238,8 +2223,7 @@ public:
      */
     Curve_2 operator()(const Rational& r, const Rational& s, const Rational& t,
                        const Rational& u, const Rational& v, const Rational& w)
-      const
-    {
+      const {
       // Ensure that the given curve is an ellipse (4rs - t^2 is positive).
       CGAL_precondition(CGAL::sign(4*r*s - t*t) == POSITIVE);
 
@@ -2445,8 +2429,7 @@ public:
 
       if (! m_traits.is_strictly_between_endpoints(arc, mp2) ||
           ! m_traits.is_strictly_between_endpoints(arc, mp3) ||
-          ! m_traits.is_strictly_between_endpoints(arc, mp4))
-      {
+          ! m_traits.is_strictly_between_endpoints(arc, mp4)) {
         arc.reset_flags();            // invalid arc
         return arc;
       }
@@ -2853,8 +2836,7 @@ public:
      * \pre both points must be interior and must lie on \c cv
      */
     X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv,
-                                  const Point_2& src, const Point_2& tgt) const
-    {
+                                  const Point_2& src, const Point_2& tgt) const {
       // make functor objects
       CGAL_precondition_code(Compare_y_at_x_2 compare_y_at_x_2 =
                              m_traits.compare_y_at_x_2_object());
@@ -3084,16 +3066,14 @@ public:
     const auto& target = cv.target();
     // Make sure both endpoint lie on the supporting conic.
     if (! is_on_supporting_conic(cv, source) ||
-        ! is_on_supporting_conic(cv, target))
-    {
+        ! is_on_supporting_conic(cv, target)) {
       cv.reset_flags();            // invalid arc
       return;
     }
 
     // Check whether we have a degree 2 curve.
     if ((CGAL::sign(r) != ZERO) || (CGAL::sign(s) != ZERO) ||
-        (CGAL::sign(t) != ZERO))
-    {
+        (CGAL::sign(t) != ZERO)) {
       if (cv.orientation() == COLLINEAR) {
         // Make sure the midpoint is on the line pair (thus making sure that
         // the two points are not taken from different lines).
@@ -3105,8 +3085,7 @@ public:
                         m_nt_traits->convert(u)) * p_mid.x() +
                        (m_nt_traits->convert(s)*p_mid.y() +
                         m_nt_traits->convert(v)) * p_mid.y() +
-                       m_nt_traits->convert(w)) != ZERO)
-        {
+                       m_nt_traits->convert(w)) != ZERO) {
           cv.reset_flags();    // invalid arc
           return;
         }
@@ -3645,8 +3624,7 @@ public:
       // Compute the degree of the underlying conic.
       if ((CGAL::sign(xcv.r()) != ZERO) ||
           (CGAL::sign(xcv.s()) != ZERO) ||
-          (CGAL::sign(xcv.t()) != ZERO))
-      {
+          (CGAL::sign(xcv.t()) != ZERO)) {
         xcv.set_flag(X_monotone_curve_2::DEGREE_2);
         xcv.set_flag(X_monotone_curve_2::IS_SPECIAL_SEGMENT);
       }
@@ -3856,8 +3834,7 @@ public:
         for (int j = 0; j < n_ys; ++j) {
           if (CGAL::compare(m_nt_traits->convert(Integer(two*s)) * ys[j],
                             -(m_nt_traits->convert(t) * xs[i] +
-                              m_nt_traits->convert(v))) == EQUAL)
-          {
+                              m_nt_traits->convert(v))) == EQUAL) {
             ps[n++] = Point_2(xs[i], ys[j]);
             break;
           }
@@ -4128,8 +4105,7 @@ public:
                            double& xs_t, double& ys_t, double& ts,
                            double& xt_t, double& yt_t, double& tt,
                            double& a, double& b, double& cx, double& cy,
-                           bool l2r = true)
-    const {
+                           bool l2r = true) const {
     auto min_vertex = construct_min_vertex_2_object();
     auto max_vertex = construct_max_vertex_2_object();
     const auto& src = (l2r) ? min_vertex(xcv) : max_vertex(xcv);
@@ -4206,8 +4182,7 @@ public:
                              double& xs_t, double& ys_t, double& ts,
                              double& xt_t, double& yt_t, double& tt,
                              double& a, double& b, double& cx, double& cy,
-                             bool l2r = true)
-    const {
+                             bool l2r = true) const {
     auto min_vertex = construct_min_vertex_2_object();
     auto max_vertex = construct_max_vertex_2_object();
     const auto& src = (l2r) ? min_vertex(xcv) : max_vertex(xcv);

Arrangement_on_surface_2/include/CGAL/Arr_do_intersect_overlay_2.h

@@ -0,0 +1,236 @@
+// Copyright (c) 2025 Tel-Aviv University (Israel).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
+//
+//
+// Author(s):      Efi Fogel <efifogel@gmail.com>
+
+#ifndef CGAL_ARR_DO_INTERSECT_OVERLAY_2_H
+#define CGAL_ARR_DO_INTERSECT_OVERLAY_2_H
+
+#include <CGAL/license/Arrangement_on_surface_2.h>
+
+#include <CGAL/disable_warnings.h>
+
+/*! \file
+ *
+ * Definition of the global do_intersect_overlay_2() function.
+ */
+
+#include <CGAL/Arrangement_on_surface_2.h>
+#include <CGAL/Surface_sweep_2.h>
+#include <CGAL/Surface_sweep_2/Arr_default_overlay_traits_base.h>
+#include <CGAL/Surface_sweep_2/Arr_overlay_traits_2.h>
+#include <CGAL/Surface_sweep_2/Arr_do_intersect_overlay_ss_visitor.h>
+#include <CGAL/Surface_sweep_2/Arr_overlay_event.h>
+#include <CGAL/Surface_sweep_2/Arr_overlay_subcurve.h>
+#include <CGAL/assertions.h>
+
+namespace CGAL {
+
+/*! Compute the overlay of two input arrangements.
+ * \tparam GeometryTraitsA_2 the geometry traits of the first arrangement.
+ * \tparam GeometryTraitsB_2 the geometry traits of the second arrangement.
+ * \tparam GeometryTraitsRes_2 the geometry traits of the resulting arrangement.
+ * \tparam TopologyTraitsA the topology traits of the first arrangement.
+ * \tparam TopologyTraitsB the topology traits of the second arrangement.
+ * \tparam TopologyTraitsRes the topology traits of the resulting arrangement.
+ * \tparam OverlayTraits An overlay-traits class. As arr1, arr2 and res can be
+ *               templated with different geometry-traits class and
+ *               different DCELs (encapsulated in the various topology-traits
+ *               classes). The geometry-traits of the result arrangement is
+ *               used to construct the result arrangement. This means that all
+ *               the types (e.g., Point_2, Curve_2 and X_monotone_2) of both
+ *               arr1 and arr2 have to be convertible to the types
+ *               in the result geometry-traits.
+ *               The overlay-traits class defines the various
+ *               overlay operations of pairs of DCEL features from
+ *               TopologyTraitsA and TopologyTraitsB to the resulting ResDcel.
+ */
+template <typename GeometryTraitsA_2,
+          typename GeometryTraitsB_2,
+          typename GeometryTraitsRes_2,
+          typename TopologyTraitsA,
+          typename TopologyTraitsB,
+          typename TopologyTraitsRes,
+          typename OverlayTraits>
+bool do_intersect_overlay(const Arrangement_on_surface_2<GeometryTraitsA_2, TopologyTraitsA>& arr1,
+                          const Arrangement_on_surface_2<GeometryTraitsB_2, TopologyTraitsB>& arr2,
+                          Arrangement_on_surface_2<GeometryTraitsRes_2, TopologyTraitsRes>& arr,
+                          OverlayTraits& ovl_tr,
+                          bool ignore_isolated_vertices = true) {
+  using Agt2 = GeometryTraitsA_2;
+  using Bgt2 = GeometryTraitsB_2;
+  using Rgt2 = GeometryTraitsRes_2;
+  using Att = TopologyTraitsA;
+  using Btt = TopologyTraitsB;
+  using Rtt = TopologyTraitsRes;
+  using Overlay_traits = OverlayTraits;
+
+  using Arr_a = Arrangement_on_surface_2<Agt2, Att>;
+  using Arr_b = Arrangement_on_surface_2<Bgt2, Btt>;
+  using Arr_res = Arrangement_on_surface_2<Rgt2, Rtt>;
+  using Allocator = typename Arr_res::Allocator;
+
+  // some type assertions (not all, but better than nothing).
+  using A_point = typename Agt2::Point_2;
+  using B_point = typename Bgt2::Point_2;
+  using Res_point = typename Rgt2::Point_2;
+  static_assert(std::is_convertible<A_point, Res_point>::value);
+  static_assert(std::is_convertible<B_point, Res_point>::value);
+
+  using A_xcv = typename Agt2::X_monotone_curve_2;
+  using B_xcv = typename Bgt2::X_monotone_curve_2;
+  using Res_xcv = typename Rgt2::X_monotone_curve_2;
+  static_assert(std::is_convertible<A_xcv, Res_xcv>::value);
+  static_assert(std::is_convertible<B_xcv, Res_xcv>::value);
+
+  using Gt_adaptor_2 = Arr_traits_basic_adaptor_2<Rgt2>;
+  using Ovl_gt2 = Arr_overlay_traits_2<Gt_adaptor_2, Arr_a, Arr_b>;
+  using Ovl_event = Arr_overlay_event<Ovl_gt2, Arr_res, Allocator>;
+  using Ovl_curve = Arr_overlay_subcurve<Ovl_gt2, Ovl_event, Allocator>;
+  using Ovl_helper = typename TopologyTraitsRes::template Overlay_helper<Ovl_gt2, Ovl_event, Ovl_curve, Arr_a, Arr_b>;
+  using Diovl_visitor = Arr_do_intersect_overlay_ss_visitor<Ovl_helper, Overlay_traits>;
+
+  using Ovl_x_monotone_curve_2 = typename Ovl_gt2::X_monotone_curve_2;
+  using Ovl_point_2 = typename Ovl_gt2::Point_2;
+  using Cell_handle_red = typename Ovl_gt2::Cell_handle_red;
+  using Optional_cell_red = typename Ovl_gt2::Optional_cell_red;
+  using Cell_handle_blue = typename Ovl_gt2::Cell_handle_blue;
+  using Optional_cell_blue = typename Ovl_gt2::Optional_cell_blue;
+
+  CGAL_USE_TYPE(Optional_cell_red);
+  CGAL_USE_TYPE(Optional_cell_blue);
+
+  // The result arrangement cannot be on of the input arrangements.
+  CGAL_precondition(((void*)(&arr) != (void*)(&arr1)) && ((void*)(&arr) != (void*)(&arr2)));
+
+  // Prepare a vector of extended x-monotone curves that represent all edges
+  // in both input arrangements. Each curve is associated with a halfedge
+  // directed from right to left.
+  typename Arr_a::Halfedge_const_handle invalid_he1;
+  typename Arr_b::Halfedge_const_handle invalid_he2;
+  std::vector<Ovl_x_monotone_curve_2> xcvs(arr1.number_of_edges() + arr2.number_of_edges());
+  std::size_t i = 0;
+
+  for (auto eit1 = arr1.edges_begin(); eit1 != arr1.edges_end(); ++eit1, ++i) {
+    typename Arr_a::Halfedge_const_handle he1 = eit1;
+    if (he1->direction() != ARR_RIGHT_TO_LEFT) he1 = he1->twin();
+    xcvs[i] = Ovl_x_monotone_curve_2(eit1->curve(), he1, invalid_he2);
+  }
+
+  for (auto eit2 = arr2.edges_begin(); eit2 != arr2.edges_end(); ++eit2, ++i) {
+    typename Arr_b::Halfedge_const_handle he2 = eit2;
+    if (he2->direction() != ARR_RIGHT_TO_LEFT) he2 = he2->twin();
+    xcvs[i] = Ovl_x_monotone_curve_2(eit2->curve(), invalid_he1, he2);
+  }
+
+  // Obtain an extended traits-class object and define the sweep-line visitor.
+  const typename Arr_res::Traits_adaptor_2* traits_adaptor = arr.traits_adaptor();
+
+  /* We would like to avoid copy construction of the geometry traits class.
+   * Copy construction is undesired, because it may results with data
+   * duplication or even data loss.
+   *
+   * If the type Ovl_gt2 is the same as the type
+   * GeomTraits, use a reference to GeomTraits to avoid constructing a new one.
+   * Otherwise, instantiate a local variable of the former and provide
+   * the latter as a single parameter to the constructor.
+   *
+   * Use the form 'A a(*b);' and not ''A a = b;' to handle the case where A has
+   * only an implicit constructor, (which takes *b as a parameter).
+   */
+  std::conditional_t<std::is_same_v<Gt_adaptor_2, Ovl_gt2>, const Ovl_gt2&, Ovl_gt2> ex_traits(*traits_adaptor);
+
+  Diovl_visitor visitor(&arr1, &arr2, &arr, &ovl_tr);
+  Ss2::Surface_sweep_2<Diovl_visitor> surface_sweep(&ex_traits, &visitor);
+
+  // In case both arrangement do not contain isolated vertices, go on and overlay them.
+  if (ignore_isolated_vertices ||
+      ((arr1.number_of_isolated_vertices() == 0) && (arr2.number_of_isolated_vertices() == 0))) {
+    // Clear the result arrangement and perform the sweep to construct it.
+    arr.clear();
+    if (std::is_same<typename Agt2::Bottom_side_category, Arr_contracted_side_tag>::value) {
+      surface_sweep.sweep(xcvs.begin(), xcvs.end());
+      xcvs.clear();
+      return visitor.found_intersection();
+    }
+    surface_sweep.indexed_sweep(xcvs, Indexed_sweep_accessor<Arr_a, Arr_b, Ovl_x_monotone_curve_2>(arr1, arr2));
+    xcvs.clear();
+    return visitor.found_intersection();
+  }
+
+  // Prepare a vector of extended points that represent all isolated vertices
+  // in both input arrangements.
+  std::vector<Ovl_point_2> pts_vec(arr1.number_of_isolated_vertices() + arr2.number_of_isolated_vertices());
+
+  i = 0;
+  for (auto vit1 = arr1.vertices_begin(); vit1 != arr1.vertices_end(); ++vit1) {
+    if (vit1->is_isolated()) {
+      typename Arr_a::Vertex_const_handle v1 = vit1;
+      pts_vec[i++] = Ovl_point_2(vit1->point(), std::make_optional(Cell_handle_red(v1)),
+                                 std::optional<Cell_handle_blue>());
+    }
+  }
+
+  for (auto vit2 = arr2.vertices_begin(); vit2 != arr2.vertices_end(); ++vit2) {
+    if (vit2->is_isolated()) {
+      typename Arr_b::Vertex_const_handle v2 = vit2;
+      pts_vec[i++] = Ovl_point_2(vit2->point(), std::optional<Cell_handle_red>(),
+                                 std::make_optional(Cell_handle_blue(v2)));
+    }
+  }
+
+  // Clear the result arrangement and perform the sweep to construct it.
+  arr.clear();
+  if (std::is_same<typename Agt2::Bottom_side_category, Arr_contracted_side_tag>::value) {
+    surface_sweep.sweep(xcvs.begin(), xcvs.end(), pts_vec.begin(), pts_vec.end());
+    xcvs.clear();
+    pts_vec.clear();
+    return visitor.found_intersection();
+  }
+  surface_sweep.indexed_sweep(xcvs, Indexed_sweep_accessor<Arr_a, Arr_b, Ovl_x_monotone_curve_2>(arr1, arr2),
+                              pts_vec.begin(), pts_vec.end());
+  xcvs.clear();
+  pts_vec.clear();
+  return visitor.found_intersection();
+}
+
+/*! Compute the (simple) overlay of two input arrangements.
+ * \param[in] arr1 the first arrangement.
+ * \param[in] arr2 the second arrangement.
+ * \param[out] arr the resulting arrangement.
+ */
+template <typename GeometryTraitsA_2,
+          typename GeometryTraitsB_2,
+          typename GeometryTraitsRes_2,
+          typename TopologyTraitsA,
+          typename TopologyTraitsB,
+          typename TopologyTraitsRes>
+bool do_intersect_overlay(const Arrangement_on_surface_2<GeometryTraitsA_2, TopologyTraitsA>& arr1,
+                          const Arrangement_on_surface_2<GeometryTraitsB_2, TopologyTraitsB>& arr2,
+                          Arrangement_on_surface_2<GeometryTraitsRes_2, TopologyTraitsRes>& arr) {
+  using Agt2 = GeometryTraitsA_2;
+  using Bgt2 = GeometryTraitsB_2;
+  using Rgt2 = GeometryTraitsRes_2;
+  using Att = TopologyTraitsA;
+  using Btt = TopologyTraitsB;
+  using Rtt = TopologyTraitsRes;
+  using Arr_a = Arrangement_on_surface_2<Agt2, Att>;
+  using Arr_b = Arrangement_on_surface_2<Bgt2, Btt>;
+  using Arr_res = Arrangement_on_surface_2<Rgt2, Rtt>;
+
+  _Arr_default_overlay_traits_base<Arr_a, Arr_b, Arr_res> ovl_traits;
+  return do_intersect_overlay(arr1, arr2, arr, ovl_traits);
+}
+
+} // namespace CGAL
+
+#include <CGAL/enable_warnings.h>
+
+#endif

Arrangement_on_surface_2/include/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h

@@ -28,7 +28,7 @@
 #include <variant>
 
 #include <CGAL/config.h>
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/tags.h>
 #include <CGAL/tss.h>
 #include <CGAL/intersections.h>
@@ -2856,7 +2856,7 @@ public:
   /// \name Functor definitions for the landmarks point-location strategy.
   //@{
   using Approximate_number_type = double;
-  using Approximate_kernel = CGAL::Cartesian<Approximate_number_type>;
+  using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
   using Approximate_point_2 = Arr_extended_direction_3<Approximate_kernel>;
   using Approximate_kernel_vector_3 = Approximate_kernel::Vector_3;
   using Approximate_kernel_direction_3 = Approximate_kernel::Direction_3;

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_bounding_rational_traits.h

@@ -21,7 +21,6 @@
  * Definition of the Bezier_bounding_rational_traits<Kernel> class.
  */
 
-#include <CGAL/Cartesian.h>
 #include <CGAL/Polygon_2_algorithms.h>
 #include <CGAL/Arr_geometry_traits/de_Casteljau_2.h>
 

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Circle_segment_2.h

@@ -41,9 +41,9 @@ class _One_root_point_2_rep {
   friend class _One_root_point_2<NumberType_, Filter_>;
 
 public:
-  typedef NumberType_                               NT;
-  typedef _One_root_point_2_rep<NT, Filter_>        Self;
-  typedef Sqrt_extension<NT, NT, Tag_true,Boolean_tag<Filter_> >    CoordNT;
+  using NT = NumberType_;
+  using Self = _One_root_point_2_rep<NT, Filter_>;
+  using CoordNT = Sqrt_extension<NT, NT, Tag_true,Boolean_tag<Filter_> >;
 
 private:
   CoordNT _x;            // The coordinates.
@@ -70,18 +70,17 @@ public:
  */
 template <typename NumberType_, bool Filter_>
 class _One_root_point_2 :
-  public Handle_for<_One_root_point_2_rep<NumberType_, Filter_> >
-{
+  public Handle_for<_One_root_point_2_rep<NumberType_, Filter_>> {
 public:
-  typedef NumberType_                           NT;
-  typedef _One_root_point_2<NT, Filter_>        Self;
+  using NT = NumberType_;
+  using Self = _One_root_point_2<NT, Filter_>;
 
 private:
-  typedef _One_root_point_2_rep<NT, Filter_>    Point_rep;
-  typedef Handle_for<Point_rep>                 Point_handle;
+  using Point_rep = _One_root_point_2_rep<NT, Filter_>;
+  using Point_handle = Handle_for<Point_rep>;
 
 public:
-  typedef typename Point_rep::CoordNT           CoordNT;
+  using CoordNT = typename Point_rep::CoordNT;
 
   /*! constructs default. */
   _One_root_point_2() : Point_handle(Point_rep()) {}
@@ -106,8 +105,7 @@ public:
   const CoordNT& y() const { return (this->ptr()->_y); }
 
   /*! checks for equality. */
-  bool equals(const Self& p) const
-  {
+  bool equals(const Self& p) const {
     if (this->identical(p)) return (true);
 
     return (CGAL::compare(this->ptr()->_x, p.ptr()->_x) == EQUAL &&
@@ -119,8 +117,7 @@ public:
   bool operator == (const Self& p) const { return equals(p); }
 
   /*! sets the point coordinates. */
-  void set(const NT& x, const NT& y)
-  {
+  void set(const NT& x, const NT& y) {
     this->copy_on_write();
     this->ptr()->_x = CoordNT(x);
     this->ptr()->_y = CoordNT(y);
@@ -128,8 +125,7 @@ public:
   }
 
   /*! sets the point coordinates. */
-  void set(const CoordNT& x, const CoordNT& y)
-  {
+  void set(const CoordNT& x, const CoordNT& y) {
     this->copy_on_write();
     this->ptr()->_x = x;
     this->ptr()->_y = y;
@@ -141,8 +137,7 @@ public:
  */
 template <typename NT, bool Filter>
 std::ostream& operator<<(std::ostream& os,
-                         const _One_root_point_2<NT, Filter>& p)
-{
+                         const _One_root_point_2<NT, Filter>& p) {
   os << CGAL::to_double(p.x()) << ' ' << CGAL::to_double(p.y());
   return (os);
 }
@@ -165,15 +160,15 @@ std::istream & operator >> (std::istream & is,
 template <typename Kernel_, bool Filter_>
 class _Circle_segment_2 {
 public:
-  typedef Kernel_                                          Kernel;
-  typedef typename Kernel::FT                              NT;
-  typedef _One_root_point_2<NT, Filter_>                   Point_2;
-  typedef typename Kernel::Circle_2                        Circle_2;
-  typedef typename Kernel::Segment_2                       Segment_2;
-  typedef typename Kernel::Line_2                          Line_2;
+  using Kernel = Kernel_;
+  using NT = typename Kernel::FT;
+  using Point_2 = _One_root_point_2<NT, Filter_>;
+  using Circle_2 = typename Kernel::Circle_2;
+  using Segment_2 = typename Kernel::Segment_2;
+  using Line_2 = typename Kernel::Line_2;
 
 protected:
-  typedef typename Point_2::CoordNT                        CoordNT;
+  using CoordNT = typename Point_2::CoordNT;
 
   // Data members:
   Line_2 m_line;              // The supporting line (for line segments).
@@ -234,8 +229,7 @@ public:
     m_has_radius(false),
     m_source(source),
     m_target(target),
-    m_orient(COLLINEAR)
-  {
+    m_orient(COLLINEAR) {
     CGAL_precondition(CGAL::compare(source.x() * line.a() + line.c(),
                                     -source.y() * line.b()) == EQUAL);
 
@@ -282,8 +276,7 @@ public:
     m_has_radius(false),
     m_source(source),
     m_target(target),
-    m_orient(circ.orientation())
-  {
+    m_orient(circ.orientation()) {
     CGAL_assertion(m_orient != COLLINEAR);
 
     CGAL_precondition
@@ -315,8 +308,7 @@ public:
     m_radius(r),
     m_source(source),
     m_target(target),
-    m_orient(orient)
-  {
+    m_orient(orient) {
     CGAL_assertion(orient != COLLINEAR);
 
     CGAL_precondition
@@ -343,8 +335,7 @@ public:
      m_is_full(false),
      m_has_radius(false),
      m_source(p1.x(), p1.y()),
-     m_target(p3.x(), p3.y())
-  {
+     m_target(p3.x(), p3.y()) {
     // Set the source and target.
     NT x1 = p1.x();
     NT y1 = p1.y();
@@ -359,7 +350,7 @@ public:
     // Compute the lines: A1*x + B1*y + C1 = 0,
     //               and: A2*x + B2*y + C2 = 0,
     // where:
-    const NT _two  = 2;
+    const NT _two = 2;
 
     const NT A1 = _two*(x1 - x2);
     const NT B1 = _two*(y1 - y2);
@@ -423,8 +414,7 @@ public:
   /*! obtains the supporting line.
    * \pre The curve orientation is COLLINEAR.
    */
-  const Line_2& supporting_line() const
-  {
+  const Line_2& supporting_line() const {
     CGAL_precondition(m_orient == COLLINEAR);
     return m_line;
   }
@@ -432,8 +422,7 @@ public:
   /*! obtains the supporting circle.
    * \pre The curve orientation is not COLLINEAR.
    */
-  const Circle_2& supporting_circle() const
-  {
+  const Circle_2& supporting_circle() const {
     CGAL_precondition(m_orient != COLLINEAR);
     return m_circ;
   }
@@ -444,8 +433,7 @@ public:
   /*! obtains the source point.
    * \pre The curve is not a full circle.
    */
-  const Point_2& source() const
-  {
+  const Point_2& source() const {
     CGAL_precondition(! m_is_full);
     return (m_source);
   }
@@ -453,8 +441,7 @@ public:
   /*! obtains the target point.
    * \pre The curve is not a full circle.
    */
-  const Point_2& target() const
-  {
+  const Point_2& target() const {
     CGAL_precondition(! m_is_full);
     return (m_target);
   }
@@ -464,8 +451,7 @@ public:
    * \pre The curve is circular.
    * \return The number of points (0, 1, or 2).
    */
-  unsigned int vertical_tangency_points(Point_2* vpts) const
-  {
+  unsigned int vertical_tangency_points(Point_2* vpts) const {
     CGAL_precondition(m_orient != COLLINEAR);
     unsigned int n_vpts = 0;
 
@@ -519,8 +505,7 @@ private:
    */
   unsigned int _ccw_vertical_tangency_points(const Point_2& src,
                                              const Point_2& trg,
-                                             Point_2* vpts) const
-  {
+                                             Point_2* vpts) const {
     unsigned int n_vpts = 0;
     const NT& x0 = m_circ.center().x();
     const NT& y0 = m_circ.center().y();
@@ -547,8 +532,7 @@ private:
       if ((qs % 4) == 1) {
         // We collect the left tangency point when going from Q[1] to Q[2]:
         if (CGAL::compare(x0, trg.x()) != LARGER ||
-            CGAL::compare(y0, trg.y()) != EQUAL)
-        {
+            CGAL::compare(y0, trg.y()) != EQUAL) {
           if (m_has_radius)
             vpts[n_vpts] = Point_2(CoordNT(x0 - m_radius), y0);
           else
@@ -561,8 +545,7 @@ private:
       else if ((qs % 4) == 3) {
         // We collect the right tangency point when going from Q[3] to Q[0]:
         if (CGAL::compare(x0, trg.x()) != SMALLER ||
-            CGAL::compare(y0, trg.y()) != EQUAL)
-        {
+            CGAL::compare(y0, trg.y()) != EQUAL) {
           if (m_has_radius)
             vpts[n_vpts] = Point_2(CoordNT(x0 + m_radius), y0);
           else
@@ -581,8 +564,7 @@ private:
   /*! obtains the index of the quarter-plane containing the given point,
    * where the circle center is considered to be the origin.
    */
-  int _quart_index(const Point_2& p) const
-  {
+  int _quart_index(const Point_2& p) const {
     // The plane looks like:
     //
     //      Q[1] :  |   Q[0]:
@@ -608,8 +590,7 @@ private:
  */
 template <typename Kernel, bool Filter>
 std::ostream&
-operator<<(std::ostream& os, const _Circle_segment_2<Kernel, Filter>& c)
-{
+operator<<(std::ostream& os, const _Circle_segment_2<Kernel, Filter>& c) {
   if (c.orientation() == COLLINEAR) {
     os<< "segment: " << c.source() << " -> " << c.target();
   }
@@ -632,35 +613,33 @@ operator<<(std::ostream& os, const _Circle_segment_2<Kernel, Filter>& c)
 template <typename Kernel_, bool Filter_>
 class _X_monotone_circle_segment_2 {
 public:
-  typedef Kernel_                                          Kernel;
-  typedef _X_monotone_circle_segment_2<Kernel, Filter_>    Self;
-  typedef typename Kernel::FT                              NT;
-  typedef _One_root_point_2<NT, Filter_>                   Point_2;
-  typedef typename Kernel::Circle_2                        Circle_2;
-  typedef typename Kernel::Line_2                          Line_2;
-  typedef typename Point_2::CoordNT                        CoordNT;
+  using Kernel = Kernel_;
+  using Self = _X_monotone_circle_segment_2<Kernel, Filter_>;
+  using NT = typename Kernel::FT;
+  using Point_2 = _One_root_point_2<NT, Filter_>;
+  using Circle_2 = typename Kernel::Circle_2;
+  using Line_2 = typename Kernel::Line_2;
+  using CoordNT = typename Point_2::CoordNT;
 
   // Type definition for the intersection points mapping.
-  typedef std::pair<unsigned int, unsigned int>         Curve_id_pair;
-  typedef unsigned int                                  Multiplicity;
-  typedef std::pair<Point_2, Multiplicity>              Intersection_point;
-  typedef std::list<Intersection_point>                 Intersection_list;
+  using Curve_id_pair = std::pair<unsigned int, unsigned int>;
+  using Multiplicity = std::size_t;
+  using Intersection_point = std::pair<Point_2, Multiplicity>;
+  using Intersection_list = std::list<Intersection_point>;
 
   /*! \struct Less functor for Curve_id_pair.
    */
   struct Less_id_pair {
-    bool operator()(const Curve_id_pair& ip1, const Curve_id_pair& ip2) const
-    {
+    bool operator()(const Curve_id_pair& ip1, const Curve_id_pair& ip2) const {
       // Compare the pairs of IDs lexicographically.
       return (ip1.first < ip2.first ||
               (ip1.first == ip2.first && ip1.second < ip2.second));
     }
   };
 
-  typedef std::map<Curve_id_pair, Intersection_list, Less_id_pair>
-                                                  Intersection_map;
-  typedef typename Intersection_map::value_type   Intersection_map_entry;
-  typedef typename Intersection_map::iterator     Intersection_map_iterator;
+  using Intersection_map = std::map<Curve_id_pair, Intersection_list, Less_id_pair>;
+  using Intersection_map_entry = typename Intersection_map::value_type;
+  using Intersection_map_iterator = typename Intersection_map::iterator;
 
 protected:
   NT m_first;           // The x-coordinate of the circle center.
@@ -713,8 +692,7 @@ public:
     m_third(line.c()),
     m_source(source),
     m_target(target),
-    m_info(index << INDEX_SHIFT_BITS)
-  {
+    m_info(index << INDEX_SHIFT_BITS) {
     // Check if the segment is directed left or right:
     Comparison_result res = CGAL::compare(source.x(), target.x());
 
@@ -740,8 +718,7 @@ public:
                                const typename Kernel::Point_2& target) :
     m_source(source.x(), source.y()),
     m_target(target.x(), target.y()),
-    m_info(0)
-  {
+    m_info(0) {
     Line_2 line(source, target);
     m_first  = line.a();
     m_second = line.b();
@@ -778,8 +755,7 @@ public:
     m_third(circ.squared_radius()),
     m_source(source),
     m_target(target),
-    m_info(index << INDEX_SHIFT_BITS)
-  {
+    m_info(index << INDEX_SHIFT_BITS) {
     // Check if the segment is directed left or right:
     Comparison_result res = CGAL::compare (source.x(), target.x());
 
@@ -802,8 +778,7 @@ public:
   /*! obtains the supporting line.
    * \pre The arc is linear (a line segment).
    */
-  Line_2 supporting_line() const
-  {
+  Line_2 supporting_line() const {
     CGAL_precondition (is_linear());
     return (Line_2 (a(), b(), c()));
   }
@@ -811,8 +786,7 @@ public:
   /*! obtains the supporting circle.
    * \pre The arc is circular.
    */
-  Circle_2 supporting_circle() const
-  {
+  Circle_2 supporting_circle() const {
     CGAL_precondition (is_circular());
 
     typename Kernel::Point_2 center(x0(), y0());
@@ -843,8 +817,7 @@ public:
 
   /*! checks whether the given point is in the x-range of the arc.
    */
-  bool is_in_x_range(const Point_2& p) const
-  {
+  bool is_in_x_range(const Point_2& p) const {
     Comparison_result res = CGAL::compare (p.x(), left().x());
 
     if (res == SMALLER) return false;
@@ -858,8 +831,7 @@ public:
   { return ((m_info & IS_VERTICAL_SEGMENT_MASK) != 0); }
 
   /*! obtains the orientation of the arc. */
-  inline Orientation orientation() const
-  {
+  inline Orientation orientation() const {
     unsigned int or_ = (m_info & ORIENTATION_MASK);
     if (or_ == COUNTERCLOCKWISE_CODE) return (CGAL::COUNTERCLOCKWISE);
     else if (or_ == CLOCKWISE_CODE) return (CGAL::CLOCKWISE);
@@ -870,16 +842,14 @@ public:
 
   /*! checks the position of a given point with respect to the arc.
    */
-  Comparison_result point_position(const Point_2& p) const
-  {
+  Comparison_result point_position(const Point_2& p) const {
     if (is_linear()) return (_line_point_position(p));
     else return (_circ_point_position (p));
   }
 
   /*! compares the two arcs to the right of their intersection point.
    */
-  Comparison_result compare_to_right(const Self& cv, const Point_2& p) const
-  {
+  Comparison_result compare_to_right(const Self& cv, const Point_2& p) const {
     if (is_linear()) {
       if (cv.is_linear()) return (_lines_compare_to_right (cv, p));
       Comparison_result res = cv._circ_line_compare_to_right (*this, p);
@@ -894,8 +864,7 @@ public:
 
   /*! compares the two arcs to the left of their intersection point.
    */
-  Comparison_result compare_to_left(const Self& cv, const Point_2& p) const
-  {
+  Comparison_result compare_to_left(const Self& cv, const Point_2& p) const {
     if (is_linear()) {
       if (cv.is_linear()) return (_lines_compare_to_left (cv, p));
       Comparison_result res = cv._circ_line_compare_to_left(*this, p);
@@ -910,8 +879,7 @@ public:
 
   /*! checks whether the two arcs have the same supporting curve.
    */
-  bool has_same_supporting_curve(const Self& cv) const
-  {
+  bool has_same_supporting_curve(const Self& cv) const {
     // Check if the curve indices are the same.
     if (_index() != 0 && _index() == cv._index()) return true;
 
@@ -950,8 +918,7 @@ public:
 
   /*! checks whether the two curves are equal.
    */
-  bool equals(const Self& cv) const
-  {
+  bool equals(const Self& cv) const {
     if (! this->has_same_supporting_curve(cv)) return false;
 
     if (is_linear()) {
@@ -969,8 +936,7 @@ public:
 
   /*! splits the curve at a given point into two sub-arcs.
    */
-  void split(const Point_2& p, Self& c1, Self& c2) const
-  {
+  void split(const Point_2& p, Self& c1, Self& c2) const {
     // Copy the properties of this arc to the sub-arcs.
     c1 = *this;
     c2 = *this;
@@ -990,8 +956,7 @@ public:
    */
   template <typename OutputIterator>
   OutputIterator intersect(const Self& cv, OutputIterator oi,
-                           Intersection_map* inter_map = nullptr) const
-  {
+                           Intersection_map* inter_map = nullptr) const {
     // First check whether the two arcs have the same supporting curve.
     if (has_same_supporting_curve(cv)) {
       // Check for overlaps between the two arcs.
@@ -1064,8 +1029,7 @@ public:
     // Report only the intersection points that lie on both arcs.
     for (auto iter = inter_list.begin(); iter != inter_list.end(); ++iter) {
       if (this->_is_between_endpoints (iter->first) &&
-          cv._is_between_endpoints (iter->first))
-      {
+          cv._is_between_endpoints (iter->first)) {
         *oi++ = *iter;
       }
     }
@@ -1075,8 +1039,7 @@ public:
 
   /*! checks whether it is possible to merge our arc with the given arc.
    */
-  bool can_merge_with(const Self& cv) const
-  {
+  bool can_merge_with(const Self& cv) const {
     // In order to merge the two arcs, they should have the same supporting
     // curve.
     if (! this->has_same_supporting_curve(cv)) return false;
@@ -1089,8 +1052,7 @@ public:
   /*! merges our arc with the given arc.
    * \pre The two arcs are mergeable.
    */
-  void merge(const Self& cv)
-  {
+  void merge(const Self& cv) {
     CGAL_precondition(this->can_merge_with (cv));
 
     // Check if we should extend the arc to the left or to the right.
@@ -1109,8 +1071,7 @@ public:
   }
 
   /*! constructs an opposite arc. */
-  Self construct_opposite() const
-  {
+  Self construct_opposite() const {
     Self opp_cv;
     opp_cv.m_first = this->m_first;
     opp_cv.m_second = this->m_second;
@@ -1127,8 +1088,7 @@ public:
     return (opp_cv);
   }
 
-  Bbox_2 bbox() const
-  {
+  Bbox_2 bbox() const {
     double x_min = to_double(left().x());
     double x_max = to_double(right().x());
     double y_min = to_double(left().y());
@@ -1167,8 +1127,7 @@ protected:
 
   /*! checks if the circular arc lies on the upper half of the supporting circle.
    */
-  inline bool _is_upper() const
-  {
+  inline bool _is_upper() const {
     Orientation orient = orientation();
     bool dir_right = ((m_info & IS_DIRECTED_RIGHT_MASK) != 0);
 
@@ -1197,8 +1156,7 @@ protected:
 
   /*! checks the position of a given point with respect to a line segment.
    */
-  Comparison_result _line_point_position(const Point_2& p) const
-  {
+  Comparison_result _line_point_position(const Point_2& p) const {
     // Check if we have a vertical segment.
 
     CGAL_precondition(is_in_x_range(p));
@@ -1229,20 +1187,17 @@ protected:
 
   /*! checks the position of a given point with respect to a circular arc.
    */
-  Comparison_result _circ_point_position(const Point_2& p) const
-  {
+  Comparison_result _circ_point_position(const Point_2& p) const {
 
     Comparison_result c_res = CGAL::compare (p.y(), y0());
 
     if (_is_upper()) {
       // Check if p lies below the "equator" (while the arc lies above it):
-      if (c_res == SMALLER)
-        return (SMALLER);
+      if (c_res == SMALLER) return (SMALLER);
     }
     else {
       // Check if p lies above the "equator" (while the arc lies below it):
-      if (c_res == LARGER)
-        return (LARGER);
+      if (c_res == LARGER) return (LARGER);
     }
 
     // Check if p lies inside the supporting circle, namely we have to check
@@ -1271,8 +1226,7 @@ protected:
   /*! compares two line segments to the right of their intersection point.
    */
   Comparison_result _lines_compare_to_right(const Self& cv,
-                                            const Point_2& /* p */) const
-  {
+                                            const Point_2& /* p */) const {
     if (_index() != 0 && _index() == cv._index()) return (EQUAL);
 
     // Special treatment for vertical segments: a vertical segment is larger
@@ -1292,8 +1246,7 @@ protected:
    * their intersection point.
    */
   Comparison_result _circ_line_compare_to_right(const Self& cv,
-                                                const Point_2& p) const
-  {
+                                                const Point_2& p) const {
     // A vertical segment lies above any other circle to the right of p:
     if (cv.is_vertical()) return (SMALLER);
 
@@ -1334,8 +1287,7 @@ protected:
   /*! compares two circular arcs to the right of their intersection point.
    */
   Comparison_result _circs_compare_to_right(const Self& cv,
-                                            const Point_2& p) const
-  {
+                                            const Point_2& p) const {
     if (_index() != 0 && _index() == cv._index()) {
       // Check the case of comparing two circular arcs that originate from the
       // same supporting circle. Their comparison result is not EQUAL only if
@@ -1413,13 +1365,11 @@ protected:
     // Compare the slopes of the two tangents to the circles.
     Comparison_result  slope_res;
 
-    if (sign_slope1 == ZERO && sign_slope2 == ZERO)
-    {
+    if (sign_slope1 == ZERO && sign_slope2 == ZERO) {
       // Special case were both circles have a horizontal tangent:
       slope_res = EQUAL;
     }
-    else
-    {
+    else {
       // Actually compare the slopes.
       const bool swap_res = (sign_denom1 != sign_denom2);
       const CoordNT A = NT(cv.y0() - y0())*p.x() + (y0()*cv.x0() - cv.y0()*x0());
@@ -1466,8 +1416,7 @@ protected:
   /*! compares two line segments to the left of their intersection point.
    */
   Comparison_result _lines_compare_to_left(const Self& cv,
-                                           const Point_2& ) const
-  {
+                                           const Point_2& ) const {
     if (_index() != 0 && _index() == cv._index()) return (EQUAL);
 
     // Special treatment for vertical segments: a vertical segment is smaller
@@ -1489,8 +1438,7 @@ protected:
    * their intersection point.
    */
   Comparison_result _circ_line_compare_to_left(const Self& cv,
-                                               const Point_2& p) const
-  {
+                                               const Point_2& p) const {
     // A vertical segment lies below any other circle to the left of p:
     if (cv.is_vertical()) return (LARGER);
 
@@ -1534,8 +1482,7 @@ protected:
   /*! compares the two arcs to the left of their intersection point.
    */
   Comparison_result _circs_compare_to_left(const Self& cv,
-                                           const Point_2& p) const
-  {
+                                           const Point_2& p) const {
     if (_index() != 0 && _index() == cv._index()) {
       // Check the case of comparing two circular arcs that originate from the
       // same supporting circle. Their comparison result is not EQUAL only if
@@ -1614,8 +1561,7 @@ protected:
     // Compare the slopes of the two tangents to the circles.
     Comparison_result  slope_res;
 
-    if (sign_slope1 == ZERO && sign_slope2 == ZERO)
-    {
+    if (sign_slope1 == ZERO && sign_slope2 == ZERO) {
       // Special case were both circles have a horizontal tangent:
       slope_res = EQUAL;
     }
@@ -1668,8 +1614,7 @@ protected:
   /*! computes the intersections between two line segments.
    */
   void _lines_intersect(const Self& cv,
-                        Intersection_list& inter_list) const
-  {
+                        Intersection_list& inter_list) const {
     // The intersection of the lines:
     //   a1*x + b1*y + c1 = 0   and   a2*x + b2*y + c2 = 0 ,
     // is given by:
@@ -1695,8 +1640,7 @@ protected:
    * the supporting line of the segment cv.
    */
   void _circ_line_intersect(const Self& cv,
-                            Intersection_list& inter_list) const
-  {
+                            Intersection_list& inter_list) const {
     Point_2 p;
     unsigned int mult;
 
@@ -1818,8 +1762,7 @@ protected:
 
   /*! computes the intersections between two circles.
    */
-  void _circs_intersect(const Self& cv, Intersection_list& inter_list) const
-  {
+  void _circs_intersect(const Self& cv, Intersection_list& inter_list) const {
     Point_2 p;
     unsigned int mult;
 
@@ -1884,8 +1827,7 @@ protected:
   /*! checks if the given point lies on the arc.
    * \pre p lies on the supporting curve.
    */
-  bool _is_between_endpoints(const Point_2& p) const
-  {
+  bool _is_between_endpoints(const Point_2& p) const {
     if (is_linear()) {
       if (is_vertical()) {
         // Check if the point is in the y-range of the arc.
@@ -1908,8 +1850,7 @@ protected:
     // Check whether p lies on the upper or on the lower part of the circle.
     Comparison_result c_res = CGAL::compare(p.y(), y0());
 
-    if ((_is_upper() && c_res == SMALLER) || (! _is_upper() && c_res == LARGER))
-    {
+    if ((_is_upper() && c_res == SMALLER) || (! _is_upper() && c_res == LARGER)) {
       // The point lies on the other half of the circle:
       return false;
     }
@@ -1921,8 +1862,7 @@ protected:
   /*! checks whether the given point lies in the interior of the arc.
    * \pre p lies on the supporting curve.
    */
-  bool _is_strictly_between_endpoints(const Point_2& p) const
-  {
+  bool _is_strictly_between_endpoints(const Point_2& p) const {
     if (p.equals (m_source) || p.equals (m_target)) return false;
     return (_is_between_endpoints(p));
   }
@@ -1932,8 +1872,7 @@ protected:
    * \param overlap Output: The overlapping arc (if any).
    * \return Whether we found an overlap.
    */
-  bool _compute_overlap(const Self& cv, Self& overlap) const
-  {
+  bool _compute_overlap(const Self& cv, Self& overlap) const {
     // Check if the two arcs are identical.
     if (is_linear()) {
       // In case of line segments we can swap the source and target:
@@ -1999,10 +1938,9 @@ protected:
     return false;
   }
 
-  public:
+public:
   template <class OutputIterator>
-  void approximate(OutputIterator oi, unsigned int n) const
-  {
+  void approximate(OutputIterator oi, unsigned int n) const {
     const double x_left = CGAL::to_double(this->source().x());
     const double y_left = CGAL::to_double(this->source().y());
 
@@ -2045,8 +1983,7 @@ protected:
    * \pre Both ps and pt lies on the arc and must conform with the current
    *      direction of the arc.
    */
-  Self trim(const Point_2& ps, const Point_2& pt) const
-  {
+  Self trim(const Point_2& ps, const Point_2& pt) const {
     Self arc = *this;
 
     arc.m_source = ps;
@@ -2063,8 +2000,7 @@ protected:
 template <class Kernel, bool Filter>
 std::ostream&
 operator<<(std::ostream& os,
-           const _X_monotone_circle_segment_2<Kernel, Filter> & arc)
-{
+           const _X_monotone_circle_segment_2<Kernel, Filter>& arc) {
   if (! arc.is_linear())
     os << "(" << arc.supporting_circle() << ") ";
 

Arrangement_on_surface_2/include/CGAL/Arr_line_arc_traits_2.h

@@ -43,46 +43,41 @@ namespace CGAL {
 // Traits class for CGAL::Arrangement_2 (and similar) based on a
 // CircularKernel.
 
-template < typename CircularKernel >
+template <typename CircularKernel>
 class Arr_line_arc_traits_2 {
-
   CircularKernel ck;
 
 public:
+  using Kernel = CircularKernel;
+  using Curve_2 = typename CircularKernel::Line_arc_2;
+  using X_monotone_curve_2 = typename CircularKernel::Line_arc_2;
+  using Multiplicity = std::size_t;
 
-  typedef CircularKernel Kernel;
-  typedef typename CircularKernel::Line_arc_2  Curve_2;
-  typedef typename CircularKernel::Line_arc_2  X_monotone_curve_2;
-  typedef unsigned int                         Multiplicity;
+  using Point = typename CircularKernel::Circular_arc_point_2;
+  using Point_2 = typename CircularKernel::Circular_arc_point_2;
 
-  typedef typename CircularKernel::Circular_arc_point_2      Point;
-  typedef typename CircularKernel::Circular_arc_point_2      Point_2;
+  using Has_left_category = CGAL::Tag_false;
+  using Has_merge_category = CGAL::Tag_false;
+  using Has_do_intersect_category = CGAL::Tag_false;
 
-  typedef CGAL::Tag_false                        Has_left_category;
-  typedef CGAL::Tag_false                          Has_merge_category;
-  typedef CGAL::Tag_false                        Has_do_intersect_category;
+  using Left_side_category = Arr_oblivious_side_tag;
+  using Bottom_side_category = Arr_oblivious_side_tag;
+  using Top_side_category = Arr_oblivious_side_tag;
+  using Right_side_category = Arr_oblivious_side_tag;
 
-  typedef Arr_oblivious_side_tag                 Left_side_category;
-  typedef Arr_oblivious_side_tag                 Bottom_side_category;
-  typedef Arr_oblivious_side_tag                 Top_side_category;
-  typedef Arr_oblivious_side_tag                 Right_side_category;
+  Arr_line_arc_traits_2(const CircularKernel& k = CircularKernel()) : ck(k) {}
 
-  Arr_line_arc_traits_2(const CircularKernel &k = CircularKernel())
-    : ck(k) {}
-
-  typedef typename CircularKernel::Compare_x_2          Compare_x_2;
-  typedef typename CircularKernel::Compare_xy_2         Compare_xy_2;
-  typedef typename CircularKernel::Compare_y_at_x_2     Compare_y_at_x_2;
-  typedef typename CircularKernel::Compare_y_to_right_2 Compare_y_at_x_right_2;
-  typedef typename CircularKernel::Equal_2              Equal_2;
-  // typedef typename CircularKernel::Make_x_monotone_2    Make_x_monotone_2;
-  typedef typename CircularKernel::Split_2              Split_2;
-  typedef typename CircularKernel::Construct_circular_min_vertex_2
-                                                        Construct_min_vertex_2;
-  typedef typename CircularKernel::Construct_circular_max_vertex_2
-                                                        Construct_max_vertex_2;
-  typedef typename CircularKernel::Is_vertical_2        Is_vertical_2;
-  typedef typename CircularKernel::Intersect_2          Intersect_2;
+  using Compare_x_2 = typename CircularKernel::Compare_x_2;
+  using Compare_xy_2 = typename CircularKernel::Compare_xy_2;
+  using Compare_y_at_x_2 = typename CircularKernel::Compare_y_at_x_2;
+  using Compare_y_at_x_right_2 = typename CircularKernel::Compare_y_to_right_2;
+  using Equal_2 = typename CircularKernel::Equal_2;
+  // using Make_x_monotone_2 = typename CircularKernel::Make_x_monotone_2;
+  using Split_2 = typename CircularKernel::Split_2;
+  using Construct_min_vertex_2 = typename CircularKernel::Construct_circular_min_vertex_2;
+  using Construct_max_vertex_2 = typename CircularKernel::Construct_circular_max_vertex_2;
+  using Is_vertical_2 = typename CircularKernel::Is_vertical_2;
+  using Intersect_2 = typename CircularKernel::Intersect_2;
 
   Compare_x_2 compare_x_2_object() const
   { return ck.compare_x_2_object(); }
@@ -106,7 +101,7 @@ public:
   { return ck.split_2_object(); }
 
   Intersect_2 intersect_2_object() const
-    { return ck.intersect_2_object(); }
+  { return ck.intersect_2_object(); }
 
   Construct_min_vertex_2 construct_min_vertex_2_object() const
   { return ck.construct_circular_min_vertex_2_object(); }
@@ -121,9 +116,8 @@ public:
   class Make_x_monotone_2 {
   public:
     template <typename OutputIterator>
-    OutputIterator operator()(const Curve_2& line, OutputIterator oi) const
-    {
-      typedef std::variant<Point_2, X_monotone_curve_2> Make_x_monotone_result;
+    OutputIterator operator()(const Curve_2& line, OutputIterator oi) const {
+      using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
       *oi++ = Make_x_monotone_result(line);
       return oi;
     }
@@ -137,4 +131,4 @@ public:
 
 #include <CGAL/enable_warnings.h>
 
-#endif // CGAL_CIRCULAR_KERNEL_LINE_ARC_TRAITS_H
+#endif

Arrangement_on_surface_2/include/CGAL/Arr_linear_traits_2.h

@@ -28,7 +28,7 @@
 
 #include <variant>
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/tags.h>
 #include <CGAL/intersections.h>
 #include <CGAL/Arr_tags.h>
@@ -49,58 +49,55 @@ class Arr_linear_traits_2 : public Kernel_ {
   friend class Arr_linear_object_2<Kernel_>;
 
 public:
-  typedef Kernel_                         Kernel;
-  typedef typename Kernel::FT             FT;
+  using Kernel = Kernel_;
+  using FT = typename Kernel::FT;
 
-  typedef typename Algebraic_structure_traits<FT>::Is_exact
-                                          Has_exact_division;
+  using Has_exact_division = typename Algebraic_structure_traits<FT>::Is_exact;
 
   // Category tags:
-  typedef Tag_true                        Has_left_category;
-  typedef Tag_true                        Has_merge_category;
-  typedef Tag_false                       Has_do_intersect_category;
+  using Has_left_category = Tag_true;
+  using Has_merge_category = Tag_true;
+  using Has_do_intersect_category = Tag_false;
 
-  typedef Arr_open_side_tag               Left_side_category;
-  typedef Arr_open_side_tag               Bottom_side_category;
-  typedef Arr_open_side_tag               Top_side_category;
-  typedef Arr_open_side_tag               Right_side_category;
+  using Left_side_category = Arr_open_side_tag;
+  using Bottom_side_category = Arr_open_side_tag;
+  using Top_side_category = Arr_open_side_tag;
+  using Right_side_category = Arr_open_side_tag;
 
-  typedef typename Kernel::Line_2         Line_2;
-  typedef typename Kernel::Ray_2          Ray_2;
-  typedef typename Kernel::Segment_2      Segment_2;
+  using Line_2 = typename Kernel::Line_2;
+  using Ray_2 = typename Kernel::Ray_2;
+  using Segment_2 = typename Kernel::Segment_2;
 
-  typedef CGAL::Segment_assertions<Arr_linear_traits_2<Kernel> >
-                                          Segment_assertions;
+  using Segment_assertions = CGAL::Segment_assertions<Arr_linear_traits_2<Kernel>>;
 
   /*! \class Representation of a linear with cached data.
    */
   class _Linear_object_cached_2 {
   public:
-    typedef typename Kernel::Line_2                Line_2;
-    typedef typename Kernel::Ray_2                 Ray_2;
-    typedef typename Kernel::Segment_2             Segment_2;
-    typedef typename Kernel::Point_2               Point_2;
+    using Line_2 = typename Kernel::Line_2;
+    using Ray_2 = typename Kernel::Ray_2;
+    using Segment_2 = typename Kernel::Segment_2;
+    using Point_2 = typename Kernel::Point_2;
 
   protected:
-    Line_2    l;                // The supporting line.
-    Point_2   ps;               // The source point (if exists).
-    Point_2   pt;               // The target point (if exists).
-    bool      has_source;       // Is the source point valid
+    Line_2 l;                   // The supporting line.
+    Point_2 ps;                 // The source point (if exists).
+    Point_2 pt;                 // The target point (if exists).
+    bool has_source;            // Is the source point valid
                                 // (false for a line).
-    bool      has_target;       // Is the target point valid
+    bool has_target;            // Is the target point valid
                                 // (false for a line and for a ray).
-    bool      is_right;         // Is the object directed to the right
+    bool is_right;              // Is the object directed to the right
                                 // (for segments and rays).
-    bool      is_vert;          // Is this a vertical object.
-    bool      is_horiz;         // Is this a horizontal object.
-    bool      has_pos_slope;    // Does the supporting line has a positive
+    bool is_vert;               // Is this a vertical object.
+    bool is_horiz;              // Is this a horizontal object.
+    bool has_pos_slope;         // Does the supporting line has a positive
                                 // slope (if all three flags is_vert, is_horiz
                                 // and has_pos_slope are false, then the line
                                 // has a negative slope).
-    bool      is_degen;         // Is the object degenerate (a single point).
+    bool is_degen;              // Is the object degenerate (a single point).
 
   public:
-
     /*! constructs default.
      */
     _Linear_object_cached_2() :
@@ -121,8 +118,7 @@ public:
       ps(source),
       pt(target),
       has_source(true),
-      has_target(true)
-    {
+      has_target(true) {
       Kernel kernel;
 
       Comparison_result res = kernel.compare_xy_2_object()(source, target);
@@ -144,8 +140,7 @@ public:
      */
     _Linear_object_cached_2(const Segment_2& seg) :
       has_source(true),
-      has_target(true)
-    {
+      has_target(true) {
       Kernel kernel;
 
       CGAL_assertion_msg(! kernel.is_degenerate_2_object()(seg),
@@ -172,8 +167,7 @@ public:
      */
     _Linear_object_cached_2(const Ray_2& ray) :
       has_source(true),
-      has_target(false)
-    {
+      has_target(false) {
       Kernel kernel;
 
       CGAL_assertion_msg(! kernel.is_degenerate_2_object()(ray),
@@ -201,8 +195,7 @@ public:
     _Linear_object_cached_2(const Line_2& ln) :
       l(ln),
       has_source(false),
-      has_target(false)
-    {
+      has_target(false) {
       Kernel kernel;
 
       CGAL_assertion_msg(! kernel.is_degenerate_2_object()(ln),
@@ -226,8 +219,7 @@ public:
      * \return `ARR_LEFT_BOUNDARY` if the left point is near the boundary;
      *         `ARR_INTERIOR` if the \f$x\f$-coordinate is finite.
      */
-    Arr_parameter_space left_infinite_in_x() const
-    {
+    Arr_parameter_space left_infinite_in_x() const {
       if (is_vert || is_degen) return (ARR_INTERIOR);
 
       return (is_right) ?
@@ -240,8 +232,7 @@ public:
      *         `ARR_INTERIOR` if the \f$y\f$-coordinate is finite.
      *         `ARR_TOP_BOUNDARY` if the left point is at \f$y = +\infty\f$;
      */
-    Arr_parameter_space left_infinite_in_y() const
-    {
+    Arr_parameter_space left_infinite_in_y() const {
       if (is_horiz || is_degen) return ARR_INTERIOR;
 
       if (is_vert) {
@@ -263,8 +254,7 @@ public:
     /*! obtains the (lexicographically) left endpoint.
      * \pre The left point is finite.
      */
-    const Point_2& left() const
-    {
+    const Point_2& left() const {
       CGAL_precondition(has_left());
       return (is_right ? ps : pt);
     }
@@ -274,8 +264,7 @@ public:
      * \pre p lies on the supporting line to the left of the right endpoint.
      */
     void set_left(const Point_2& p,
-                  bool CGAL_assertion_code(check_validity) = true)
-    {
+                  bool CGAL_assertion_code(check_validity) = true) {
       CGAL_precondition(! is_degen);
 
       CGAL_precondition_code(Kernel kernel);
@@ -296,8 +285,7 @@ public:
 
     /*! sets the (lexicographically) left endpoint as infinite.
      */
-    void set_left()
-    {
+    void set_left() {
       CGAL_precondition(! is_degen);
 
       if (is_right) has_source = false;
@@ -308,8 +296,7 @@ public:
      * \return `ARR_RIGHT_BOUNDARY` if the right point is near the boundary;
      *         `ARR_INTERIOR` if the \f$x\f$-coordinate is finite.
      */
-    Arr_parameter_space right_infinite_in_x() const
-    {
+    Arr_parameter_space right_infinite_in_x() const {
       if (is_vert || is_degen) return ARR_INTERIOR;
 
       return (is_right) ?
@@ -322,8 +309,7 @@ public:
      *         `ARR_INTERIOR` if the \f$y\f$-coordinate is finite.
      *         `ARR_TOP_BOUNDARY` if the right point is at \f$y = +\infty\f$;
      */
-    Arr_parameter_space right_infinite_in_y() const
-    {
+    Arr_parameter_space right_infinite_in_y() const {
       if (is_horiz || is_degen) return ARR_INTERIOR;
 
       if (is_vert) {
@@ -345,8 +331,7 @@ public:
     /*! obtains the (lexicographically) right endpoint.
      * \pre The right endpoint is finite.
      */
-    const Point_2& right() const
-    {
+    const Point_2& right() const {
       CGAL_precondition(has_right());
       return (is_right ? pt : ps);
     }
@@ -356,8 +341,7 @@ public:
      * \pre p lies on the supporting line to the right of the left endpoint.
      */
     void set_right(const Point_2& p,
-                   bool CGAL_assertion_code(check_validity) = true)
-    {
+                   bool CGAL_assertion_code(check_validity) = true) {
       CGAL_precondition(! is_degen);
       CGAL_precondition_code(Kernel kernel);
       CGAL_precondition
@@ -377,8 +361,7 @@ public:
 
     /*! sets the (lexicographically) right endpoint as infinite.
      */
-    void set_right()
-    {
+    void set_right() {
       CGAL_precondition(! is_degen);
 
       if (is_right) has_target = false;
@@ -387,16 +370,14 @@ public:
 
     /*! obtains the supporting line.
      */
-    const Line_2& supp_line() const
-    {
+    const Line_2& supp_line() const {
       CGAL_precondition(! is_degen);
       return (l);
     }
 
     /*! checks whether the curve is vertical.
      */
-    bool is_vertical() const
-    {
+    bool is_vertical() const {
       CGAL_precondition(! is_degen);
       return (is_vert);
     }
@@ -414,8 +395,7 @@ public:
      * \return (true) is in the \f$x\f$-range of the segment; (false) if it is
      * not.
      */
-    bool is_in_x_range(const Point_2& p) const
-    {
+    bool is_in_x_range(const Point_2& p) const {
       Kernel kernel;
       typename Kernel_::Compare_x_2 compare_x = kernel.compare_x_2_object();
       Comparison_result res1;
@@ -454,8 +434,7 @@ public:
      * \return (true) is in the \f$y\f$-range of the segment; (false) if it is
      * not.
      */
-    bool is_in_y_range(const Point_2& p) const
-    {
+    bool is_in_y_range(const Point_2& p) const {
       CGAL_precondition(is_vertical());
 
       Kernel kernel;
@@ -483,8 +462,7 @@ public:
   private:
     /*! determines if the supporting line has a positive slope.
      */
-    bool _has_positive_slope() const
-    {
+    bool _has_positive_slope() const {
       if (is_vert) return true;
       if (is_horiz) return false;
 
@@ -498,10 +476,10 @@ public:
 
 public:
   // Traits objects
-  typedef typename Kernel::Point_2              Point_2;
-  typedef Arr_linear_object_2<Kernel>           X_monotone_curve_2;
-  typedef Arr_linear_object_2<Kernel>           Curve_2;
-  typedef unsigned int                          Multiplicity;
+  using Point_2 = typename Kernel::Point_2;
+  using X_monotone_curve_2 = Arr_linear_object_2<Kernel>;
+  using Curve_2 = Arr_linear_object_2<Kernel>;
+  using Multiplicity = std::size_t;
 
 public:
   /*! constructs default.
@@ -514,7 +492,7 @@ public:
   /*! A functor that compares the \f$x\f$-coordinates of two points */
   class Compare_x_2 {
   protected:
-    typedef Arr_linear_traits_2<Kernel> Traits;
+    using Traits = Arr_linear_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -538,8 +516,7 @@ public:
      *         SMALLER if x(p1) < x(p2);
      *         EQUAL if x(p1) = x(p2).
      */
-    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const
-    {
+    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const {
       const Kernel& kernel = m_traits;
       return (kernel.compare_x_2_object()(p1, p2));
     }
@@ -567,7 +544,7 @@ public:
 
   class Trim_2 {
   protected:
-    typedef Arr_linear_traits_2<Kernel> Traits;
+    using Traits = Arr_linear_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -586,10 +563,8 @@ public:
   public:
     X_monotone_curve_2 operator()(const X_monotone_curve_2 xcv,
                                   const Point_2 src,
-                                  const Point_2 tgt)
-    {
-      /*
-       * "Line_segment, line, and ray" will become line segments
+                                  const Point_2 tgt) {
+      /* "Line_segment, line, and ray" will become line segments
        * when trimmed.
        */
       Equal_2 equal = Equal_2();
@@ -619,7 +594,7 @@ public:
 
   class Construct_opposite_2{
   protected:
-    typedef Arr_linear_traits_2<Kernel> Traits;
+    using Traits = Arr_linear_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -636,8 +611,7 @@ public:
     friend class Arr_linear_traits_2<Kernel>;
 
   public:
-    X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv) const
-    {
+    X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv) const {
       CGAL_precondition(! xcv.is_degenerate());
 
       X_monotone_curve_2 opp_xcv;
@@ -667,8 +641,7 @@ public:
      *         SMALLER if x(p1) < x(p2), or if x(p1) = x(p2) and y(p1) < y(p2);
      *         EQUAL if the two points are equal.
      */
-    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const
-    {
+    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const {
       Kernel kernel;
       return (kernel.compare_xy_2_object()(p1, p2));
     }
@@ -685,8 +658,7 @@ public:
      * \pre The left end of cv is a valid (bounded) point.
      * \return The left endpoint.
      */
-    const Point_2& operator()(const X_monotone_curve_2& cv) const
-    {
+    const Point_2& operator()(const X_monotone_curve_2& cv) const {
       CGAL_precondition(! cv.is_degenerate());
       CGAL_precondition(cv.has_left());
 
@@ -706,8 +678,7 @@ public:
      * \pre The right end of cv is a valid (bounded) point.
      * \return The right endpoint.
      */
-    const Point_2& operator()(const X_monotone_curve_2& cv) const
-    {
+    const Point_2& operator()(const X_monotone_curve_2& cv) const {
       CGAL_precondition(! cv.is_degenerate());
       CGAL_precondition(cv.has_right());
 
@@ -726,8 +697,7 @@ public:
      * \param cv The curve.
      * \return (true) if the curve is a vertical segment; (false) otherwise.
      */
-    bool operator()(const X_monotone_curve_2& cv) const
-    {
+    bool operator()(const X_monotone_curve_2& cv) const {
       CGAL_precondition(! cv.is_degenerate());
       return (cv.is_vertical());
     }
@@ -741,7 +711,7 @@ public:
    */
   class Compare_y_at_x_2 {
   protected:
-    typedef Arr_linear_traits_2<Kernel> Traits;
+    using Traits = Arr_linear_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -767,8 +737,7 @@ public:
      *         EQUAL if p lies on the curve.
      */
     Comparison_result operator()(const Point_2& p,
-                                 const X_monotone_curve_2& cv) const
-    {
+                                 const X_monotone_curve_2& cv) const {
       CGAL_precondition(! cv.is_degenerate());
       CGAL_precondition(cv.is_in_x_range(p));
 
@@ -809,8 +778,7 @@ public:
      */
     Comparison_result operator()(const X_monotone_curve_2& cv1,
                                  const X_monotone_curve_2& cv2,
-                                 const Point_2& CGAL_precondition_code(p)) const
-    {
+                                 const Point_2& CGAL_precondition_code(p)) const {
       CGAL_precondition(! cv1.is_degenerate());
       CGAL_precondition(! cv2.is_degenerate());
 
@@ -861,8 +829,7 @@ public:
      */
     Comparison_result operator()(const X_monotone_curve_2& cv1,
                                  const X_monotone_curve_2& cv2,
-                                 const Point_2& CGAL_precondition_code(p)) const
-    {
+                                 const Point_2& CGAL_precondition_code(p)) const {
       CGAL_precondition(! cv1.is_degenerate());
       CGAL_precondition(! cv2.is_degenerate());
 
@@ -906,8 +873,7 @@ public:
      * \return (true) if the two curves are the same; (false) otherwise.
      */
     bool operator()(const X_monotone_curve_2& cv1,
-                    const X_monotone_curve_2& cv2) const
-    {
+                    const X_monotone_curve_2& cv2) const {
       CGAL_precondition(! cv1.is_degenerate());
       CGAL_precondition(! cv2.is_degenerate());
 
@@ -918,17 +884,13 @@ public:
       if (! equal(cv1.supp_line(), cv2.supp_line()) &&
           ! equal(cv1.supp_line(),
                   kernel.construct_opposite_line_2_object()(cv2.supp_line())))
-      {
         return false;
-      }
 
       // Check that either the two left endpoints are at infinity, or they
       // are bounded and equal.
       if ((cv1.has_left() != cv2.has_left()) ||
           (cv1.has_left() && ! equal(cv1.left(), cv2.left())))
-      {
         return false;
-      }
 
       // Check that either the two right endpoints are at infinity, or they
       // are bounded and equal.
@@ -941,8 +903,7 @@ public:
      * \param p2 The second point.
      * \return (true) if the two point are the same; (false) otherwise.
      */
-    bool operator()(const Point_2& p1, const Point_2& p2) const
-    {
+    bool operator()(const Point_2& p1, const Point_2& p2) const {
       Kernel kernel;
       return (kernel.equal_2_object()(p1, p2));
     }
@@ -973,8 +934,7 @@ public:
      *                        the left at the line right end.
      */
     Arr_parameter_space operator()(const X_monotone_curve_2 & xcv,
-                                   Arr_curve_end ce) const
-    {
+                                   Arr_curve_end ce) const {
       CGAL_precondition(! xcv.is_degenerate());
       return (ce == ARR_MIN_END) ?
         xcv.left_infinite_in_x() : xcv.right_infinite_in_x();
@@ -1015,8 +975,7 @@ public:
      *                          right end.
      */
     Arr_parameter_space operator()(const X_monotone_curve_2 & xcv,
-                                   Arr_curve_end ce) const
-    {
+                                   Arr_curve_end ce) const {
       CGAL_precondition(! xcv.is_degenerate());
 
       return (ce == ARR_MIN_END) ?
@@ -1040,7 +999,7 @@ public:
    */
   class Compare_x_on_boundary_2 {
   protected:
-    typedef Arr_linear_traits_2<Kernel> Traits;
+    using Traits = Arr_linear_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -1074,8 +1033,7 @@ public:
      */
     Comparison_result operator()(const Point_2 & p,
                                  const X_monotone_curve_2 & xcv,
-                                 Arr_curve_end ) const
-    {
+                                 Arr_curve_end ) const {
       CGAL_precondition(! xcv.is_degenerate());
       CGAL_precondition(xcv.is_vertical());
 
@@ -1105,8 +1063,7 @@ public:
     Comparison_result operator()(const X_monotone_curve_2 & xcv1,
                                  Arr_curve_end /* ce1 */,
                                  const X_monotone_curve_2 & xcv2,
-                                 Arr_curve_end /* ce2 */) const
-    {
+                                 Arr_curve_end /* ce2 */) const {
       CGAL_precondition(! xcv1.is_degenerate());
       CGAL_precondition(! xcv2.is_degenerate());
       CGAL_precondition(xcv1.is_vertical());
@@ -1152,8 +1109,7 @@ public:
     Comparison_result
     operator()(const X_monotone_curve_2& CGAL_precondition_code(xcv1),
                const X_monotone_curve_2& CGAL_precondition_code(xcv2),
-               Arr_curve_end /* ce2 */) const
-    {
+               Arr_curve_end /* ce2 */) const {
       CGAL_precondition(! xcv1.is_degenerate());
       CGAL_precondition(! xcv2.is_degenerate());
       CGAL_precondition(xcv1.is_vertical());
@@ -1171,7 +1127,7 @@ public:
    */
   class Compare_y_near_boundary_2 {
   protected:
-    typedef Arr_linear_traits_2<Kernel> Traits;
+    using Traits = Arr_linear_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -1199,8 +1155,7 @@ public:
      */
     Comparison_result operator()(const X_monotone_curve_2 & xcv1,
                                  const X_monotone_curve_2 & xcv2,
-                                 Arr_curve_end ce) const
-    {
+                                 Arr_curve_end ce) const {
       // Make sure both curves are defined at \f$x = -\infty\f$ (or at
       // \f$x = +\infty\f$).
       CGAL_precondition(! xcv1.is_degenerate());
@@ -1252,11 +1207,9 @@ public:
      * \return The past-the-end iterator.
      */
     template <typename OutputIterator>
-    OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const
-    {
+    OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const {
       // Wrap the segment with a variant.
-      typedef std::variant<Point_2, X_monotone_curve_2>
-        Make_x_monotone_result;
+      using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
       *oi++ = Make_x_monotone_result(cv);
       return oi;
     }
@@ -1277,8 +1230,7 @@ public:
      * \pre `p` lies on `cv` but is not one of its end-points.
      */
     void operator()(const X_monotone_curve_2& cv, const Point_2& p,
-                    X_monotone_curve_2& c1, X_monotone_curve_2& c2) const
-    {
+                    X_monotone_curve_2& c1, X_monotone_curve_2& c2) const {
       CGAL_precondition(! cv.is_degenerate());
 
       // Make sure that p lies on the interior of the curve.
@@ -1306,7 +1258,7 @@ public:
 
   class Intersect_2 {
   protected:
-    typedef Arr_linear_traits_2<Kernel>        Traits;
+    using Traits = Arr_linear_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -1330,9 +1282,8 @@ public:
     template <typename OutputIterator>
     OutputIterator operator()(const X_monotone_curve_2& cv1,
                               const X_monotone_curve_2& cv2,
-                              OutputIterator oi) const
-    {
-      typedef std::pair<Point_2, Multiplicity>          Intersection_point;
+                              OutputIterator oi) const {
+      using Intersection_point = std::pair<Point_2, Multiplicity>;
 
       CGAL_precondition(! cv1.is_degenerate());
       CGAL_precondition(! cv2.is_degenerate());
@@ -1429,8 +1380,7 @@ public:
      *         by the same line and share a common endpoint; (false) otherwise.
      */
     bool operator()(const X_monotone_curve_2& cv1,
-                     const X_monotone_curve_2& cv2) const
-    {
+                     const X_monotone_curve_2& cv2) const {
       CGAL_precondition(! cv1.is_degenerate());
       CGAL_precondition(! cv2.is_degenerate());
 
@@ -1460,7 +1410,7 @@ public:
    */
   class Merge_2 {
   protected:
-    typedef Arr_linear_traits_2<Kernel> Traits;
+    using Traits = Arr_linear_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -1481,8 +1431,7 @@ public:
      */
     void operator()(const X_monotone_curve_2& cv1,
                     const X_monotone_curve_2& cv2,
-                    X_monotone_curve_2& c) const
-    {
+                    X_monotone_curve_2& c) const {
       CGAL_precondition(m_traits.are_mergeable_2_object()(cv2, cv1));
 
       CGAL_precondition(!cv1.is_degenerate());
@@ -1492,8 +1441,7 @@ public:
 
       // Check which curve extends to the right of the other.
       if (cv1.has_right() && cv2.has_left() &&
-          equal(cv1.right(), cv2.left()))
-      {
+          equal(cv1.right(), cv2.left())) {
         // cv2 extends cv1 to the right.
         c = cv1;
 
@@ -1519,9 +1467,9 @@ public:
 
   /// \name Functor definitions for the landmarks point-location strategy.
   //@{
-  typedef double                                        Approximate_number_type;
-  typedef CGAL::Cartesian<Approximate_number_type>      Approximate_kernel;
-  typedef Approximate_kernel::Point_2                   Approximate_point_2;
+  using Approximate_number_type = double;
+  using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
+  using Approximate_point_2 = Approximate_kernel::Point_2;
 
   class Approximate_2 {
   protected:
@@ -1545,8 +1493,7 @@ public:
      * \return An approximation of `p`'s \f$x\f$-coordinate (if `i` == 0), or an
      *         approximation of `p`'s \f$y\f$-coordinate (if `i` == 1).
      */
-    Approximate_number_type operator()(const Point_2& p, int i) const
-    {
+    Approximate_number_type operator()(const Point_2& p, int i) const {
       CGAL_precondition((i == 0) || (i == 1));
       return (i == 0) ? CGAL::to_double(p.x()) : CGAL::to_double(p.y());
     }
@@ -1566,12 +1513,8 @@ public:
       auto max_vertex = m_traits.construct_max_vertex_2_object();
       const auto& src = (l2r) ? min_vertex(xcv) : max_vertex(xcv);
       const auto& trg = (l2r) ? max_vertex(xcv) : min_vertex(xcv);
-      auto xs = CGAL::to_double(src.x());
-      auto ys = CGAL::to_double(src.y());
-      auto xt = CGAL::to_double(trg.x());
-      auto yt = CGAL::to_double(trg.y());
-      *oi++ = Approximate_point_2(xs, ys);
-      *oi++ = Approximate_point_2(xt, yt);
+      *oi++ = operator()(src);
+      *oi++ = operator()(trg);
       return oi;
     }
 
@@ -1580,8 +1523,7 @@ public:
     template <typename OutputIterator>
     OutputIterator operator()(const X_monotone_curve_2& xcv, double /* error */,
                               OutputIterator oi, const Bbox_2& bbox,
-                              bool l2r = true) const
-    {
+                              bool l2r = true) const {
       using Approx_pnt = Approximate_point_2;
       using Approx_seg = Approximate_kernel::Segment_2;
       using Approx_ray = Approximate_kernel::Ray_2;
@@ -1657,8 +1599,7 @@ public:
      * \pre p and q must not be the same.
      * \return A segment connecting `p` and `q`.
      */
-    X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q) const
-    {
+    X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q) const {
       Kernel kernel;
       Segment_2 seg = kernel.construct_segment_2_object()(p, q);
 
@@ -1675,7 +1616,7 @@ public:
   //@{
 
   //! Functor
-  typedef Construct_x_monotone_curve_2  Construct_curve_2;
+  using Construct_curve_2 = Construct_x_monotone_curve_2;
 
   /*! obtains a `Construct_curve_2` functor object. */
   Construct_curve_2 construct_curve_2_object() const
@@ -1688,18 +1629,16 @@ public:
  */
 template <typename Kernel_>
 class Arr_linear_object_2 :
-    public Arr_linear_traits_2<Kernel_>::_Linear_object_cached_2
-{
-  typedef typename Arr_linear_traits_2<Kernel_>::_Linear_object_cached_2
-                                                            Base;
+    public Arr_linear_traits_2<Kernel_>::_Linear_object_cached_2 {
+  using Base = typename Arr_linear_traits_2<Kernel_>::_Linear_object_cached_2;
 
 public:
-  typedef Kernel_                                           Kernel;
+  using Kernel = Kernel_;
 
-  typedef typename Kernel::Point_2                          Point_2;
-  typedef typename Kernel::Segment_2                        Segment_2;
-  typedef typename Kernel::Ray_2                            Ray_2;
-  typedef typename Kernel::Line_2                           Line_2;
+  using Point_2 = typename Kernel::Point_2;
+  using Segment_2 = typename Kernel::Segment_2;
+  using Ray_2 = typename Kernel::Ray_2;
+  using Line_2 = typename Kernel::Line_2;
 
 public:
   /*! constructs default.
@@ -1739,8 +1678,7 @@ public:
   /*! casts to a segment.
    * \pre The linear object is really a segment.
    */
-  Segment_2 segment() const
-  {
+  Segment_2 segment() const {
     CGAL_precondition(is_segment());
 
     Kernel kernel;
@@ -1756,8 +1694,7 @@ public:
   /*! casts to a ray.
    * \pre The linear object is really a ray.
    */
-  Ray_2 ray() const
-  {
+  Ray_2 ray() const {
     CGAL_precondition(is_ray());
 
     Kernel kernel;
@@ -1776,8 +1713,7 @@ public:
   /*! casts to a line.
    * \pre The linear object is really a line.
    */
-  Line_2 line() const
-  {
+  Line_2 line() const {
     CGAL_precondition(is_line());
     return (this->l);
   }
@@ -1785,8 +1721,7 @@ public:
   /*! obtains the supporting line.
    * \pre The object is not a point.
    */
-  const Line_2& supporting_line() const
-  {
+  const Line_2& supporting_line() const {
     CGAL_precondition(! this->is_degen);
     return (this->l);
   }
@@ -1794,8 +1729,7 @@ public:
   /*! obtains the source point.
    * \pre The object is a point, a segment or a ray.
    */
-  const Point_2& source() const
-  {
+  const Point_2& source() const {
     CGAL_precondition(! is_line());
 
     if (this->is_degen) return (this->ps);      // For a point.
@@ -1806,16 +1740,14 @@ public:
   /*! obtains the target point.
    * \pre The object is a point or a segment.
    */
-  const Point_2& target() const
-  {
+  const Point_2& target() const {
     CGAL_precondition(! is_line() && ! is_ray());
     return (this->pt);
   }
 
   /*! creates a bounding box for the linear object.
    */
-  Bbox_2 bbox() const
-  {
+  Bbox_2 bbox() const {
     CGAL_precondition(this->is_segment());
     Kernel kernel;
     Segment_2 seg = kernel.construct_segment_2_object()(this->ps, this->pt);
@@ -1834,8 +1766,7 @@ public:
  */
 template <typename Kernel, typename OutputStream>
 OutputStream& operator<<(OutputStream& os,
-                         const Arr_linear_object_2<Kernel>& lobj)
-{
+                         const Arr_linear_object_2<Kernel>& lobj) {
   // Print a letter identifying the object type, then the object itself.
   if (lobj.is_segment()) os << " S " << lobj.segment();
   else if (lobj.is_ray()) os << " R " << lobj.ray();
@@ -1846,8 +1777,7 @@ OutputStream& operator<<(OutputStream& os,
 /*! Importer for the segment class used by the traits-class.
  */
 template <typename Kernel, typename InputStream>
-InputStream& operator>>(InputStream& is, Arr_linear_object_2<Kernel>& lobj)
-{
+InputStream& operator>>(InputStream& is, Arr_linear_object_2<Kernel>& lobj) {
   // Read the object type.
   char c;
   do {

Arrangement_on_surface_2/include/CGAL/Arr_non_caching_segment_basic_traits_2.h

@@ -30,7 +30,7 @@
  * functors required by the concept it models.
  */
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Algebraic_structure_traits.h>
 #include <CGAL/number_utils.h>
 #include <CGAL/tags.h>
@@ -44,34 +44,28 @@ namespace CGAL {
  * A model of the AosBasicTraits_2 concept that handles \f$x\f$-monotone
  * non-intersecting line segments.
  */
-template <class T_Kernel>
-class Arr_non_caching_segment_basic_traits_2 : public T_Kernel
-{
+template <typename T_Kernel>
+class Arr_non_caching_segment_basic_traits_2 : public T_Kernel {
 public:
-
-  typedef T_Kernel                              Kernel;
-
-  typedef typename Kernel::FT                   FT;
+  using Kernel = T_Kernel;
+  using FT = typename Kernel::FT;
 
 private:
-  typedef Algebraic_structure_traits<FT> AST;
-  typedef typename AST::Is_exact FT_is_exact;
+  using AST = Algebraic_structure_traits<FT>;
+  using FT_is_exact = typename AST::Is_exact;
+
 public:
-
-  typedef Boolean_tag<FT_is_exact::value> Has_exact_division;
-
-  typedef
-  CGAL::Segment_assertions<Arr_non_caching_segment_basic_traits_2<Kernel> >
-                                                Segment_assertions;
+  using Has_exact_division = Boolean_tag<FT_is_exact::value>;
+  using Segment_assertions = CGAL::Segment_assertions<Arr_non_caching_segment_basic_traits_2<Kernel>>;
 
   // Categories:
-  typedef Tag_true                              Has_left_category;
-  typedef Tag_false                             Has_do_intersect_category;
+  using Has_left_category = Tag_true;
+  using Has_do_intersect_category = Tag_false;
 
-  typedef Arr_oblivious_side_tag                Left_side_category;
-  typedef Arr_oblivious_side_tag                Bottom_side_category;
-  typedef Arr_oblivious_side_tag                Top_side_category;
-  typedef Arr_oblivious_side_tag                Right_side_category;
+  using Left_side_category = Arr_oblivious_side_tag;
+  using Bottom_side_category = Arr_oblivious_side_tag;
+  using Top_side_category = Arr_oblivious_side_tag;
+  using Right_side_category = Arr_oblivious_side_tag;
 
   /*! constructs default */
   Arr_non_caching_segment_basic_traits_2() {}
@@ -80,30 +74,30 @@ public:
   //@{
 
   // Traits types:
-  typedef typename Kernel::Point_2                 Point_2;
-  typedef typename Kernel::Segment_2               X_monotone_curve_2;
-  typedef unsigned int                             Multiplicity;
+  using Point_2 = typename Kernel::Point_2;
+  using X_monotone_curve_2 = typename Kernel::Segment_2;
+  using Multiplicity = std::size_t;
 
-  /*! Compare the \f$x\f$-coordinates of two points. */
-  typedef typename Kernel::Compare_x_2             Compare_x_2;
+  /*! compares the \f$x\f$-coordinates of two points. */
+  using Compare_x_2 = typename Kernel::Compare_x_2;
 
-  /*! Compare two points lexigoraphically; by \f$x\f$, then by \f$y\f$. */
-  typedef typename Kernel::Compare_xy_2            Compare_xy_2;
+  /*! compares two points lexigoraphically; by \f$x\f$, then by \f$y\f$. */
+  using Compare_xy_2 = typename Kernel::Compare_xy_2;
 
-  /*! Obtain the left endpoint of a given segment. */
-  typedef typename Kernel::Construct_min_vertex_2  Construct_min_vertex_2;
+  /*! obtains the left endpoint of a given segment. */
+  using Construct_min_vertex_2 = typename Kernel::Construct_min_vertex_2;
 
-  /*! Obtain the right endpoint of a given segment. */
-  typedef typename Kernel::Construct_max_vertex_2  Construct_max_vertex_2;
+  /*! obtains the right endpoint of a given segment. */
+  using Construct_max_vertex_2 = typename Kernel::Construct_max_vertex_2;
 
-  /*! Check whether a given segment is vertical. */
-  typedef typename Kernel::Is_vertical_2           Is_vertical_2;
+  /*! checks whether a given segment is vertical. */
+  using Is_vertical_2 = typename Kernel::Is_vertical_2;
 
-  /*! Return the location of a given point with respect to an input segment. */
-  typedef typename Kernel::Compare_y_at_x_2        Compare_y_at_x_2;
+  /*! returns the location of a given point with respect to an input segment. */
+  using Compare_y_at_x_2 = typename Kernel::Compare_y_at_x_2;
 
-  /*! Check if two segments or if two points are identical. */
-  typedef typename Kernel::Equal_2                 Equal_2;
+  /*! checks if two segments or if two points are identical. */
+  using Equal_2 = typename Kernel::Equal_2;
 
   //@}
 
@@ -127,8 +121,7 @@ public:
      */
     Comparison_result operator()(const X_monotone_curve_2& cv1,
                                  const X_monotone_curve_2& cv2,
-                                 const Point_2& CGAL_precondition_code(p)) const
-    {
+                                 const Point_2& CGAL_precondition_code(p)) const {
       Kernel kernel;
 
       // The two segments must be defined at q and also to its left.
@@ -140,13 +133,13 @@ public:
         Compare_xy_2 compare_xy = kernel.compare_xy_2_object();
         typename Kernel::Construct_vertex_2 construct_vertex =
           kernel.construct_vertex_2_object();
-        const Point_2 & source1 = construct_vertex(cv1, 0);
-        const Point_2 & target1 = construct_vertex(cv1, 1);
-        const Point_2 & left1 =
+        const Point_2& source1 = construct_vertex(cv1, 0);
+        const Point_2& target1 = construct_vertex(cv1, 1);
+        const Point_2& left1 =
           (kernel.less_xy_2_object()(source1, target1)) ? source1 : target1;
-        const Point_2 & source2 = construct_vertex(cv2, 0);
-        const Point_2 & target2 = construct_vertex(cv2, 1);
-        const Point_2 & left2 =
+        const Point_2& source2 = construct_vertex(cv2, 0);
+        const Point_2& target2 = construct_vertex(cv2, 1);
+        const Point_2& left2 =
           (kernel.less_xy_2_object()(source2, target2)) ? source2 : target2;
         );
 
@@ -181,10 +174,9 @@ public:
      *         to the right of `p`: `SMALLER`, `LARGER`, or `EQUAL`.
      */
 
-    Comparison_result operator()(const X_monotone_curve_2 & cv1,
-                                 const X_monotone_curve_2 & cv2,
-                                 const Point_2 & CGAL_precondition_code(p)) const
-    {
+    Comparison_result operator()(const X_monotone_curve_2& cv1,
+                                 const X_monotone_curve_2& cv2,
+                                 const Point_2& CGAL_precondition_code(p)) const {
       Kernel kernel;
 
       // The two segments must be defined at q and also to its right.
@@ -196,13 +188,13 @@ public:
         Compare_xy_2 compare_xy = kernel.compare_xy_2_object();
         typename Kernel::Construct_vertex_2 construct_vertex =
           kernel.construct_vertex_2_object();
-        const Point_2 & source1 = construct_vertex(cv1, 0);
-        const Point_2 & target1 = construct_vertex(cv1, 1);
-        const Point_2 & right1 =
+        const Point_2& source1 = construct_vertex(cv1, 0);
+        const Point_2& target1 = construct_vertex(cv1, 1);
+        const Point_2& right1 =
           (kernel.less_xy_2_object()(source1, target1)) ? target1 : source1;
-        const Point_2 & source2 = construct_vertex(cv2, 0);
-        const Point_2 & target2 = construct_vertex(cv2, 1);
-        const Point_2 & right2 =
+        const Point_2& source2 = construct_vertex(cv2, 0);
+        const Point_2& target2 = construct_vertex(cv2, 1);
+        const Point_2& right2 =
           (kernel.less_xy_2_object()(source2, target2)) ? target2 : source2;
         );
 
@@ -222,9 +214,9 @@ public:
 
   /// \name Functor definitions for the landmarks point-location strategy.
   //@{
-  typedef double                                        Approximate_number_type;
-  typedef CGAL::Cartesian<Approximate_number_type>      Approximate_kernel;
-  typedef Approximate_kernel::Point_2                   Approximate_point_2;
+  using Approximate_number_type = double;
+  using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
+  using Approximate_point_2 = Approximate_kernel::Point_2;
 
   class Approximate_2 {
   protected:
@@ -267,12 +259,8 @@ public:
       auto max_vertex = m_traits.construct_max_vertex_2_object();
       const auto& src = (l2r) ? min_vertex(xcv) : max_vertex(xcv);
       const auto& trg = (l2r) ? max_vertex(xcv) : min_vertex(xcv);
-      auto xs = CGAL::to_double(src.x());
-      auto ys = CGAL::to_double(src.y());
-      auto xt = CGAL::to_double(trg.x());
-      auto yt = CGAL::to_double(trg.y());
-      *oi++ = Approximate_point_2(xs, ys);
-      *oi++ = Approximate_point_2(xt, yt);
+      *oi++ = operator()(src);
+      *oi++ = operator()(trg);
       return oi;
     }
   };
@@ -280,7 +268,7 @@ public:
   /*! obtains an Approximate_2 functor object. */
   Approximate_2 approximate_2_object () const { return Approximate_2(*this); }
 
-  typedef typename Kernel::Construct_segment_2    Construct_x_monotone_curve_2;
+  using Construct_x_monotone_curve_2 = typename Kernel::Construct_segment_2;
 
   /*! obtains a `Construct_x_monotone_curve_2` functor object. */
   Construct_x_monotone_curve_2 construct_x_monotone_curve_2_object () const

Arrangement_on_surface_2/include/CGAL/Arr_overlay_2.h

@@ -8,8 +8,8 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Efi Fogel <efifogel@gmail.com>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Efi Fogel <efifogel@gmail.com>
 
 #ifndef CGAL_ARR_OVERLAY_2_H
 #define CGAL_ARR_OVERLAY_2_H
@@ -40,24 +40,18 @@
 namespace CGAL {
 
 template <typename Arr1, typename Arr2, typename Curve>
-class Indexed_sweep_accessor
-{
-  const Arr1& arr1;
-  const Arr2& arr2;
-  mutable std::vector<void*> backup_inc;
+class Indexed_sweep_accessor {
+private:
+  const Arr1& m_arr1;
+  const Arr2& m_arr2;
+  mutable std::vector<void*> m_backup_inc;
 
 public:
+  Indexed_sweep_accessor(const Arr1& arr1, const Arr2& arr2) : m_arr1(arr1), m_arr2(arr2) {}
 
-  Indexed_sweep_accessor (const Arr1& arr1, const Arr2& arr2)
-    : arr1(arr1), arr2(arr2) { }
+  std::size_t nb_vertices() const { return m_arr1.number_of_vertices() + m_arr2.number_of_vertices(); }
 
-  std::size_t nb_vertices() const
-  {
-    return arr1.number_of_vertices() + arr2.number_of_vertices();
-  }
-
-  std::size_t min_end_index (const Curve& c) const
-  {
+  std::size_t min_end_index(const Curve& c) const {
     if (c.red_halfedge_handle() != typename Curve::HH_red())
       return reinterpret_cast<std::size_t>(c.red_halfedge_handle()->target()->inc());
     // else
@@ -65,8 +59,7 @@ public:
     return reinterpret_cast<std::size_t>(c.blue_halfedge_handle()->target()->inc());
   }
 
-  std::size_t max_end_index (const Curve& c) const
-  {
+  std::size_t max_end_index(const Curve& c) const {
     if (c.red_halfedge_handle() != typename Curve::HH_red())
       return reinterpret_cast<std::size_t>(c.red_halfedge_handle()->source()->inc());
     // else
@@ -74,52 +67,36 @@ public:
     return reinterpret_cast<std::size_t>(c.blue_halfedge_handle()->source()->inc());
   }
 
-  const Curve& curve (const Curve& c) const
-  {
-    return c;
-  }
+  const Curve& curve(const Curve& c) const { return c; }
 
   // Initializes indices by squatting Vertex::inc();
-  void before_init() const
-  {
+  void before_init() const {
     std::size_t idx = 0;
-    backup_inc.resize (nb_vertices());
-    for (typename Arr1::Vertex_const_iterator vit = arr1.vertices_begin();
-         vit != arr1.vertices_end(); ++vit, ++idx)
-    {
-      CGAL_assertion (idx < backup_inc.size());
-      backup_inc[idx] = vit->inc();
-      vit->set_inc (reinterpret_cast<void*>(idx));
+    m_backup_inc.resize (nb_vertices());
+    for (auto vit = m_arr1.vertices_begin(); vit != m_arr1.vertices_end(); ++vit, ++idx) {
+      CGAL_assertion(idx < m_backup_inc.size());
+      m_backup_inc[idx] = vit->inc();
+      vit->set_inc(reinterpret_cast<void*>(idx));
     }
-    for (typename Arr2::Vertex_const_iterator vit = arr2.vertices_begin();
-         vit != arr2.vertices_end(); ++vit, ++idx)
-    {
-      CGAL_assertion (idx < backup_inc.size());
-      backup_inc[idx] = vit->inc();
-      vit->set_inc (reinterpret_cast<void*>(idx));
+    for (auto vit = m_arr2.vertices_begin(); vit != m_arr2.vertices_end(); ++vit, ++idx) {
+      CGAL_assertion(idx < m_backup_inc.size());
+      m_backup_inc[idx] = vit->inc();
+      vit->set_inc(reinterpret_cast<void*>(idx));
     }
   }
 
   // Restores state of arrangements before index squatting
-  void after_init() const
-  {
+  void after_init() const {
     std::size_t idx = 0;
-    for (typename Arr1::Vertex_const_iterator vit = arr1.vertices_begin();
-         vit != arr1.vertices_end(); ++vit, ++idx)
-    {
-      CGAL_assertion (idx < backup_inc.size());
-      vit->set_inc (backup_inc[idx]);
+    for (auto vit = m_arr1.vertices_begin(); vit != m_arr1.vertices_end(); ++vit, ++idx) {
+      CGAL_assertion(idx < m_backup_inc.size());
+      vit->set_inc(m_backup_inc[idx]);
     }
-    for (typename Arr2::Vertex_const_iterator vit = arr2.vertices_begin();
-         vit != arr2.vertices_end(); ++vit, ++idx)
-    {
-      CGAL_assertion (idx < backup_inc.size());
-      vit->set_inc (backup_inc[idx]);
+    for (auto vit = m_arr2.vertices_begin(); vit != m_arr2.vertices_end(); ++vit, ++idx) {
+      CGAL_assertion(idx < m_backup_inc.size());
+      vit->set_inc(m_backup_inc[idx]);
     }
   }
-
-private:
-
 };
 
 /*! Compute the overlay of two input arrangements.
@@ -148,64 +125,55 @@ template <typename GeometryTraitsA_2,
           typename TopologyTraitsB,
           typename TopologyTraitsRes,
           typename OverlayTraits>
-void
-overlay(const Arrangement_on_surface_2<GeometryTraitsA_2, TopologyTraitsA>& arr1,
-        const Arrangement_on_surface_2<GeometryTraitsB_2, TopologyTraitsB>& arr2,
-        Arrangement_on_surface_2<GeometryTraitsRes_2, TopologyTraitsRes>& arr,
-        OverlayTraits& ovl_tr)
-{
-  typedef GeometryTraitsA_2                                     Agt2;
-  typedef GeometryTraitsB_2                                     Bgt2;
-  typedef GeometryTraitsRes_2                                   Rgt2;
-  typedef TopologyTraitsA                                       Att;
-  typedef TopologyTraitsB                                       Btt;
-  typedef TopologyTraitsRes                                     Rtt;
-  typedef OverlayTraits                                         Overlay_traits;
+void overlay(const Arrangement_on_surface_2<GeometryTraitsA_2, TopologyTraitsA>& arr1,
+             const Arrangement_on_surface_2<GeometryTraitsB_2, TopologyTraitsB>& arr2,
+             Arrangement_on_surface_2<GeometryTraitsRes_2, TopologyTraitsRes>& arr,
+             OverlayTraits& ovl_tr) {
+  using Agt2 = GeometryTraitsA_2;
+  using Bgt2 = GeometryTraitsB_2;
+  using Rgt2 = GeometryTraitsRes_2;
+  using Att = TopologyTraitsA;
+  using Btt = TopologyTraitsB;
+  using Rtt = TopologyTraitsRes;
+  using Overlay_traits = OverlayTraits;
 
-  typedef Arrangement_on_surface_2<Agt2, Att>                   Arr_a;
-  typedef Arrangement_on_surface_2<Bgt2, Btt>                   Arr_b;
-  typedef Arrangement_on_surface_2<Rgt2, Rtt>                   Arr_res;
-  typedef typename Arr_res::Allocator                           Allocator;
+  using Arr_a = Arrangement_on_surface_2<Agt2, Att>;
+  using Arr_b = Arrangement_on_surface_2<Bgt2, Btt>;
+  using Arr_res = Arrangement_on_surface_2<Rgt2, Rtt>;
+  using Allocator = typename Arr_res::Allocator;
 
   // some type assertions (not all, but better than nothing).
-  typedef typename Agt2::Point_2                                A_point;
-  typedef typename Bgt2::Point_2                                B_point;
-  typedef typename Rgt2::Point_2                                Res_point;
+  using A_point = typename Agt2::Point_2;
+  using B_point = typename Bgt2::Point_2;
+  using Res_point = typename Rgt2::Point_2;
   static_assert(std::is_convertible<A_point, Res_point>::value);
   static_assert(std::is_convertible<B_point, Res_point>::value);
 
-  typedef typename Agt2::X_monotone_curve_2                     A_xcv;
-  typedef typename Bgt2::X_monotone_curve_2                     B_xcv;
-  typedef typename Rgt2::X_monotone_curve_2                     Res_xcv;
+  using A_xcv = typename Agt2::X_monotone_curve_2;
+  using B_xcv = typename Bgt2::X_monotone_curve_2;
+  using Res_xcv = typename Rgt2::X_monotone_curve_2;
   static_assert(std::is_convertible<A_xcv, Res_xcv>::value);
   static_assert(std::is_convertible<B_xcv, Res_xcv>::value);
 
-  typedef Arr_traits_basic_adaptor_2<Rgt2>              Gt_adaptor_2;
-  typedef Arr_overlay_traits_2<Gt_adaptor_2, Arr_a, Arr_b>
-                                                        Ovl_gt2;
-  typedef Arr_overlay_event<Ovl_gt2, Arr_res, Allocator>
-                                                        Ovl_event;
-  typedef Arr_overlay_subcurve<Ovl_gt2, Ovl_event, Allocator>
-                                                        Ovl_curve;
-  typedef typename TopologyTraitsRes::template
-    Overlay_helper<Ovl_gt2, Ovl_event, Ovl_curve, Arr_a, Arr_b>
-                                                        Ovl_helper;
-  typedef Arr_overlay_ss_visitor<Ovl_helper, Overlay_traits>
-                                                        Ovl_visitor;
+  using Gt_adaptor_2 = Arr_traits_basic_adaptor_2<Rgt2>;
+  using Ovl_gt2 = Arr_overlay_traits_2<Gt_adaptor_2, Arr_a, Arr_b>;
+  using Ovl_event = Arr_overlay_event<Ovl_gt2, Arr_res, Allocator>;
+  using Ovl_curve = Arr_overlay_subcurve<Ovl_gt2, Ovl_event, Allocator>;
+  using Ovl_helper = typename TopologyTraitsRes::template Overlay_helper<Ovl_gt2, Ovl_event, Ovl_curve, Arr_a, Arr_b>;
+  using Ovl_visitor = Arr_overlay_ss_visitor<Ovl_helper, Overlay_traits>;
 
-  typedef typename Ovl_gt2::X_monotone_curve_2          Ovl_x_monotone_curve_2;
-  typedef typename Ovl_gt2::Point_2                     Ovl_point_2;
-  typedef typename Ovl_gt2::Cell_handle_red             Cell_handle_red;
-  typedef typename Ovl_gt2::Optional_cell_red           Optional_cell_red;
-  typedef typename Ovl_gt2::Cell_handle_blue            Cell_handle_blue;
-  typedef typename Ovl_gt2::Optional_cell_blue          Optional_cell_blue;
+  using Ovl_x_monotone_curve_2 = typename Ovl_gt2::X_monotone_curve_2;
+  using Ovl_point_2 = typename Ovl_gt2::Point_2;
+  using Cell_handle_red = typename Ovl_gt2::Cell_handle_red;
+  using Optional_cell_red = typename Ovl_gt2::Optional_cell_red;
+  using Cell_handle_blue = typename Ovl_gt2::Cell_handle_blue;
+  using Optional_cell_blue = typename Ovl_gt2::Optional_cell_blue;
 
   CGAL_USE_TYPE(Optional_cell_red);
   CGAL_USE_TYPE(Optional_cell_blue);
 
   // The result arrangement cannot be on of the input arrangements.
-  CGAL_precondition(((void*)(&arr) != (void*)(&arr1)) &&
-                    ((void*)(&arr) != (void*)(&arr2)));
+  CGAL_precondition(((void*)(&arr) != (void*)(&arr1)) && ((void*)(&arr) != (void*)(&arr2)));
 
   // Prepare a vector of extended x-monotone curves that represent all edges
   // in both input arrangements. Each curve is associated with a halfedge
@@ -216,23 +184,20 @@ overlay(const Arrangement_on_surface_2<GeometryTraitsA_2, TopologyTraitsA>& arr1
     xcvs_vec(arr1.number_of_edges() + arr2.number_of_edges());
   unsigned int i = 0;
 
-  typename Arr_a::Edge_const_iterator eit1;
-  for (eit1 = arr1.edges_begin(); eit1 != arr1.edges_end(); ++eit1, ++i) {
+  for (auto eit1 = arr1.edges_begin(); eit1 != arr1.edges_end(); ++eit1, ++i) {
     typename Arr_a::Halfedge_const_handle he1 = eit1;
     if (he1->direction() != ARR_RIGHT_TO_LEFT) he1 = he1->twin();
     xcvs_vec[i] = Ovl_x_monotone_curve_2(eit1->curve(), he1, invalid_he2);
   }
 
-  typename Arr_b::Edge_const_iterator eit2;
-  for (eit2 = arr2.edges_begin(); eit2 != arr2.edges_end(); ++eit2, ++i) {
+  for (auto eit2 = arr2.edges_begin(); eit2 != arr2.edges_end(); ++eit2, ++i) {
     typename Arr_b::Halfedge_const_handle he2 = eit2;
     if (he2->direction() != ARR_RIGHT_TO_LEFT) he2 = he2->twin();
     xcvs_vec[i] = Ovl_x_monotone_curve_2(eit2->curve(), invalid_he1, he2);
   }
 
   // Obtain an extended traits-class object and define the sweep-line visitor.
-  const typename Arr_res::Traits_adaptor_2* traits_adaptor =
-    arr.traits_adaptor();
+  const typename Arr_res::Traits_adaptor_2* traits_adaptor = arr.traits_adaptor();
 
   /* We would like to avoid copy construction of the geometry traits class.
    * Copy construction is undesired, because it may results with data
@@ -246,29 +211,22 @@ overlay(const Arrangement_on_surface_2<GeometryTraitsA_2, TopologyTraitsA>& arr1
    * Use the form 'A a(*b);' and not ''A a = b;' to handle the case where A has
    * only an implicit constructor, (which takes *b as a parameter).
    */
-  std::conditional_t<std::is_same_v<Gt_adaptor_2, Ovl_gt2>,
-                     const Ovl_gt2&, Ovl_gt2>
-    ex_traits(*traits_adaptor);
+  std::conditional_t<std::is_same_v<Gt_adaptor_2, Ovl_gt2>, const Ovl_gt2&, Ovl_gt2> ex_traits(*traits_adaptor);
 
   Ovl_visitor visitor(&arr1, &arr2, &arr, &ovl_tr);
   Ss2::Surface_sweep_2<Ovl_visitor> surface_sweep(&ex_traits, &visitor);
 
   // In case both arrangement do not contain isolated vertices, go on and
   // overlay them.
-  const std::size_t total_iso_verts =
-    arr1.number_of_isolated_vertices() + arr2.number_of_isolated_vertices();
+  const std::size_t total_iso_verts = arr1.number_of_isolated_vertices() + arr2.number_of_isolated_vertices();
 
   if (total_iso_verts == 0) {
     // Clear the result arrangement and perform the sweep to construct it.
     arr.clear();
-    if (std::is_same<typename Agt2::Bottom_side_category,
-                     Arr_contracted_side_tag>::value)
-      surface_sweep.sweep (xcvs_vec.begin(), xcvs_vec.end());
+    if (std::is_same<typename Agt2::Bottom_side_category, Arr_contracted_side_tag>::value)
+      surface_sweep.sweep(xcvs_vec.begin(), xcvs_vec.end());
     else
-      surface_sweep.indexed_sweep (xcvs_vec,
-                                   Indexed_sweep_accessor
-                                   <Arr_a, Arr_b, Ovl_x_monotone_curve_2>
-                                   (arr1, arr2));
+      surface_sweep.indexed_sweep(xcvs_vec, Indexed_sweep_accessor<Arr_a, Arr_b, Ovl_x_monotone_curve_2>(arr1, arr2));
     xcvs_vec.clear();
     return;
   }
@@ -278,38 +236,29 @@ overlay(const Arrangement_on_surface_2<GeometryTraitsA_2, TopologyTraitsA>& arr1
   std::vector<Ovl_point_2> pts_vec(total_iso_verts);
 
   i = 0;
-  typename Arr_a::Vertex_const_iterator  vit1;
-  for (vit1 = arr1.vertices_begin(); vit1 != arr1.vertices_end(); ++vit1) {
+  for (auto vit1 = arr1.vertices_begin(); vit1 != arr1.vertices_end(); ++vit1) {
     if (vit1->is_isolated()) {
       typename Arr_a::Vertex_const_handle v1 = vit1;
-      pts_vec[i++] =
-        Ovl_point_2(vit1->point(), std::make_optional(Cell_handle_red(v1)),
-                    std::optional<Cell_handle_blue>());
+      pts_vec[i++] = Ovl_point_2(vit1->point(), std::make_optional(Cell_handle_red(v1)),
+                                 std::optional<Cell_handle_blue>());
     }
   }
 
-  typename Arr_b::Vertex_const_iterator  vit2;
-  for (vit2 = arr2.vertices_begin(); vit2 != arr2.vertices_end(); ++vit2) {
+  for (auto vit2 = arr2.vertices_begin(); vit2 != arr2.vertices_end(); ++vit2) {
     if (vit2->is_isolated()) {
       typename Arr_b::Vertex_const_handle v2 = vit2;
-      pts_vec[i++] =
-        Ovl_point_2(vit2->point(), std::optional<Cell_handle_red>(),
-                    std::make_optional(Cell_handle_blue(v2)));
+      pts_vec[i++] = Ovl_point_2(vit2->point(), std::optional<Cell_handle_red>(),
+                                 std::make_optional(Cell_handle_blue(v2)));
     }
   }
 
   // Clear the result arrangement and perform the sweep to construct it.
   arr.clear();
-  if (std::is_same<typename Agt2::Bottom_side_category,
-      Arr_contracted_side_tag>::value)
-    surface_sweep.sweep(xcvs_vec.begin(), xcvs_vec.end(),
-                        pts_vec.begin(), pts_vec.end());
+  if (std::is_same<typename Agt2::Bottom_side_category, Arr_contracted_side_tag>::value)
+    surface_sweep.sweep(xcvs_vec.begin(), xcvs_vec.end(), pts_vec.begin(), pts_vec.end());
   else
-    surface_sweep.indexed_sweep (xcvs_vec,
-                                 Indexed_sweep_accessor
-                                 <Arr_a, Arr_b, Ovl_x_monotone_curve_2>
-                                 (arr1, arr2),
-                                 pts_vec.begin(), pts_vec.end());
+    surface_sweep.indexed_sweep(xcvs_vec, Indexed_sweep_accessor<Arr_a, Arr_b, Ovl_x_monotone_curve_2>(arr1, arr2),
+                                pts_vec.begin(), pts_vec.end());
   xcvs_vec.clear();
   pts_vec.clear();
 }
@@ -325,20 +274,18 @@ template <typename GeometryTraitsA_2,
           typename TopologyTraitsA,
           typename TopologyTraitsB,
           typename TopologyTraitsRes>
-void
-overlay(const Arrangement_on_surface_2<GeometryTraitsA_2, TopologyTraitsA>& arr1,
-        const Arrangement_on_surface_2<GeometryTraitsB_2, TopologyTraitsB>& arr2,
-        Arrangement_on_surface_2<GeometryTraitsRes_2, TopologyTraitsRes>& arr)
-{
-  typedef GeometryTraitsA_2                                     Agt2;
-  typedef GeometryTraitsB_2                                     Bgt2;
-  typedef GeometryTraitsRes_2                                   Rgt2;
-  typedef TopologyTraitsA                                       Att;
-  typedef TopologyTraitsB                                       Btt;
-  typedef TopologyTraitsRes                                     Rtt;
-  typedef Arrangement_on_surface_2<Agt2, Att>                   Arr_a;
-  typedef Arrangement_on_surface_2<Bgt2, Btt>                   Arr_b;
-  typedef Arrangement_on_surface_2<Rgt2, Rtt>                   Arr_res;
+void overlay(const Arrangement_on_surface_2<GeometryTraitsA_2, TopologyTraitsA>& arr1,
+             const Arrangement_on_surface_2<GeometryTraitsB_2, TopologyTraitsB>& arr2,
+             Arrangement_on_surface_2<GeometryTraitsRes_2, TopologyTraitsRes>& arr) {
+  using Agt2 = GeometryTraitsA_2;
+  using Bgt2 = GeometryTraitsB_2;
+  using Rgt2 = GeometryTraitsRes_2;
+  using Att = TopologyTraitsA;
+  using Btt = TopologyTraitsB;
+  using Rtt = TopologyTraitsRes;
+  using Arr_a = Arrangement_on_surface_2<Agt2, Att>;
+  using Arr_b = Arrangement_on_surface_2<Bgt2, Btt>;
+  using Arr_res = Arrangement_on_surface_2<Rgt2, Rtt>;
 
   _Arr_default_overlay_traits_base<Arr_a, Arr_b, Arr_res> ovl_traits;
   overlay(arr1, arr2, arr, ovl_traits);

Arrangement_on_surface_2/include/CGAL/Arr_segment_traits_2.h

@@ -28,7 +28,7 @@
 #include <variant>
 
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/tags.h>
 #include <CGAL/intersections.h>
 #include <CGAL/Arr_tags.h>
@@ -52,35 +52,32 @@ class Arr_segment_2;
 template <typename Kernel_ = Exact_predicates_exact_constructions_kernel>
 class Arr_segment_traits_2 : public Kernel_ {
   friend class Arr_segment_2<Kernel_>;
-
 public:
-  typedef Kernel_                         Kernel;
-  typedef typename Kernel::FT             FT;
+  using Kernel = Kernel_;
+  using FT = typename Kernel::FT;
 
-  typedef typename Algebraic_structure_traits<FT>::Is_exact
-                                          Has_exact_division;
+  using Has_exact_division = typename Algebraic_structure_traits<FT>::Is_exact;
 
   // Category tags:
-  typedef Tag_true                        Has_left_category;
-  typedef Tag_true                        Has_merge_category;
-  typedef Tag_false                       Has_do_intersect_category;
+  using Has_left_category = Tag_true;
+  using Has_merge_category = Tag_true;
+  using Has_do_intersect_category = Tag_false;
 
-  typedef Arr_oblivious_side_tag          Left_side_category;
-  typedef Arr_oblivious_side_tag          Bottom_side_category;
-  typedef Arr_oblivious_side_tag          Top_side_category;
-  typedef Arr_oblivious_side_tag          Right_side_category;
+  using Left_side_category = Arr_oblivious_side_tag;
+  using Bottom_side_category = Arr_oblivious_side_tag;
+  using Top_side_category = Arr_oblivious_side_tag;
+  using Right_side_category = Arr_oblivious_side_tag;
 
-  typedef typename Kernel::Line_2         Line_2;
-  typedef CGAL::Segment_assertions<Arr_segment_traits_2<Kernel> >
-                                          Segment_assertions;
+  using Line_2 = typename Kernel::Line_2;
+  using Segment_assertions = CGAL::Segment_assertions<Arr_segment_traits_2<Kernel>>;
 
   /*! \class Representation of a segment with cached data.
    */
   class _Segment_cached_2 {
   public:
-    typedef typename Kernel::Line_2                Line_2;
-    typedef typename Kernel::Segment_2             Segment_2;
-    typedef typename Kernel::Point_2               Point_2;
+    using Line_2 = typename Kernel::Line_2;
+    using Segment_2 = typename Kernel::Segment_2;
+    using Point_2 = typename Kernel::Point_2;
 
   protected:
     mutable Line_2 m_l;         // the line that supports the segment.
@@ -228,10 +225,10 @@ public:
 
 public:
   // Traits objects
-  typedef typename Kernel::Point_2        Point_2;
-  typedef Arr_segment_2<Kernel>           X_monotone_curve_2;
-  typedef Arr_segment_2<Kernel>           Curve_2;
-  typedef unsigned int                    Multiplicity;
+  using Point_2 = typename Kernel::Point_2;
+  using X_monotone_curve_2 = Arr_segment_2<Kernel>;
+  using Curve_2 = Arr_segment_2<Kernel>;
+  using Multiplicity = std::size_t;
 
 public:
   /*! constructs default. */
@@ -242,7 +239,7 @@ public:
 
   class Compare_x_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     //! The traits (in case it has state).
     const Traits& m_traits;
@@ -262,8 +259,7 @@ public:
      *         `SMALLER` if x(p1) < x(p2);
      *         `EQUAL` if x(p1) = x(p2).
      */
-    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const
-    {
+    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const {
       const Kernel& kernel = m_traits;
       return (kernel.compare_x_2_object()(p1, p2));
     }
@@ -274,7 +270,7 @@ public:
 
   class Compare_xy_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -294,8 +290,7 @@ public:
      *         SMALLER if x(p1) < x(p2), or if x(p1) = x(p2) and y(p1) < y(p2);
      *         EQUAL if the two points are equal.
      */
-    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const
-    {
+    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const {
       const Kernel& kernel = m_traits;
       return (kernel.compare_xy_2_object()(p1, p2));
     }
@@ -347,7 +342,7 @@ public:
 
   class Compare_y_at_x_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -369,8 +364,7 @@ public:
      *         `EQUAL` if `p` lies on the curve.
      */
     Comparison_result operator()(const Point_2& p,
-                                 const X_monotone_curve_2& cv) const
-    {
+                                 const X_monotone_curve_2& cv) const {
       CGAL_precondition(m_traits.is_in_x_range_2_object()(cv, p));
 
       const Kernel& kernel = m_traits;
@@ -396,7 +390,7 @@ public:
 
   class Compare_y_at_x_left_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -421,8 +415,7 @@ public:
      */
     Comparison_result operator()(const X_monotone_curve_2& cv1,
                                  const X_monotone_curve_2& cv2,
-                                 const Point_2& CGAL_assertion_code(p)) const
-    {
+                                 const Point_2& CGAL_assertion_code(p)) const {
       const Kernel& kernel = m_traits;
 
       // Make sure that p lies on both curves, and that both are defined to its
@@ -450,7 +443,7 @@ public:
 
   class Compare_y_at_x_right_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -475,8 +468,7 @@ public:
      */
     Comparison_result operator()(const X_monotone_curve_2& cv1,
                                  const X_monotone_curve_2& cv2,
-                                 const Point_2& CGAL_assertion_code(p)) const
-    {
+                                 const Point_2& CGAL_assertion_code(p)) const {
       const Kernel& kernel = m_traits;
 
       // Make sure that p lies on both curves, and that both are defined to its
@@ -502,7 +494,7 @@ public:
 
   class Equal_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -522,8 +514,7 @@ public:
      * \return (true) if the two curves are the same; (false) otherwise.
      */
     bool operator()(const X_monotone_curve_2& cv1,
-                    const X_monotone_curve_2& cv2) const
-    {
+                    const X_monotone_curve_2& cv2) const {
       const Kernel& kernel = m_traits;
       typename Kernel::Equal_2  equal = kernel.equal_2_object();
 
@@ -536,8 +527,7 @@ public:
      * \param p2 the second point.
      * \return (true) if the two point are the same; (false) otherwise.
      */
-    bool operator()(const Point_2& p1, const Point_2& p2) const
-    {
+    bool operator()(const Point_2& p1, const Point_2& p2) const {
       const Kernel& kernel = m_traits;
       return (kernel.equal_2_object()(p1, p2));
     }
@@ -566,11 +556,9 @@ public:
      * \return the past-the-end output iterator.
      */
     template <typename OutputIterator>
-    OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const
-    {
+    OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const {
       // Wrap the segment with a variant.
-      typedef std::variant<Point_2, X_monotone_curve_2>
-        Make_x_monotone_result;
+      using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
       *oi++ = Make_x_monotone_result(cv);
       return oi;
     }
@@ -582,7 +570,7 @@ public:
 
   class Split_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -595,7 +583,7 @@ public:
     friend class Arr_segment_traits_2<Kernel>;
 
   public:
-    /*! split a given \f$x\f$-monotone curve at a given point into two
+    /*! splits a given \f$x\f$-monotone curve at a given point into two
      * sub-curves.
      * \param cv the curve to split
      * \param p the split point.
@@ -604,8 +592,7 @@ public:
      * \pre `p` lies on cv but is not one of its endpoints.
      */
     void operator()(const X_monotone_curve_2& cv, const Point_2& p,
-                    X_monotone_curve_2& c1, X_monotone_curve_2& c2) const
-    {
+                    X_monotone_curve_2& c1, X_monotone_curve_2& c2) const {
       // Make sure that p lies on the interior of the curve.
       CGAL_precondition_code(const Kernel& kernel = m_traits;
                              auto compare_xy = kernel.compare_xy_2_object());
@@ -628,7 +615,7 @@ public:
 
   class Intersect_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -644,8 +631,7 @@ public:
     // this point, we already know which point is left / right for
     // both segments
     bool do_intersect(const Point_2& A1, const Point_2& A2,
-                      const Point_2& B1, const Point_2& B2) const
-    {
+                      const Point_2& B1, const Point_2& B2) const {
       const Kernel& kernel = m_traits;
       auto compare_xy = kernel.compare_xy_2_object();
       namespace interx = CGAL::Intersections::internal;
@@ -686,8 +672,7 @@ public:
     /*! determines whether the bounding boxes of two segments overlap
      */
     bool do_bboxes_overlap(const X_monotone_curve_2& cv1,
-                           const X_monotone_curve_2& cv2) const
-    {
+                           const X_monotone_curve_2& cv2) const {
       const Kernel& kernel = m_traits;
       auto construct_bbox = kernel.construct_bbox_2_object();
       auto bbox1 = construct_bbox(cv1.source()) + construct_bbox(cv1.target());
@@ -707,9 +692,8 @@ public:
     template <typename OutputIterator>
     OutputIterator operator()(const X_monotone_curve_2& cv1,
                               const X_monotone_curve_2& cv2,
-                              OutputIterator oi) const
-    {
-      typedef std::pair<Point_2, Multiplicity>          Intersection_point;
+                              OutputIterator oi) const {
+      using Intersection_point = std::pair<Point_2, Multiplicity>;
 
       // Early ending with Bbox overlapping test
       if (! do_bboxes_overlap(cv1, cv2)) return oi;
@@ -787,7 +771,7 @@ public:
 
   class Are_mergeable_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -808,8 +792,7 @@ public:
      * \pre `cv1` and `cv2` share a common endpoint.
      */
     bool operator()(const X_monotone_curve_2& cv1,
-                    const X_monotone_curve_2& cv2) const
-    {
+                    const X_monotone_curve_2& cv2) const {
       const Kernel& kernel = m_traits;
       typename Kernel::Equal_2 equal = kernel.equal_2_object();
       if (! equal(cv1.right(), cv2.left()) &&
@@ -832,7 +815,7 @@ public:
    */
   class Merge_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     /*! The traits (in case it has state) */
     const Traits& m_traits;
@@ -853,14 +836,13 @@ public:
      */
     void operator()(const X_monotone_curve_2& cv1,
                     const X_monotone_curve_2& cv2,
-                    X_monotone_curve_2& c) const
-    {
+                    X_monotone_curve_2& c) const {
       CGAL_precondition(m_traits.are_mergeable_2_object()(cv1, cv2));
 
       const Kernel& kernel = m_traits;
       auto equal = kernel.equal_2_object();
 
-      // Check which curve extends to the right of the other.
+      // checks which curve extends to the right of the other.
       if (equal(cv1.right(), cv2.left())) {
         // cv2 extends cv1 to the right.
         c = cv1;
@@ -882,9 +864,9 @@ public:
 
   /// \name Functor definitions for the landmarks point-location strategy.
   //@{
-  typedef double                                        Approximate_number_type;
-  typedef CGAL::Cartesian<Approximate_number_type>      Approximate_kernel;
-  typedef Approximate_kernel::Point_2                   Approximate_point_2;
+  using Approximate_number_type = double;
+  using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
+  using Approximate_point_2 = Approximate_kernel::Point_2;
 
   class Approximate_2 {
   protected:
@@ -927,12 +909,8 @@ public:
       auto max_vertex = m_traits.construct_max_vertex_2_object();
       const auto& src = (l2r) ? min_vertex(xcv) : max_vertex(xcv);
       const auto& trg = (l2r) ? max_vertex(xcv) : min_vertex(xcv);
-      auto xs = CGAL::to_double(src.x());
-      auto ys = CGAL::to_double(src.y());
-      auto xt = CGAL::to_double(trg.x());
-      auto yt = CGAL::to_double(trg.y());
-      *oi++ = Approximate_point_2(xs, ys);
-      *oi++ = Approximate_point_2(xt, yt);
+      *oi++ = operator()(src);
+      *oi++ = operator()(trg);
       return oi;
     }
   };
@@ -943,7 +921,7 @@ public:
   //! Functor
   class Construct_x_monotone_curve_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     //! The traits (in case it has state).
     const Traits& m_traits;
@@ -956,7 +934,7 @@ public:
     friend class Arr_segment_traits_2<Kernel>;
 
   public:
-    typedef typename Kernel::Segment_2          Segment_2;
+    using Segment_2 = typename Kernel::Segment_2;
 
     /*! obtains an \f$x\f$-monotone curve connecting two given endpoints.
      * \param source the first point.
@@ -965,8 +943,7 @@ public:
      * \return a segment connecting `source` and `target`.
      */
     X_monotone_curve_2 operator()(const Point_2& source,
-                                  const Point_2& target) const
-    {
+                                  const Point_2& target) const {
       const Kernel& kernel = m_traits;
       auto line = kernel.construct_line_2_object()(source, target);
       Comparison_result res = kernel.compare_xy_2_object()(source, target);
@@ -985,8 +962,7 @@ public:
      * \pre the segment is not degenerate.
      * \return a segment that is the same as `seg`..
      */
-    X_monotone_curve_2 operator()(const Segment_2& seg) const
-    {
+    X_monotone_curve_2 operator()(const Segment_2& seg) const {
       const Kernel& kernel = m_traits;
       auto line = kernel.construct_line_2_object()(seg);
       auto vertex_ctr = kernel.construct_vertex_2_object();
@@ -1011,8 +987,7 @@ public:
      */
     X_monotone_curve_2 operator()(const Line_2& line,
                                   const Point_2& source,
-                                  const Point_2& target) const
-    {
+                                  const Point_2& target) const {
       const Kernel& kernel = m_traits;
       CGAL_precondition
         (Segment_assertions::_assert_is_point_on(source, line,
@@ -1039,7 +1014,7 @@ public:
   //@{
 
   //! Functor
-  typedef Construct_x_monotone_curve_2  Construct_curve_2;
+  using Construct_curve_2 = Construct_x_monotone_curve_2;
 
   /*! obtains a `Construct_curve_2` functor object. */
   Construct_curve_2 construct_curve_2_object() const
@@ -1051,7 +1026,7 @@ public:
 
   class Trim_2 {
    protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     /*! The traits (in case it has state). */
     const Traits& m_traits;
@@ -1074,8 +1049,7 @@ public:
   public:
     X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv,
                                   const Point_2& src,
-                                  const Point_2& tgt)const
-    {
+                                  const Point_2& tgt) const {
       CGAL_precondition_code(Equal_2 equal = m_traits.equal_2_object());
       CGAL_precondition_code(Compare_y_at_x_2 compare_y_at_x =
                              m_traits.compare_y_at_x_2_object());
@@ -1119,7 +1093,7 @@ public:
 
   class Construct_opposite_2 {
   public:
-    /*! Construct an opposite \f$x\f$-monotone (with swapped source and target).
+    /*! constructs an opposite \f$x\f$-monotone (with swapped source and target).
      * \param cv the curve.
      * \return the opposite curve.
      */
@@ -1137,12 +1111,12 @@ public:
 
   class Is_in_x_range_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     //! The traits (in case it has state).
     const Traits& m_traits;
 
-    /*! Construct
+    /*! constructs
      * \param traits the traits (in case it has state)
      */
     Is_in_x_range_2(const Traits& traits) : m_traits(traits) {}
@@ -1156,8 +1130,7 @@ public:
      * \param p the point.
      * \return true if p is in the \f$x\f$-range of cv; false otherwise.
      */
-    bool operator()(const X_monotone_curve_2& cv, const Point_2& p) const
-    {
+    bool operator()(const X_monotone_curve_2& cv, const Point_2& p) const {
       const Kernel& kernel = m_traits;
       auto compare_x = kernel.compare_x_2_object();
       Comparison_result res1 = compare_x(p, cv.left());
@@ -1176,7 +1149,7 @@ public:
 
   class Is_in_y_range_2 {
   protected:
-    typedef Arr_segment_traits_2<Kernel>        Traits;
+    using Traits = Arr_segment_traits_2<Kernel>;
 
     //! The traits (in case it has state).
     const Traits& m_traits;
@@ -1195,8 +1168,7 @@ public:
      * \param p the point.
      * \return true if p is in the \f$y\f$-range of cv; false otherwise.
      */
-    bool operator()(const X_monotone_curve_2& cv, const Point_2& p) const
-    {
+    bool operator()(const X_monotone_curve_2& cv, const Point_2& p) const {
       const Kernel& kernel = m_traits;
       auto compare_y = kernel.compare_y_2_object();
       Comparison_result res1 = compare_y(p, cv.left());
@@ -1232,8 +1204,7 @@ template <typename Kernel>
 Arr_segment_traits_2<Kernel>::
 _Segment_cached_2::_Segment_cached_2(const Segment_2& seg) :
   m_is_vert(false),
-  m_is_computed(false)
-{
+  m_is_computed(false) {
   Kernel kernel;
   auto vertex_ctr = kernel.construct_vertex_2_object();
 
@@ -1255,8 +1226,7 @@ _Segment_cached_2::_Segment_cached_2(const Point_2& source,
   m_ps(source),
   m_pt(target),
   m_is_vert(false),
-  m_is_computed(false)
-{
+  m_is_computed(false) {
   Kernel kernel;
 
   Comparison_result res = kernel.compare_xy_2_object()(m_ps, m_pt);
@@ -1274,8 +1244,7 @@ _Segment_cached_2::_Segment_cached_2(const Line_2& line,
                                      const Point_2& target) :
   m_l(line),
   m_ps(source),
-  m_pt(target)
-{
+  m_pt(target) {
   Kernel kernel;
 
   CGAL_precondition
@@ -1312,8 +1281,7 @@ _Segment_cached_2(const Line_2& line,
 //! \brief assigns.
 template <typename Kernel>
 const typename Arr_segment_traits_2<Kernel>::_Segment_cached_2&
-Arr_segment_traits_2<Kernel>::_Segment_cached_2::operator=(const Segment_2& seg)
-{
+Arr_segment_traits_2<Kernel>::_Segment_cached_2::operator=(const Segment_2& seg) {
   Kernel kernel;
   auto vertex_ctr = kernel.construct_vertex_2_object();
 
@@ -1338,8 +1306,7 @@ Arr_segment_traits_2<Kernel>::_Segment_cached_2::operator=(const Segment_2& seg)
 //! \brief obtains the supporting line.
 template <typename Kernel>
 const typename Kernel::Line_2&
-Arr_segment_traits_2<Kernel>::_Segment_cached_2::line() const
-{
+Arr_segment_traits_2<Kernel>::_Segment_cached_2::line() const {
   if (!m_is_computed) {
     Kernel kernel;
     m_l = kernel.construct_line_2_object()(m_ps, m_pt);
@@ -1351,8 +1318,7 @@ Arr_segment_traits_2<Kernel>::_Segment_cached_2::line() const
 
 //! \brief determines whether the curve is vertical.
 template <typename Kernel>
-bool Arr_segment_traits_2<Kernel>::_Segment_cached_2::is_vertical() const
-{
+bool Arr_segment_traits_2<Kernel>::_Segment_cached_2::is_vertical() const {
   // Force computation of line is orientation is still unknown
   if (! m_is_computed) line();
   CGAL_precondition(!m_is_degen);
@@ -1397,8 +1363,7 @@ Arr_segment_traits_2<Kernel>::_Segment_cached_2::right() const
 
 //! \brief sets the (lexicographically) left endpoint.
 template <typename Kernel>
-void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_left(const Point_2& p)
-{
+void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_left(const Point_2& p) {
   CGAL_precondition(! m_is_degen);
   CGAL_precondition_code(Kernel kernel);
   CGAL_precondition
@@ -1411,8 +1376,7 @@ void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_left(const Point_2& p)
 
 //! \brief sets the (lexicographically) right endpoint.
 template <typename Kernel>
-void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_right(const Point_2& p)
-{
+void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_right(const Point_2& p) {
   CGAL_precondition(! m_is_degen);
   CGAL_precondition_code(Kernel kernel);
   CGAL_precondition
@@ -1428,8 +1392,7 @@ void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_right(const Point_2& p
  */
 template <typename Kernel>
 bool Arr_segment_traits_2<Kernel>::_Segment_cached_2::
-is_in_x_range(const Point_2& p) const
-{
+is_in_x_range(const Point_2& p) const {
   Kernel kernel;
   typename Kernel::Compare_x_2 compare_x = kernel.compare_x_2_object();
   const Comparison_result res1 = compare_x(p, left());
@@ -1446,8 +1409,7 @@ is_in_x_range(const Point_2& p) const
  */
 template <typename Kernel>
 bool Arr_segment_traits_2<Kernel>::_Segment_cached_2::
-is_in_y_range(const Point_2& p) const
-{
+is_in_y_range(const Point_2& p) const {
   Kernel kernel;
   typename Kernel::Compare_y_2 compare_y = kernel.compare_y_2_object();
   const Comparison_result res1 = compare_y(p, left());
@@ -1464,31 +1426,31 @@ is_in_y_range(const Point_2& p) const
  */
 template <typename Kernel_>
 class Arr_segment_2 : public Arr_segment_traits_2<Kernel_>::_Segment_cached_2 {
-  typedef Kernel_                                                  Kernel;
+  using Kernel = Kernel_;
 
-  typedef typename Arr_segment_traits_2<Kernel>::_Segment_cached_2 Base;
-  typedef typename Kernel::Segment_2                               Segment_2;
-  typedef typename Kernel::Point_2                                 Point_2;
-  typedef typename Kernel::Line_2                                  Line_2;
+  using Base = typename Arr_segment_traits_2<Kernel>::_Segment_cached_2;
+  using Segment_2 = typename Kernel::Segment_2;
+  using Point_2 = typename Kernel::Point_2;
+  using Line_2 = typename Kernel::Line_2;
 
 public:
-  /*! Construct default. */
+  /*! constructs default. */
   Arr_segment_2();
 
-  /*! Construct a segment from a "kernel" segment.
+  /*! constructs a segment from a "kernel" segment.
    * \param seg the segment.
    * \pre the segment is not degenerate.
    */
   Arr_segment_2(const Segment_2& seg);
 
-  /*! Construct a segment from two endpoints.
+  /*! constructs a segment from two endpoints.
    * \param source the source point.
    * \param target the target point.
    * \pre `source` and `target` are not equal.
    */
   Arr_segment_2(const Point_2& source, const Point_2& target);
 
-  /*! Construct a segment from a line and two endpoints.
+  /*! constructs a segment from a line and two endpoints.
    * \param line the supporting line.
    * \param source the source point.
    * \param target the target point.
@@ -1498,7 +1460,7 @@ public:
   Arr_segment_2(const Line_2& line,
                 const Point_2& source, const Point_2& target);
 
-  /*! Construct a segment from all fields.
+  /*! constructs a segment from all fields.
    * \param line the supporting line.
    * \param source the source point.
    * \param target the target point.
@@ -1510,11 +1472,11 @@ public:
                 const Point_2& source, const Point_2& target,
                 bool is_directed_right, bool is_vert, bool is_degen);
 
-  /*! Cast to a segment.
+  /*! casts to a segment.
    */
   operator Segment_2() const;
 
-  /*! Flip the segment (swap its source and target).
+  /*! flips the segment (swap its source and target).
    */
   Arr_segment_2 flip() const;
 
@@ -1558,8 +1520,7 @@ Arr_segment_2<Kernel>::Arr_segment_2(const Line_2& line,
 
 //! \brief casts to a segment.
 template <typename Kernel>
-Arr_segment_2<Kernel>::operator typename Kernel::Segment_2() const
-{
+Arr_segment_2<Kernel>::operator typename Kernel::Segment_2() const {
   Kernel kernel;
   auto seg_ctr = kernel.construct_segment_2_object();
   return seg_ctr(this->source(), this->target());
@@ -1567,8 +1528,7 @@ Arr_segment_2<Kernel>::operator typename Kernel::Segment_2() const
 
 //! \brief flips the segment (swap its source and target).
 template <typename Kernel>
-Arr_segment_2<Kernel> Arr_segment_2<Kernel>::flip() const
-{
+Arr_segment_2<Kernel> Arr_segment_2<Kernel>::flip() const {
   return Arr_segment_2(this->line(), this->target(), this->source(),
                        ! (this->is_directed_right()), this->is_vertical(),
                        this->is_degenerate());
@@ -1586,8 +1546,7 @@ Bbox_2 Arr_segment_2<Kernel>::bbox() const
 /*! Exporter for the segment class used by the traits-class.
  */
 template <typename Kernel, typename OutputStream>
-OutputStream& operator<<(OutputStream& os, const Arr_segment_2<Kernel>& seg)
-{
+OutputStream& operator<<(OutputStream& os, const Arr_segment_2<Kernel>& seg) {
   os << static_cast<typename Kernel::Segment_2>(seg);
   return (os);
 }
@@ -1595,8 +1554,7 @@ OutputStream& operator<<(OutputStream& os, const Arr_segment_2<Kernel>& seg)
 /*! Importer for the segment class used by the traits-class.
  */
 template <typename Kernel, typename InputStream>
-InputStream& operator>>(InputStream& is, Arr_segment_2<Kernel>& seg)
-{
+InputStream& operator>>(InputStream& is, Arr_segment_2<Kernel>& seg) {
   typename Kernel::Segment_2   kernel_seg;
   is >> kernel_seg;
   seg = kernel_seg;

Arrangement_on_surface_2/include/CGAL/Surface_sweep_2/Arr_do_intersect_overlay_ss_visitor.h

@@ -0,0 +1,110 @@
+// Copyright (c) 2006,2007,2009,2010,2011,2025 Tel-Aviv University (Israel).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
+//
+//
+// Author(s) : Efi Fogel <efif@post.tau.ac.il>
+
+#ifndef CGAL_DO_INTERSECT_ARR_OVERLAY_SS_VISITOR_H
+#define CGAL_DO_INTERSECT_ARR_OVERLAY_SS_VISITOR_H
+
+#include <CGAL/license/Arrangement_on_surface_2.h>
+
+/*! \file
+ *
+ * Definition of the Arr_do_intersect_overlay_ss_visitor class-template.
+ */
+
+#include <CGAL/Default.h>
+#include <CGAL/Surface_sweep_2/Arr_overlay_ss_visitor.h>
+
+namespace CGAL {
+
+/*! \class Arr_do_intersect_overlay_ss_visitor
+ *
+ * A sweep-line visitor for overlaying a "red" arrangement and a "blue"
+ * arrangement as long as the edges do not intersect in their interiors. If
+ * there are no intersections, the overlay arrangement is constructed. All three
+ * arrangements are embedded on the same type of surface and use the same
+ * geometry traits. Otherwise, the process is terminated without any delay (that
+ * is, once an intersection is detected).
+ */
+template <typename OverlayHelper, typename OverlayTraits, typename Visitor_ = Default>
+class Arr_do_intersect_overlay_ss_visitor :
+    public Arr_overlay_ss_visitor<
+      OverlayHelper, OverlayTraits,
+      typename Default::Get<Visitor_,
+                            Arr_do_intersect_overlay_ss_visitor<OverlayHelper, OverlayTraits, Visitor_> >::type> {
+private:
+  using Overlay_helper = OverlayHelper;
+  using Overlay_traits = OverlayTraits;
+
+  using Self = Arr_do_intersect_overlay_ss_visitor<Overlay_helper, Overlay_traits, Visitor_>;
+  using Visitor = typename Default::Get<Visitor_, Self>::type;
+  using Base = Arr_overlay_ss_visitor<Overlay_helper, Overlay_traits, Visitor>;
+
+protected:
+  bool m_found_x;
+
+public:
+  using Arrangement_red_2 = typename Base::Arrangement_red_2;
+  using Arrangement_blue_2 = typename Base::Arrangement_blue_2;
+  using Arrangement_2 = typename Base::Arrangement_2;
+  using Event = typename Base::Event;
+  using Subcurve = typename Base::Subcurve;
+  using Status_line_iterator = typename Base::Status_line_iterator;
+  using X_monotone_curve_2 = typename Base::X_monotone_curve_2;
+  using Point_2 = typename Base::Point_2;
+  using Multiplicity = typename Base::Multiplicity;
+
+  /*! Constructor */
+  Arr_do_intersect_overlay_ss_visitor(const Arrangement_red_2* red_arr,
+                                      const Arrangement_blue_2* blue_arr,
+                                      Arrangement_2* res_arr,
+                                      Overlay_traits* overlay_traits) :
+    Base(red_arr, blue_arr, res_arr, overlay_traits),
+    m_found_x(false)
+  {}
+
+  /*! Destructor */
+  virtual ~Arr_do_intersect_overlay_ss_visitor() {}
+
+  /*! Update an event that corresponds to a curve endpoint. */
+  void update_event(Event* e, const Point_2& end_point, const X_monotone_curve_2& cv, Arr_curve_end cv_end, bool is_new)
+  { return Base::update_event(e, end_point, cv, cv_end, is_new); }
+
+  /*! Update an event that corresponds to a curve endpoint */
+  void update_event(Event* e, const X_monotone_curve_2& cv, Arr_curve_end cv_end, bool is_new )
+  { return Base::update_event(e, cv, cv_end, is_new); }
+
+  /*! Update an event that corresponds to a curve endpoint */
+  void update_event(Event* e, const Point_2& p, bool is_new)
+  { return Base::update_event(e, p, is_new); }
+
+  /*! Update an event that corresponds to an intersection */
+  void update_event(Event* e, Subcurve* sc) { return Base::update_event(e, sc); }
+
+  /*! Update an event that corresponds to an intersection between curves */
+  void update_event(Event* e, Subcurve* sc1, Subcurve* sc2, bool is_new, Multiplicity multiplicity) {
+    if ((multiplicity % 2) == 1) m_found_x = true;
+    Base::update_event(e, sc1, sc2, is_new, multiplicity);
+  }
+
+  bool after_handle_event(Event* e, Status_line_iterator iter, bool flag) {
+    auto res = Base::after_handle_event(e, iter, flag);
+    if (m_found_x) this->surface_sweep()->stop_sweep();
+    return res;
+  }
+
+  /*! Getter */
+  bool found_intersection() { return m_found_x; }
+};
+
+} // namespace CGAL
+
+#endif

Arrangement_on_surface_2/include/CGAL/Surface_sweep_2/Arr_no_intersection_insertion_ss_visitor.h

@@ -8,9 +8,9 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s): Baruch Zukerman <baruchzu@post.tau.ac.il>
-//            Ron Wein <wein@post.tau.ac.il>
-//            Efi Fogel <efif@post.tau.ac.il>
+// Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
+//             Ron Wein         <wein@post.tau.ac.il>
+//             Efi Fogel        <efif@post.tau.ac.il>
 
 #ifndef CGAL_ARR_NO_INTERSECTION_INSERTION_SS_VISITOR_H
 #define CGAL_ARR_NO_INTERSECTION_INSERTION_SS_VISITOR_H
@@ -42,35 +42,33 @@ class Arr_no_intersection_insertion_ss_visitor :
   public Arr_construction_ss_visitor<
     Helper_,
     typename Default::Get<Visitor_, Arr_no_intersection_insertion_ss_visitor<
-                                      Helper_, Visitor_> >::type>
-{
+                                      Helper_, Visitor_> >::type> {
 public:
-  typedef Helper_                                       Helper;
+  using Helper = Helper_;
 
-  typedef typename Helper::Geometry_traits_2            Geometry_traits_2;
-  typedef typename Helper::Event                        Event;
-  typedef typename Helper::Subcurve                     Subcurve;
+  using Geometry_traits_2 = typename Helper::Geometry_traits_2;
+  using Event = typename Helper::Event;
+  using Subcurve = typename Helper::Subcurve;
 
 private:
-  typedef Geometry_traits_2                             Gt2;
-  typedef Arr_no_intersection_insertion_ss_visitor<Helper, Visitor_>
-                                                        Self;
-  typedef typename Default::Get<Visitor_, Self>::type   Visitor;
-  typedef Arr_construction_ss_visitor<Helper, Visitor>  Base;
+  using Gt2 = Geometry_traits_2;
+  using Self = Arr_no_intersection_insertion_ss_visitor<Helper, Visitor_>;
+  using Visitor = typename Default::Get<Visitor_, Self>::type;
+  using Base = Arr_construction_ss_visitor<Helper, Visitor>;
 
 public:
-  typedef typename Gt2::X_monotone_curve_2              X_monotone_curve_2;
-  typedef typename Gt2::Point_2                         Point_2;
+  using X_monotone_curve_2 = typename Gt2::X_monotone_curve_2;
+  using Point_2 = typename Gt2::Point_2;
+  using Multiplicity = typename Gt2::Multiplicity;
 
 protected:
-  typedef typename Subcurve::Status_line_iterator       Status_line_iterator;
-  typedef typename Base::Event_subcurve_reverse_iterator
-    Event_subcurve_reverse_iterator;
+  using Status_line_iterator = typename Subcurve::Status_line_iterator;
+  using Event_subcurve_reverse_iterator = typename Base::Event_subcurve_reverse_iterator;
 
-  typedef typename Helper::Arrangement_2                Arrangement_2;
-  typedef typename Arrangement_2::Vertex_handle         Vertex_handle;
-  typedef typename Arrangement_2::Halfedge_handle       Halfedge_handle;
-  typedef typename Arrangement_2::Face_handle           Face_handle;
+  using Arrangement_2 = typename Helper::Arrangement_2;
+  using Vertex_handle = typename Arrangement_2::Vertex_handle;
+  using Halfedge_handle = typename Arrangement_2::Halfedge_handle;
+  using Face_handle = typename Arrangement_2::Face_handle;
 
 public:
   /*! Constructor. */
@@ -103,13 +101,12 @@ public:
   {}
 
   void update_event(Event* /* e */, Subcurve* /* sc1 */, Subcurve* /* sc2 */,
-                    bool /* is_new */)
+                    bool /* is_new */, Multiplicity /* multiplicity */)
   {}
 
   void update_event(Event* /* e */, Subcurve* /* sc1 */) {}
 
-  void update_event(Event* e, const Point_2& pt, bool /* is_new */)
-  {
+  void update_event(Event* e, const Point_2& pt, bool /* is_new */) {
     Vertex_handle invalid_v;
     if (e->point().vertex_handle() == invalid_v)
       e->point().set_vertex_handle(pt.vertex_handle());
@@ -241,8 +238,7 @@ void Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::before_sweep()
 //
 template <typename Hlpr, typename Vis>
 void Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
-before_handle_event(Event* event)
-{
+before_handle_event(Event* event) {
   // First we notify the helper class on the event.
   this->m_helper.before_handle_event(event);
 
@@ -330,8 +326,7 @@ before_handle_event(Event* event)
 //
 template <typename Hlpr, typename Vis>
 bool Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
-add_subcurve_(const X_monotone_curve_2& cv, Subcurve* sc)
-{
+add_subcurve_(const X_monotone_curve_2& cv, Subcurve* sc) {
   const Halfedge_handle invalid_he;
   if (cv.halfedge_handle() != invalid_he) return false;
   // Insert the curve into the arrangement
@@ -344,8 +339,7 @@ add_subcurve_(const X_monotone_curve_2& cv, Subcurve* sc)
 //
 template <typename Hlpr, typename Vis>
 void Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
-add_subcurve(const X_monotone_curve_2& cv, Subcurve* sc)
-{
+add_subcurve(const X_monotone_curve_2& cv, Subcurve* sc) {
   if (add_subcurve_(cv, sc)) return;
 
   Halfedge_handle next_ccw_he =
@@ -359,8 +353,7 @@ add_subcurve(const X_monotone_curve_2& cv, Subcurve* sc)
 template <typename Hlpr, typename Vis>
 typename Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::Halfedge_handle
 Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
-insert_in_face_interior(const X_monotone_curve_2& cv, Subcurve* sc)
-{
+insert_in_face_interior(const X_monotone_curve_2& cv, Subcurve* sc) {
   Event* last_event = this->last_event_on_subcurve(sc);
   Vertex_handle last_v = last_event->point().vertex_handle();
   Vertex_handle curr_v = this->current_event()->point().vertex_handle();
@@ -385,8 +378,7 @@ template <typename Hlpr, typename Vis>
 typename Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::Halfedge_handle
 Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
 insert_from_left_vertex(const X_monotone_curve_2& cv, Halfedge_handle he,
-                        Subcurve* sc)
-{
+                        Subcurve* sc) {
   Vertex_handle curr_v = this->current_event()->point().vertex_handle();
   if (curr_v != Vertex_handle())
     return (this->m_arr->insert_at_vertices(cv.base(), he, curr_v));
@@ -400,8 +392,7 @@ template <typename Hlpr, typename Vis>
 typename Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::Halfedge_handle
 Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
 insert_from_right_vertex(const X_monotone_curve_2& cv, Halfedge_handle he,
-                         Subcurve* sc)
-{
+                         Subcurve* sc) {
   Event* last_event = this->last_event_on_subcurve(sc);
   Vertex_handle last_v = last_event->point().vertex_handle();
   if (last_v != Vertex_handle())
@@ -426,8 +417,7 @@ insert_at_vertices(const X_monotone_curve_2& cv,
 template <typename Hlpr, typename Vis>
 typename Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::Vertex_handle
 Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
-insert_isolated_vertex(const Point_2& pt, Status_line_iterator iter)
-{
+insert_isolated_vertex(const Point_2& pt, Status_line_iterator iter) {
   // If the isolated vertex is already at the arrangement, return:
   if (pt.vertex_handle() != Vertex_handle()) return Vertex_handle();
 
@@ -443,8 +433,7 @@ insert_isolated_vertex(const Point_2& pt, Status_line_iterator iter)
 template <typename Hlpr, typename Vis>
 typename Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::Halfedge_handle
 Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
-_insert_in_face_interior(const X_monotone_curve_2& cv, Subcurve* sc)
-{
+_insert_in_face_interior(const X_monotone_curve_2& cv, Subcurve* sc) {
   // Check if the vertex to be associated with the left end of the curve has
   // already been created.
   Event* last_event = this->last_event_on_subcurve(sc);
@@ -514,8 +503,7 @@ template <typename Hlpr, typename Vis>
 typename Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::Halfedge_handle
 Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
 _insert_from_left_vertex(const X_monotone_curve_2& cv,
-                         Halfedge_handle prev, Subcurve* sc)
-{
+                         Halfedge_handle prev, Subcurve* sc) {
   // Check if the vertex to be associated with the right end of the curve has
   // already been created.
   Event* curr_event = this->current_event();
@@ -551,8 +539,7 @@ template <typename Hlpr, typename Vis>
 typename Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::Halfedge_handle
 Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
 _insert_from_right_vertex(const X_monotone_curve_2& cv, Halfedge_handle prev,
-                          Subcurve* sc)
-{
+                          Subcurve* sc) {
   // Check if the vertex to be associated with the left end of the curve has
   // already been created.
   Event* last_event = this->last_event_on_subcurve(sc);
@@ -589,8 +576,7 @@ typename Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::Halfedge_handle
 Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
 _insert_at_vertices(const X_monotone_curve_2& cv,
                     Halfedge_handle prev1, Halfedge_handle prev2,
-                    Subcurve* sc, bool& new_face_created)
-{
+                    Subcurve* sc, bool& new_face_created) {
   // Perform the insertion.
   new_face_created = false;
   bool swapped_predecessors = false;
@@ -632,8 +618,7 @@ _insert_at_vertices(const X_monotone_curve_2& cv,
 template <typename Hlpr, typename Vis>
 typename Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::Face_handle
 Arr_no_intersection_insertion_ss_visitor<Hlpr, Vis>::
-_ray_shoot_up(Status_line_iterator iter)
-{
+_ray_shoot_up(Status_line_iterator iter) {
   // Go up the status line and try to locate a curve which is associated
   // with a valid arrangement halfedge.
   const Halfedge_handle invalid_he;

Arrangement_on_surface_2/include/CGAL/Surface_sweep_2/Arr_overlay_ss_visitor.h

@@ -8,9 +8,9 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Ron Wein <wein@post.tau.ac.il>
-//                 Efi Fogel <efif@post.tau.ac.il>
+// Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
+//             Ron Wein         <wein@post.tau.ac.il>
+//             Efi Fogel        <efif@post.tau.ac.il>
 
 #ifndef CGAL_ARR_OVERLAY_SS_VISITOR_H
 #define CGAL_ARR_OVERLAY_SS_VISITOR_H
@@ -40,92 +40,80 @@ namespace CGAL {
  * arrangement, creating a result arrangement. All three arrangements are
  * embedded on the same type of surface and use the same geometry traits.
  */
-template <typename OverlayHelper, typename OverlayTraits,
-          typename Visitor_ = Default>
+template <typename OverlayHelper, typename OverlayTraits, typename Visitor_ = Default>
 class Arr_overlay_ss_visitor :
   public Arr_construction_ss_visitor<
     typename OverlayHelper::Construction_helper,
     typename Default::Get<Visitor_,
-                          Arr_overlay_ss_visitor<OverlayHelper, OverlayTraits,
-                                                 Visitor_> >::type>
-{
+                          Arr_overlay_ss_visitor<OverlayHelper, OverlayTraits, Visitor_> >::type> {
 public:
-  typedef OverlayHelper                                 Overlay_helper;
-  typedef OverlayTraits                                 Overlay_traits;
+  using Overlay_helper = OverlayHelper;
+  using Overlay_traits = OverlayTraits;
 
-  typedef typename Overlay_helper::Geometry_traits_2    Geometry_traits_2;
-  typedef typename Overlay_helper::Event                Event;
-  typedef typename Overlay_helper::Subcurve             Subcurve;
+  using Geometry_traits_2 = typename Overlay_helper::Geometry_traits_2;
+  using Event = typename Overlay_helper::Event;
+  using Subcurve = typename Overlay_helper::Subcurve;
 
-  typedef typename Overlay_helper::Arrangement_red_2    Arrangement_red_2;
-  typedef typename Overlay_helper::Arrangement_blue_2   Arrangement_blue_2;
-
-  typedef typename Overlay_helper::Construction_helper  Construction_helper;
+  using Arrangement_red_2 = typename Overlay_helper::Arrangement_red_2;
+  using Arrangement_blue_2 = typename Overlay_helper::Arrangement_blue_2;
 
+  using Construction_helper = typename Overlay_helper::Construction_helper;
 
 private:
-  typedef Geometry_traits_2                             Gt2;
-  typedef Arrangement_red_2                             Ar2;
-  typedef Arrangement_blue_2                            Ab2;
+  using Gt2 = Geometry_traits_2;
+  using Ar2 = Arrangement_red_2;
+  using Ab2 = Arrangement_blue_2;
 
-  typedef Arr_overlay_ss_visitor<Overlay_helper, Overlay_traits, Visitor_>
-                                                        Self;
-  typedef typename Default::Get<Visitor_, Self>::type   Visitor;
-  typedef Arr_construction_ss_visitor<Construction_helper, Visitor>
-                                                        Base;
+  using Self = Arr_overlay_ss_visitor<Overlay_helper, Overlay_traits, Visitor_>;
+  using Visitor = typename Default::Get<Visitor_, Self>::type;
+  using Base = Arr_construction_ss_visitor<Construction_helper, Visitor>;
 
 public:
-  typedef typename Gt2::X_monotone_curve_2              X_monotone_curve_2;
-  typedef typename Gt2::Point_2                         Point_2;
+  using X_monotone_curve_2 = typename Gt2::X_monotone_curve_2;
+  using Point_2 = typename Gt2::Point_2;
+  using Multiplicity = typename Gt2::Multiplicity;
 
   // The input arrangements (the "red" and the "blue" one):
-  typedef typename Ar2::Halfedge_const_handle           Halfedge_handle_red;
-  typedef typename Ar2::Face_const_handle               Face_handle_red;
-  typedef typename Ar2::Vertex_const_handle             Vertex_handle_red;
+  using Halfedge_handle_red = typename Ar2::Halfedge_const_handle;
+  using Face_handle_red = typename Ar2::Face_const_handle;
+  using Vertex_handle_red = typename Ar2::Vertex_const_handle;
 
-  typedef typename Ab2::Halfedge_const_handle           Halfedge_handle_blue;
-  typedef typename Ab2::Face_const_handle               Face_handle_blue;
-  typedef typename Ab2::Vertex_const_handle             Vertex_handle_blue;
+  using Halfedge_handle_blue = typename Ab2::Halfedge_const_handle;
+  using Face_handle_blue = typename Ab2::Face_const_handle;
+  using Vertex_handle_blue = typename Ab2::Vertex_const_handle;
 
   // The resulting arrangement:
-  typedef typename Overlay_helper::Arrangement_2        Arrangement_2;
-  typedef typename Arrangement_2::Halfedge_handle       Halfedge_handle;
-  typedef typename Arrangement_2::Face_handle           Face_handle;
-  typedef typename Arrangement_2::Vertex_handle         Vertex_handle;
-  typedef typename Arrangement_2::Ccb_halfedge_circulator
-    Ccb_halfedge_circulator;
-  typedef typename Arrangement_2::Outer_ccb_iterator    Outer_ccb_iterator;
+  using Arrangement_2 = typename Overlay_helper::Arrangement_2;
+  using Halfedge_handle = typename Arrangement_2::Halfedge_handle;
+  using Face_handle = typename Arrangement_2::Face_handle;
+  using Vertex_handle = typename Arrangement_2::Vertex_handle;
+  using Ccb_halfedge_circulator = typename Arrangement_2::Ccb_halfedge_circulator;
+  using Outer_ccb_iterator = typename Arrangement_2::Outer_ccb_iterator;
 
-  typedef typename Base::Event_subcurve_iterator
-    Event_subcurve_iterator;
-  typedef typename Base::Event_subcurve_reverse_iterator
-    Event_subcurve_reverse_iterator;
-  typedef typename Base::Status_line_iterator           Status_line_iterator;
+  using Event_subcurve_iterator = typename Base::Event_subcurve_iterator;
+  using Event_subcurve_reverse_iterator = typename Base::Event_subcurve_reverse_iterator;
+  using Status_line_iterator = typename Base::Status_line_iterator;
 
 protected:
-  typedef typename Gt2::Cell_handle_red                 Cell_handle_red;
-  typedef typename Gt2::Optional_cell_red               Optional_cell_red;
-  typedef typename Gt2::Cell_handle_blue                Cell_handle_blue;
-  typedef typename Gt2::Optional_cell_blue              Optional_cell_blue;
+  using Cell_handle_red = typename Gt2::Cell_handle_red;
+  using Optional_cell_red = typename Gt2::Optional_cell_red;
+  using Cell_handle_blue = typename Gt2::Cell_handle_blue;
+  using Optional_cell_blue = typename Gt2::Optional_cell_blue;
 
-  typedef std::pair<Halfedge_handle_red, Halfedge_handle_blue>
-                                                        Halfedge_info;
-  typedef Unique_hash_map<Halfedge_handle, Halfedge_info>
-                                                        Halfedge_map;
+  using Halfedge_info = std::pair<Halfedge_handle_red, Halfedge_handle_blue>;
+  using Halfedge_map = Unique_hash_map<Halfedge_handle, Halfedge_info>;
 
-  typedef std::pair<Cell_handle_red, Cell_handle_blue>  Handle_info;
-  typedef std::unordered_map<Vertex_handle, Handle_info, Handle_hash_function>
-                                                        Vertex_map;
+  using Handle_info = std::pair<Cell_handle_red, Cell_handle_blue>;
+  using Vertex_map = std::unordered_map<Vertex_handle, Handle_info, Handle_hash_function>;
 
   // Side categoties:
-  typedef typename Gt2::Left_side_category              Left_side_category;
-  typedef typename Gt2::Bottom_side_category            Bottom_side_category;
-  typedef typename Gt2::Top_side_category               Top_side_category;
-  typedef typename Gt2::Right_side_category             Right_side_category;
+  using Left_side_category = typename Gt2::Left_side_category;
+  using Bottom_side_category = typename Gt2::Bottom_side_category;
+  using Top_side_category = typename Gt2::Top_side_category;
+  using Right_side_category = typename Gt2::Right_side_category;
 
-  typedef typename Arr_has_identified_sides<Left_side_category,
-                                            Bottom_side_category>::result
-    Has_identified_sides_category;
+  using Has_identified_sides_category =
+    typename Arr_has_identified_sides<Left_side_category, Bottom_side_category>::result;
 
   // Data members:
   Overlay_traits* m_overlay_traits;     // The overlay traits object.
@@ -195,10 +183,9 @@ public:
   void update_event(Event* /* e */,
                     Subcurve* /* c1 */,
                     Subcurve* /* c2 */,
-                    bool CGAL_assertion_code(is_new))
-  {
-    CGAL_assertion(is_new == true);
-  }
+                    bool CGAL_assertion_code(is_new),
+                    Multiplicity /* multiplicity */)
+  { CGAL_assertion(is_new == true); }
 
   /*! Update an event. */
   void update_event(Event* e, Subcurve* sc);
@@ -407,9 +394,8 @@ protected:
 //-----------------------------------------------------------------------------
 // A notification issued before the sweep process starts.
 //
-  template <typename OvlHlpr, typename OvlTr, typename Vis>
-  void Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::before_sweep()
-{
+template <typename OvlHlpr, typename OvlTr, typename Vis>
+void Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::before_sweep() {
   // Initialize the necessary fields in the base construction visitor.
   // Note that the construction visitor also informs its helper class that
   // the sweep process is about to start.
@@ -425,8 +411,7 @@ protected:
 //
 template <typename OvlHlpr, typename OvlTr, typename Vis>
 void
-Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::before_handle_event(Event* event)
-{
+Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::before_handle_event(Event* event) {
   // Let the base construction visitor do the work (and also inform its helper
   // class on the event).
   Base::before_handle_event(event);
@@ -441,8 +426,7 @@ Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::before_handle_event(Event* event)
 //
 template <typename OvlHlpr, typename OvlTr, typename Vis>
 bool Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::
-after_handle_event(Event* event, Status_line_iterator iter, bool flag)
-{
+after_handle_event(Event* event, Status_line_iterator iter, bool flag) {
   // Let the base construction visitor handle the event.
   bool res = Base::after_handle_event(event, iter, flag);
 
@@ -497,8 +481,7 @@ update_event(Event* e,
              const Point_2& end_point,
              const X_monotone_curve_2& /* cv */,
              Arr_curve_end /* cv_end */,
-             bool /* is_new */)
-{
+             bool /* is_new */) {
   // Nothing to do in case of an event at infinity.
   CGAL_assertion(e->is_closed());
 
@@ -513,8 +496,7 @@ update_event(Event* e,
 //
 template <typename OvlHlpr, typename OvlTr, typename Vis>
 void Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::update_event(Event* e,
-                                                               Subcurve* sc)
-{
+                                                               Subcurve* sc) {
   // Update the red and blue halfedges associated with the point as necessary.
   Point_2& pt = e->point();
 
@@ -538,8 +520,7 @@ template <typename OvlHlpr, typename OvlTr, typename Vis>
 void
 Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::update_event(Event* e,
                                                           const Point_2& p,
-                                                          bool /* is_new */)
-{
+                                                          bool /* is_new */) {
   // Update the red and blue objects associated with the point as necessary.
   Point_2& pt = e->point();
   if (pt.is_red_cell_empty()) pt.set_red_cell(p.red_cell());
@@ -550,8 +531,7 @@ Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::update_event(Event* e,
 // A notification issued when the sweep process has ended.
 //
 template <typename OvlHlpr, typename OvlTr, typename Vis>
-void Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::after_sweep()
-{
+void Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::after_sweep() {
   Base::after_sweep();
 
   // Notify boundary vertices:
@@ -580,8 +560,7 @@ void Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::after_sweep()
 template <typename OvlHlpr, typename OvlTr, typename Vis>
 typename Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::Halfedge_handle
 Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::
-insert_in_face_interior(const X_monotone_curve_2& cv, Subcurve* sc)
-{
+insert_in_face_interior(const X_monotone_curve_2& cv, Subcurve* sc) {
   // Insert the halfedge using the base construction visitor.
   Halfedge_handle new_he = Base::insert_in_face_interior(cv, sc);
   _map_halfedge_and_twin(new_he,
@@ -615,8 +594,7 @@ typename Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::Halfedge_handle
 Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::
 insert_from_left_vertex(const X_monotone_curve_2& cv,
                         Halfedge_handle prev,
-                        Subcurve* sc)
-{
+                        Subcurve* sc) {
   _map_boundary_vertices(this->last_event_on_subcurve(sc), prev->target(),
                          Has_identified_sides_category());
 
@@ -647,8 +625,7 @@ typename Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::Halfedge_handle
 Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::
 insert_from_right_vertex(const X_monotone_curve_2& cv,
                          Halfedge_handle prev,
-                         Subcurve* sc)
-{
+                         Subcurve* sc) {
   _map_boundary_vertices(this->current_event(), prev->target(),
                          Has_identified_sides_category());
 
@@ -680,8 +657,7 @@ insert_at_vertices(const X_monotone_curve_2& cv,
                    Halfedge_handle prev1,
                    Halfedge_handle prev2,
                    Subcurve* sc,
-                   bool& new_face_created)
-{
+                   bool& new_face_created) {
   // Insert the halfedge using the base construction visitor. Note that the
   // resulting halfedge is always incident to the new face (if one created).
   Halfedge_handle new_he =
@@ -795,8 +771,7 @@ template <typename OvlHlpr, typename OvlTr, typename Vis>
 typename Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::Vertex_handle
 Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::
 insert_isolated_vertex(const Point_2& pt,
-                       Status_line_iterator iter)
-{
+                       Status_line_iterator iter) {
   // Insert the isolated vertex using the base construction visitor.
   Vertex_handle new_v = Base::insert_isolated_vertex(pt, iter);
 
@@ -897,14 +872,13 @@ template <typename OvlHlpr, typename OvlTr, typename Vis>
 void Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::
 _map_halfedge_and_twin(Halfedge_handle he,
                        Halfedge_handle_red red_he,
-                       Halfedge_handle_blue blue_he)
-{
+                       Halfedge_handle_blue blue_he) {
   if (he->direction() == ARR_LEFT_TO_RIGHT) he = he->twin();
 
   // Obtain the twin red and blue halfedges (if they are valid). Note that
   // the original halfedges are always directed from right to left.
-  Halfedge_handle_red     red_he_twin;
-  Halfedge_handle_blue    blue_he_twin;
+  Halfedge_handle_red red_he_twin;
+  Halfedge_handle_blue blue_he_twin;
 
   if (red_he != Halfedge_handle_red()) red_he_twin = red_he->twin();
   if (blue_he != Halfedge_handle_blue()) blue_he_twin = blue_he->twin();
@@ -922,8 +896,7 @@ _map_halfedge_and_twin(Halfedge_handle he,
 //
 template <typename OvlHlpr, typename OvlTr, typename Vis>
 void Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::
-_map_boundary_vertices(Event* event, Vertex_handle v, std::bool_constant<true>)
-{
+_map_boundary_vertices(Event* event, Vertex_handle v, std::bool_constant<true>) {
   // Update the red and blue object if the last event on sc is on the boundary.
   if ((event->parameter_space_in_x() != ARR_INTERIOR) ||
       (event->parameter_space_in_y() != ARR_INTERIOR))
@@ -938,8 +911,7 @@ _map_boundary_vertices(Event* event, Vertex_handle v, std::bool_constant<true>)
     if (red_handle_p) info.first = *red_handle_p;
 
     if (!std::get_if<Face_handle_red>(&(info.first)) &&
-        !std::get_if<Face_handle_blue>(&(info.second)))
-    {
+        !std::get_if<Face_handle_blue>(&(info.second))) {
       // If both, the red and blue, variants do not represent face handles,
       // they must represt either vertex or edge handles. In this case it is
       // safe to apply the call to the overlay traits and erase the record,
@@ -974,8 +946,7 @@ void Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::
 _create_vertex(Event* event,
                Vertex_handle new_v,
                Subcurve* sc,
-               std::bool_constant<true>)
-{
+               std::bool_constant<true>) {
   const Point_2& pt = event->point();
   const Cell_handle_red* red_handle = pt.red_cell_handle();
   const Cell_handle_blue* blue_handle = pt.blue_cell_handle();
@@ -983,8 +954,7 @@ _create_vertex(Event* event,
   // If the vertex is on the boundary, postpone the notification, but
   // update the red and objects in case they are empty.
   if ((event->parameter_space_in_x() != ARR_INTERIOR) ||
-      (event->parameter_space_in_y() != ARR_INTERIOR))
-  {
+      (event->parameter_space_in_y() != ARR_INTERIOR)) {
     if (!red_handle) {
       CGAL_assertion(blue_handle != nullptr);
       // Obtain the red face by looking for a subcurve above.
@@ -1020,8 +990,7 @@ void Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::
 _create_vertex(Event* event,
                Vertex_handle new_v,
                Subcurve* sc,
-               std::bool_constant<false>)
-{
+               std::bool_constant<false>) {
   const Point_2& pt = event->point();
   const Cell_handle_red* red_handle = pt.red_cell_handle();
   const Cell_handle_blue* blue_handle = pt.blue_cell_handle();
@@ -1063,8 +1032,7 @@ _create_vertex(Event* event,
 template <typename OvlHlpr, typename OvlTr, typename Vis>
 void Arr_overlay_ss_visitor<OvlHlpr, OvlTr, Vis>::
 _create_edge(Subcurve* sc,
-             Halfedge_handle new_he)
-{
+             Halfedge_handle new_he) {
   // Note that the "red" and "blue" halfedges are always directed from right
   // to left, so we make sure the overlaid halfedge is also directed from
   // right to left.

Arrangement_on_surface_2/include/CGAL/draw_arrangement_2.h

@@ -588,7 +588,7 @@ private:
 
 #ifdef CGAL_USE_BASIC_VIEWER
 //!
-void draw_unimplemented() {
+inline void draw_unimplemented() {
   CGAL_error_msg("Geometry traits type of arrangement is required to support approximation of Point_2 and "
                  "X_monotone_curve_2. Traits on curved surfaces needs additional support for parameterization.");
 }

Boolean_set_operations_2/doc/Boolean_set_operations_2/Boolean_set_operations_2.txt

@@ -700,15 +700,29 @@ swap its source and target points).
 The traits classes `Arr_segment_traits_2`,
 `Arr_non_caching_segment_traits_2`, `Arr_circle_segment_traits_2`,
 `Arr_conic_traits_2` and `Arr_rational_function_traits_2`, which are
-bundled in the `Arrangement_2` package and distributed with \cgal,
-are all models of the refined concept
-`AosDirectionalXMonotoneTraits_2`.\cgalFootnote{The \cgalFootnoteCode{Arr_polyline_traits_2} class is <I>not</I> a model of the, \cgalFootnoteCode{AosDirectionalXMonotoneTraits_2} concept, as the \f$ x\f$-monotone curve it defines is always directed from left to right. Thus, an opposite curve cannot be constructed. However, it is not very useful to construct a polygon whose edges are polylines, as an ordinary polygon with linear edges can represent the same entity.}
+bundled in the `Arrangement_2` package and distributed with \cgal, are
+all models of the refined concept
+`AosDirectionalXMonotoneTraits_2`.\cgalFootnote{The
+\cgalFootnoteCode{Arr_polyline_traits_2} class is <I>not</I> a model
+of the, \cgalFootnoteCode{AosDirectionalXMonotoneTraits_2} concept, as
+the \f$ x\f$-monotone curve it defines is always directed from left to
+right. Thus, an opposite curve cannot be constructed. However, it is
+not very useful to construct a polygon whose edges are polylines, as
+an ordinary polygon with linear edges can represent the same entity.}
 
-Just as with the case of computations using models of the
-`AosXMonotoneTraits_2` concept, operations are robust only
-when exact arithmetic is used. When inexact arithmetic is used,
-(nearly) degenerate configurations may result in abnormal termination
-of the program or even incorrect results.
+Operations on polygons (or general polygons) are guaranteed to be
+robust only if the operations of the geometry traits used to carry out
+the high-level operations are robust. Most operations on polygons use
+geometry traits constructors, as they generate new polygons; such
+constructors are guaranteed to be robust only if the kernel in use
+supports exact constructions, such as the EPEC (Exact Predicate Exact
+Construction) kernel. The `do_intersect()` overloaded predicates that
+operate on (linear) polygons are exceptions, as they only use geometry
+traits predicates; such predicates are guaranteed to be robust only if
+the kernel in use supports exact predicates, such as the EPIC (Exact
+Predicate Inexact Construction) kernel. When inexact arithmetic is
+used, (nearly) degenerate configurations may result in abnormal
+termination of the program or even incorrect results.
 
 \subsection bso_sseccirc_seg Operating on Polygons with Circular Arcs
 

Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/Boolean_set_operations_2.h

@@ -19,6 +19,10 @@ namespace CGAL {
  * <tr><td align="right"><b>2.</b></td><td>`void complement(const Type1& pgn, Type2& res, const GpsTraits& traits);`</td></tr>
  * </table>
  *
+ * \tparam Kernel    a model of the concept `PolygonTraits_2`.
+ * \tparam Container a model of the concept `Container`; defaults to `std::vector<Kernel::Point_2`>.
+ * \tparam ArrTraits a model of the concept `AosDirectionalXMonotoneTraits_2`.
+ * \tparam GpsTraits a model of the concept `GeneralPolygonSetTraits_2`, which must be convertible to `ArrTraits`.
  * \tparam UsePolylines determines whether the boundary of the input polygon is
  * treated as a cyclic sequence of single (\f$x\f$-monotone) segments or as a
  * cyclic sequence of (\f$x\f$-monotone) polylines. If substituted with
@@ -28,7 +32,7 @@ namespace CGAL {
  * to a standard polygon. If substituted with `CGAL::Tag_false`, the input
  * polygon is used as is. Refer to \ref bso_ssectraits_sel for more information.
  *
- *   - The types `Type` and `Type2` of the parameters must be convertible to the
+ *   - The types `Type1` and `Type2` of the parameters must be convertible to the
  * types specified in a row in the table below, respectively.
  *   - The types that apply to signature (<b>1.1.</b>) above are restricted to those
  * listed in rows <b>1</b> and <b>2</b> in the table below.
@@ -54,6 +58,8 @@ namespace CGAL {
  * \sa \link boolean_join `CGAL::join()` \endlink
  * \sa \link boolean_difference `CGAL::difference()` \endlink
  * \sa \link boolean_symmetric_difference `CGAL::symmetric_difference()` \endlink
+ * \sa Polygon_2<Kernel, Container>
+ * \sa Polygon_with_holes_2<Kernel, Container>
  */
 
 /// @{
@@ -224,6 +230,10 @@ namespace CGAL {
  * <tr><td align="right"><b>2.</b></td><td>`OutputIterator difference(const Type1& pgn1, const Type2& pgn2, OutputIterator oi, const GpsTraits& traits);`</td></tr>
  * </table>
  *
+ * \tparam Kernel    a model of the concept `PolygonTraits_2`
+ * \tparam Container a model of the concept `Container`; defaults to `std::vector<Kernel::Point_2`>.
+ * \tparam ArrTraits a model of the concept `AosDirectionalXMonotoneTraits_2`
+ * \tparam GpsTraits a model of the concept `GeneralPolygonSetTraits_2`, which must be convertible to `ArrTraits`.
  * \tparam UsePolylines determines whether the boundaries of the input polygons
  * are treated as cyclic sequences of single (\f$x\f$-monotone) segments or as
  * cyclic sequences of (\f$x\f$-monotone) polylines. If substituted with
@@ -264,6 +274,8 @@ namespace CGAL {
  * \sa \link boolean_intersection `CGAL::intersection()` \endlink
  * \sa \link boolean_join `CGAL::join()` \endlink
  * \sa \link boolean_symmetric_difference `CGAL::symmetric_difference()` \endlink
+ * \sa Polygon_2<Kernel, Container>
+ * \sa Polygon_with_holes_2<Kernel, Container>
  */
 
 /// @{
@@ -660,48 +672,22 @@ namespace CGAL {
  * A function template in this group that accepts two input polygons has one of
  * the following signatures:
  * <table cellpadding=3 border="0">
- * <tr><td align="right"><b>1.1.</b></td><td>`bool do_intersect(const Type1& pgn1, const Type2& pgn2, UsePolylines = Tag_true());`</td></tr>
- * <tr><td align="right"><b>1.2.</b></td><td>`bool do_intersect(const Type1& pgn1, const Type2& pgn2);`</td></tr>
- * <tr><td align="right"><b>  2.</b></td><td>`bool do_intersect(const Type1& pgn1, const Type2& pgn2, const GpsTraits& traits);`</td></tr>
+ * <tr><td align="right"><b>1.</b></td><td>`bool do_intersect(const Type1& pgn1, const Type2& pgn2);`</td></tr>
+ * <tr><td align="right"><b>2.</b></td><td>`bool do_intersect(const Type1& pgn1, const Type2& pgn2, const GpsTraits& traits);`</td></tr>
  * </table>
  *
  * There are also function templates that accept one or two ranges of input polygons:
  * <table cellpadding=3 border="0">
- * <tr><td align="right"><b>3.1.</b></td><td>`bool do_intersect(InputIterator begin, InputIterator end, UsePolylines = Tag_true());`</td></tr>
- * <tr><td align="right"><b>3.2.</b></td><td>`bool do_intersect(InputIterator begin, InputIterator end);`</td></tr>
- * <tr><td align="right"><b>  4.</b></td><td>`bool do_intersect(InputIterator begin, InputIterator end, const GpsTraits& traits);`</td></tr>
- * <tr><td align="right"><b>5.1.</b></td><td>`bool do_intersect(InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, UsePolylines = Tag_true());`</td></tr>
- * <tr><td align="right"><b>5.2.</b></td><td>`bool do_intersect(InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2);`</td></tr>
- * <tr><td align="right"><b>  6.</b></td><td>`bool do_intersect(InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, const GpsTraits& traits);`</td></tr>
+ * <tr><td align="right"><b>3.</b></td><td>`bool do_intersect(InputIterator begin, InputIterator end);`</td></tr>
+ * <tr><td align="right"><b>4.</b></td><td>`bool do_intersect(InputIterator begin, InputIterator end, const GpsTraits& traits);`</td></tr>
+ * <tr><td align="right"><b>5.</b></td><td>`bool do_intersect(InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2);`</td></tr>
+ * <tr><td align="right"><b>6.</b></td><td>`bool do_intersect(InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, const GpsTraits& traits);`</td></tr>
  * </table>
  *
- * \tparam UsePolylines determines whether the boundary of the input polygons
- * are treated as a cyclic sequence of single (\f$x\f$-monotone) segments or as
- * a cyclic sequence of (\f$x\f$-monotone) polylines. If substituted with
- * `CGAL::Tag_true`, which is the default, the input polygons are converted to
- * general polygons bounded by polylines before the operation is actually
- * performed. If substituted with `CGAL::Tag_false`, the input polygons are used
- * as is. Refer to \ref bso_ssectraits_sel for more information.
- *
- *   - The types `Type1` and `Type2` of the parameters of
- *     `InputIterator1::value_type` and `InputIterator2::value_type` must be
- *     convertible to the types specified in a row in the table below,
- *     respectively.
- *
- *   - The types that apply to signatures (<b>1.1.</b>) and (<b>5.1.</b>) above
- *     are restricted to those listed in rows <b>1&ndash;4</b> in the table
- *     below.
- *
- *   - The types that apply to signatures (<b>1.2.</b>) and (<b>5.2.</b>) above
- *     are restricted to those listed in rows <b>5&ndash;8</b> in the table
- *     below.
- *
- *   - The type of `InputIterator::value_type` in (<b>3.1.</b>) above
- *     must be convertible to either `Polygon_2` or `Polygon_with_holes_2`.
- *
- *   - The type of `InputIterator::value_type` in (<b>3.2.</b>) above must be
- *     convertible to either `General_polygon_2` or
- *     `General_polygon_with_holes_2`.
+ * \tparam Kernel    a model of the concept `PolygonTraits_2`.
+ * \tparam Container a model of the concept `Container`; defaults to `std::vector<Kernel::Point_2`>.
+ * \tparam ArrTraits a model of the concept `AosDirectionalXMonotoneTraits_2`.
+ * \tparam GpsTraits a model of the concept `GeneralPolygonSetTraits_2`, which must be convertible to `ArrTraits`.
  *
  * <div align="left">
  * <table cellpadding=3 border="1">
@@ -728,6 +714,8 @@ namespace CGAL {
  * \sa \link boolean_join `CGAL::join()` \endlink
  * \sa \link boolean_difference `CGAL::difference()` \endlink
  * \sa \link boolean_symmetric_difference `CGAL::symmetric_difference()` \endlink
+ * \sa Polygon_2<Kernel, Container>
+ * \sa Polygon_with_holes_2<Kernel, Container>
  */
 
 /// @{
@@ -735,6 +723,11 @@ namespace CGAL {
 //////// Traits-less
 
 /*! determines whether two polygons intersect in their interior.
+ *
+ * The kernel used to instantiate the type of the input polygons must support
+ * exact predicates to guarantee correct results; however, inexact constructions
+ * are tolerated.
+ *
  * \param pgn1 the 1st input polygon.
  * \param pgn2 the 2nd input polygon.
  * \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
@@ -745,25 +738,11 @@ bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
                   const Polygon_2<Kernel, Container>& pgn2);
 
 /*! determines whether two polygons intersect in their interior.
- * \tparam UsePolylines determines whether the boundaries of `pgn1` and `pgn2`
- *         are treated as cyclic sequences of single (\f$x\f$-monotone) segments
- *         or as a cyclic sequences of (\f$x\f$-monotone) polylines. If
- *         substituted with `CGAL::Tag_true`, which is the default, `pgn1` and
- *         `pgn2` are converted to general polygons, bounded by polylines
- *         before the operation is actually performed. If substituted with
- *         `CGAL::Tag_false`, `pgn1` and `pgn2` are used as is. Refer to \ref
- *         bso_ssectraits_sel for more information.
- * \param pgn1 the 1st input polygon.
- * \param pgn2 the 2nd input polygon.
- * \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
- *         otherwise.
- */
-template <typename Kernel, typename Container, typename UsePolylines>
-bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
-                  const Polygon_2<Kernel, Container>& pgn2,
-                  UsePolylines = Tag_true());
-
-/*! determines whether two polygons intersect in their interior.
+ *
+ * The kernel used to instantiate the type of the input polygons must support
+ * exact predicates to guarantee correct results; however, inexact constructions
+ * are tolerated.
+ *
  * \param pgn1 the 1st input polygon.
  * \param pgn2 the 2nd input polygon.
  * \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
@@ -774,26 +753,11 @@ bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
                   const Polygon_with_holes_2<Kernel, Container>& pgn2);
 
 /*! determines whether two polygons intersect in their interior.
- * \tparam UsePolylines determines whether the boundaries of `pgn1` and `pgn2`
- *         are treated as cyclic sequences of single (\f$x\f$-monotone) segments
- *         or as a cyclic sequences of (\f$x\f$-monotone) polylines. If
- *         substituted with `CGAL::Tag_true`, which is the default, `pgn1` and
- *         `pgn2` are converted to a general polygon and a general polygon
- *         with holes, respectively, bounded by polylines before the operation
- *         is actually performed. If substituted with `CGAL::Tag_false`, `pgn1`
- *         and `pgn2` are used as is. Refer to \ref bso_ssectraits_sel for more
- *         information.
- * \param pgn1 the 1st input polygon.
- * \param pgn2 the 2nd input polygon.
- * \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
- *         otherwise.
- */
-template <typename Kernel, typename Container, typename UsePolylines>
-bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
-                  const Polygon_with_holes_2<Kernel, Container>& pgn2,
-                  UsePolylines = Tag_true());
-
-/*! determines whether two polygons intersect in their interior.
+ *
+ * The kernel used to instantiate the type of the input polygons must support
+ * exact predicates to guarantee correct results; however, inexact constructions
+ * are tolerated.
+ *
  * \param pgn1 the 1st input polygon.
  * \param pgn2 the 2nd input polygon.
  * \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
@@ -803,27 +767,12 @@ template <typename Kernel, typename Container>
 bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
                   const Polygon_2<Kernel, Container>& pgn2);
 
-/*! determines whether two polygons intersect in their interior.
- * \tparam UsePolylines determines whether the boundaries of `pgn1` and `pgn2`
- *         are treated as cyclic sequences of single (\f$x\f$-monotone) segments
- *         or as a cyclic sequences of (\f$x\f$-monotone) polylines. If
- *         substituted with `CGAL::Tag_true`, which is the default, `pgn1` and
- *         `pgn2` are converted to a general polygon with holes and a general
- *         polygon, respectively, bounded by polylines before the operation
- *         is actually performed. If substituted with `CGAL::Tag_false`, `pgn1`
- *         and `pgn2` are used as is. Refer to \ref bso_ssectraits_sel for more
- *         information.
- * \param pgn1 the 1st input polygon.
- * \param pgn2 the 2nd input polygon.
- * \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
- *         otherwise.
- */
-template <typename Kernel, typename Container, typename UsePolylines>
-bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
-                  const Polygon_2<Kernel, Container>& pgn2,
-                  UsePolylines = Tag_true());
-
 /*! determines whether two polygons with holes intersect in their interior.
+ *
+ * The kernel used to instantiate the type of the input polygons must support
+ * exact predicates to guarantee correct results; however, inexact constructions
+ * are tolerated.
+ *
  * \param pgn1 the 1st input polygon.
  * \param pgn2 the 2nd input polygon.
  * \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
@@ -833,25 +782,6 @@ template <typename Kernel, typename Container>
 bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
                   const Polygon_with_holes_2<Kernel, Container>& pgn2);
 
-/*! determines whether two polygons with holes intersect in their interior.
- * \tparam UsePolylines determines whether the boundaries of `pgn1` and `pgn2`
- *         are treated as cyclic sequences of single (\f$x\f$-monotone) segments
- *         or as a cyclic sequences of (\f$x\f$-monotone) polylines. If
- *         substituted with `CGAL::Tag_true`, which is the default, `pgn1` and
- *         `pgn2` are converted to general polygon with holes , bounded by
- *         polylines before the operation is actually performed. If substituted
- *         with `CGAL::Tag_false`, `pgn1` and `pgn2` are used as is. Refer to
- *         \ref bso_ssectraits_sel for more information.
- * \param pgn1 the 1st input polygon.
- * \param pgn2 the 2nd input polygon.
- * \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
- *         otherwise.
- */
-template <typename Kernel, typename Container, typename UsePolylines>
-bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
-                  const Polygon_with_holes_2<Kernel, Container>& pgn2,
-                  UsePolylines = Tag_true());
-
 /*! determines whether two general polygons intersect in their interior.
  * \param pgn1 the 1st input polygon.
  * \param pgn2 the 2nd input polygon.
@@ -904,6 +834,13 @@ bool do_intersect(const General_polygon_with_holes_2<Polygon>& pgn1,
  * of general polygons or a range of general polygons with holes) determines
  * whether the open polygons (respectively general polygons) in the range have a common
  * point.
+ *
+ * When the operation is applied to linear polygons (that is, the value type of
+ * the input iterator is either `Polygon_2` or `Polygon_with_holes_2`), the
+ * kernel used to instantiate the type of the input polygons must support exact
+ * predicates to guarantee correct results; however, inexact constructions are
+ * tolerated.
+ *
  * \param begin the first iterator of the input range. Its value type is
  *        either `Polygon_2` (respectively `General_polygon_2`) or
  *        `Polygon_with_holes_2` (respectively `General_polygon_with_holes_2`).
@@ -917,36 +854,16 @@ bool do_intersect(const General_polygon_with_holes_2<Polygon>& pgn1,
 template <typename InputIterator>
 bool do_intersect(InputIterator begin, InputIterator end);
 
-/*! Given a range of polygons or a range of polygons with holes (respectively a range
- * of general polygons or a range of general polygons with holes) determines
- * whether the open polygons (respectively general polygons) in the range have a common
- * point.
- * \tparam UsePolylines determines whether the boundaries of the polygons in the
- *         input range are treated as cyclic sequences of single
- *         (\f$x\f$-monotone) segments or as a cyclic sequences of
- *         (\f$x\f$-monotone) polylines. If substituted with `CGAL::Tag_true`,
- *         which is the default, the input polygons are converted to general
- *         polygon with holes , bounded by polylines before the operation is
- *         actually performed. If substituted with `CGAL::Tag_false`, `pgn1` and
- *         `pgn2` are used as is. Refer to \ref bso_ssectraits_sel for more
- *         information.
- * \param begin the first iterator of the input range. Its value type is
- *        either `Polygon_2` (respectively `General_polygon_2`) or
- *        `Polygon_with_holes_2` (respectively `General_polygon_with_holes_2`).
- * \param end the past-the-end iterator of the input range. Its value type is
- *        either `Polygon_2` (respectively `General_polygon_2`) or
- *        `Polygon_with_holes_2` (respectively `General_polygon_with_holes_2`).
- * \return `true` if the pairwise intersections of all open polygons or polygons
- *         with holes (respectively general polygons or general polygons with holes) in
- *         the range [*begin,*end) overlap, and `false` otherwise.
- */
-template <typename InputIterator, typename UsePolylines>
-bool do_intersect(InputIterator begin, InputIterator end,
-                  UsePolylines = Tag_true());
-
 /*! Given a range of polygons (respectively general polygons) and a range of polygons
  * with holes (respectively general polygons with holes) determines whether the open
  * polygons (respectively general polygons) in the two ranges have a common point.
+ *
+ * When the operation is applied to linear polygons (that is, the value type of
+ * any input iterator is either `Polygon_2` or `Polygon_with_holes_2`), the
+ * kernel used to instantiate the type of the input polygons must support exact
+ * predicates to guarantee correct results; however, inexact constructions are
+ * tolerated.
+ *
  * \param begin1 the first iterator of the 1st input range. Its value type is
  *        `Polygon_2` (respectively `General_polygon_2`).
  * \param end1 the past-the-end iterator of the 1st input range. Its value
@@ -964,40 +881,14 @@ template <typename InputIterator1, typename InputIterator2>
 bool do_intersect(InputIterator1 begin1, InputIterator1 end1,
                   InputIterator2 begin2, InputIterator2 end2);
 
-/*! Given a range of polygons (respectively general polygons) and a range of polygons
- * with holes (respectively general polygons with holes) determines whether the open
- * polygons (respectively general polygons) in the two ranges have a common point.
- * \tparam UsePolylines determines whether the boundaries of the polygons in the
- *         input ranges are treated as cyclic sequences of single
- *         (\f$x\f$-monotone) segments or as a cyclic sequences of
- *         (\f$x\f$-monotone) polylines. If substituted with `CGAL::Tag_true`,
- *         which is the default, the input polygons are converted to general
- *         polygon with holes , bounded by polylines before the operation is
- *         actually performed. If substituted with `CGAL::Tag_false`, `pgn1` and
- *         `pgn2` are used as is. Refer to \ref bso_ssectraits_sel for more
- *         information.
- * \param begin1 the first iterator of the 1st input range. Its value type is
- *        `Polygon_2` (respectively `General_polygon_2`).
- * \param end1 the past-the-end iterator of the 1st input range. Its value
- *        type is `Polygon_2` (respectively `General_polygon_2`).
- * \param begin2 the first iterator of the 2nd input range. Its value type
- *        is `Polygon_with_holes_2` (respectively `General_polygon_with_holes_2`).
- * \param end2 the past-the-end iterator of the 2nd input range. Its value
- *        type is `Polygon_with_holes_2` (respectively `General_polygon_with_holes_2`).
- * \return `true` if the pairwise intersections of all open polygons (respectively
- *        general polygons) and polygons with holes (respectively general polygons with
- *        holes) in the ranges [*begin1,*end1) and [*begin2,*end2),
- *        respectively, overlap, and `false` otherwise.
- */
-template <typename InputIterator1, typename InputIterator2,
-          typename UsePolylines>
-bool do_intersect(InputIterator1 begin1, InputIterator1 end1,
-                  InputIterator2 begin2, InputIterator2 end2,
-                  UsePolylines = Tag_true());
-
 //////// With Traits
 
 /*! determines whether two polygons intersect in their interior.
+ *
+ * The kernel used to instantiate the type of the input polygons must support
+ * exact predicates to guarantee correct results; however, inexact constructions
+ * are tolerated.
+ *
  * \param pgn1 the 1st input polygon.
  * \param pgn2 the 2nd input polygon.
  * \param traits a traits object.
@@ -1011,6 +902,11 @@ bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
                   const GpsTraits& traits);
 
 /*! determines whether two polygons intersect in their interior.
+ *
+ * The kernel used to instantiate the type of the input polygons must support
+ * exact predicates to guarantee correct results; however, inexact constructions
+ * are tolerated.
+ *
  * \param pgn1 the 1st input polygon.
  * \param pgn2 the 2nd input polygon.
  * \param traits a traits object.
@@ -1021,10 +917,14 @@ bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
 template <typename Kernel, typename Container, typename GpsTraits>
 bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
                   const Polygon_with_holes_2<Kernel, Container>& pgn2,
-                  const GpsTraits& traits,
                   const GpsTraits& traits);
 
 /*! determines whether two polygons intersect in their interior.
+ *
+ * The kernel used to instantiate the type of the input polygons must support
+ * exact predicates to guarantee correct results; however, inexact constructions
+ * are tolerated.
+ *
  * \param pgn1 the 1st input polygon.
  * \param pgn2 the 2nd input polygon.
  * \param traits a traits object.
@@ -1038,6 +938,11 @@ bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
                   const GpsTraits& traits);
 
 /*! determines whether two polygons with holes intersect in their interior.
+ *
+ * The kernel used to instantiate the type of the input polygons must support
+ * exact predicates to guarantee correct results; however, inexact constructions
+ * are tolerated.
+ *
  * \param pgn1 the 1st input polygon.
  * \param pgn2 the 2nd input polygon.
  * \param traits a traits object.
@@ -1116,6 +1021,12 @@ bool do_intersect(const General_polygon_with_holes_2<Polygon>& pgn1,
  * of general polygons or a range of general polygons with holes) determines
  * whether the open polygons (respectively general polygons) in the range have a common
  * point.
+ *
+ * When the operation is applied to linear polygons (that is, the value type of
+ * the input iterator is either `Polygon_2` or `Polygon_with_holes_2`), the
+ * traits parameter `GpsTraits` must support exact predicates to guarantee
+ * correct results; however, inexact constructions are tolerated.
+ *
  * \param begin the first iterator of the input range. Its value type is
  *        either `Polygon_2` (respectively `General_polygon_2`) or
  *        `Polygon_with_holes_2` (respectively `General_polygon_with_holes_2`).
@@ -1135,6 +1046,12 @@ bool do_intersect(InputIterator begin, InputIterator end,
 /*! Given a range of polygons (respectively general polygons) and a range of polygons
  * with holes (respectively general polygons with holes) determines whether the open
  * polygons (respectively general polygons) in the two ranges have a common point.
+ *
+ * When the operation is applied to linear polygons (that is, the value type of
+ * any input iterator is either `Polygon_2` or `Polygon_with_holes_2`), the
+ * traits parameter `GpsTraits` must support exact predicates to guarantee
+ * correct results; however, inexact constructions are tolerated.
+ *
  * \param begin1 the first iterator of the 1st input range. Its value type is
  *        `Polygon_2` (respectively `General_polygon_2`).
  * \param end1 the past-the-end iterator of the 1st input range. Its value
@@ -1186,6 +1103,10 @@ namespace CGAL {
  * <tr><td align="right"><b>6.</b></td><td>`OutputIterator intersection(InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, OutputIterator oi, const GpsTraits& traits);`</td></tr>
  * </table>
  *
+ * \tparam Kernel    a model of the concept `PolygonTraits_2`.
+ * \tparam Container a model of the concept `Container`; defaults to `std::vector<Kernel::Point_2`>.
+ * \tparam ArrTraits a model of the concept `AosDirectionalXMonotoneTraits_2`.
+ * \tparam GpsTraits a model of the concept `GeneralPolygonSetTraits_2`, which must be convertible to `ArrTraits`.
  * \tparam UsePolylines determines whether the boundaries of the input polygons
  * are treated as cyclic sequences of single (\f$x\f$-monotone) segments or as
  * cyclic sequences of (\f$x\f$-monotone) polylines. If substituted with
@@ -1244,6 +1165,8 @@ namespace CGAL {
  * \sa \link boolean_join `CGAL::join()` \endlink
  * \sa \link boolean_difference `CGAL::difference()` \endlink
  * \sa \link boolean_symmetric_difference `CGAL::symmetric_difference()` \endlink
+ * \sa Polygon_2<Kernel, Container>
+ * \sa Polygon_with_holes_2<Kernel, Container>
  */
 
 /// @{
@@ -1825,6 +1748,10 @@ namespace CGAL {
  * <tr><td align="right"><b>6.</b></td><td>`OutputIterator join(InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, OutputIterator oi, const GpsTraits& traits);`</td></tr>
  * </table>
  *
+ * \tparam Kernel    a model of the concept `PolygonTraits_2`.
+ * \tparam Container a model of the concept `Container`; defaults to `std::vector<Kernel::Point_2`>.
+ * \tparam ArrTraits a model of the concept `AosDirectionalXMonotoneTraits_2`.
+ * \tparam GpsTraits a model of the concept `GeneralPolygonSetTraits_2`, which must be convertible to `ArrTraits`.
  * \tparam UsePolylines determines whether the boundaries of the input polygons
  * are treated as cyclic sequences of single (\f$x\f$-monotone) segments or as
  * cyclic sequences of (\f$x\f$-monotone) polylines. If substituted with
@@ -1882,6 +1809,8 @@ namespace CGAL {
  * \sa \link boolean_intersection `CGAL::intersection()` \endlink
  * \sa \link boolean_difference `CGAL::difference()` \endlink
  * \sa \link boolean_symmetric_difference `CGAL::symmetric_difference()` \endlink
+ * \sa Polygon_2<Kernel, Container>
+ * \sa Polygon_with_holes_2<Kernel, Container>
  */
 
 /// @{
@@ -2407,6 +2336,10 @@ namespace CGAL {
  * <tr><td align="right"><b>  4.</b></td><td>`Oriented_side oriented_side(const Point_2& p, const Type& pgn, const GpsTraits& traits);`</td></tr>
  * </table>
  *
+ * \tparam Kernel    a model of the concept `PolygonTraits_2`.
+ * \tparam Container a model of the concept `Container`; defaults to `std::vector<Kernel::Point_2`>.
+ * \tparam ArrTraits a model of the concept `AosDirectionalXMonotoneTraits_2`.
+ * \tparam GpsTraits a model of the concept `GeneralPolygonSetTraits_2`, which must be convertible to `ArrTraits`.
  * \tparam UsePolylines determines whether the boundaries of the input polygons
  * are treated as cyclic sequences of single (\f$x\f$-monotone) segments or as
  * cyclic sequences of (\f$x\f$-monotone) polylines. If substituted with
@@ -2446,6 +2379,8 @@ namespace CGAL {
  * \param traits an optional traits object.
  *
  * \sa \link boolean_do_intersect `CGAL::do_intersect()` \endlink
+ * \sa Polygon_2<Kernel, Container>
+ * \sa Polygon_with_holes_2<Kernel, Container>
  */
 
 /// @{
@@ -2823,6 +2758,10 @@ namespace CGAL {
  * <tr><td align="right"><b>6.</b></td><td>`OutputIterator symmetric_difference(InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, OutputIterator oi, const GpsTraits& traits);`</td></tr>
  * </table>
  *
+ * \tparam Kernel    a model of the concept `PolygonTraits_2`.
+ * \tparam Container a model of the concept `Container`; defaults to `std::vector<Kernel::Point_2`>.
+ * \tparam ArrTraits a model of the concept `AosDirectionalXMonotoneTraits_2`.
+ * \tparam GpsTraits a model of the concept `GeneralPolygonSetTraits_2`, which must be convertible to `ArrTraits`.
  * \tparam UsePolylines determines whether the boundaries of the input polygons
  * are treated as cyclic sequences of single (\f$x\f$-monotone) segments or as
  * cyclic sequences of (\f$x\f$-monotone) polylines. If substituted with
@@ -2879,6 +2818,8 @@ namespace CGAL {
  * \sa \link boolean_intersection `CGAL::intersection()` \endlink
  * \sa \link boolean_join `CGAL::join()` \endlink
  * \sa \link boolean_difference `CGAL::difference()` \endlink
+ * \sa Polygon_2<Kernel, Container>
+ * \sa Polygon_with_holes_2<Kernel, Container>
  */
 
 /// @{

Boolean_set_operations_2/examples/Boolean_set_operations_2/do_intersect.cpp

@@ -5,27 +5,26 @@
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 #include <CGAL/Boolean_set_operations_2.h>
 
-typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
-typedef Kernel::Point_2                                   Point_2;
-typedef CGAL::Polygon_2<Kernel>                           Polygon_2;
+using Kernel = CGAL::Exact_predicates_exact_constructions_kernel;
+using Point_2 = Kernel::Point_2;
+using Polygon_2 = CGAL::Polygon_2<Kernel>;
 
 #include "print_utils.h"
 
-int main ()
-{
+int main() {
   Polygon_2 P;
-  P.push_back (Point_2 (-1,1));
-  P.push_back (Point_2 (0,-1));
-  P.push_back (Point_2 (1,1));
-  std::cout << "P = "; print_polygon (P);
+  P.push_back(Point_2(-1, 1));
+  P.push_back(Point_2(0, -1));
+  P.push_back(Point_2(1, 1));
+  std::cout << "P = "; print_polygon(P);
 
   Polygon_2 Q;
-  Q.push_back(Point_2 (-1,-1));
-  Q.push_back(Point_2 (1,-1));
-  Q.push_back(Point_2 (0,1));
-  std::cout << "Q = "; print_polygon (Q);
+  Q.push_back(Point_2(-1, -1));
+  Q.push_back(Point_2(1, -1));
+  Q.push_back(Point_2(0, 1));
+  std::cout << "Q = "; print_polygon(Q);
 
-  if ((CGAL::do_intersect (P, Q)))
+  if ((CGAL::do_intersect(P, Q)))
     std::cout << "The two polygons intersect in their interior." << std::endl;
   else
     std::cout << "The two polygons do not intersect." << std::endl;

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Bso_internal_functions.h

@@ -8,10 +8,10 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s): Baruch Zukerman <baruchzu@post.tau.ac.il>
-//            Ron Wein        <wein@post.tau.ac.il>
-//            Efi Fogel       <efif@post.tau.ac.il>
-//            Simon Giraudot  <simon.giraudot@geometryfactory.com>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Ron Wein        <wein@post.tau.ac.il>
+//             Efi Fogel       <efif@post.tau.ac.il>
+//             Simon Giraudot  <simon.giraudot@geometryfactory.com>
 
 #ifndef CGAL_BSO_INTERNAL_FUNCTIONS_H
 #define CGAL_BSO_INTERNAL_FUNCTIONS_H
@@ -33,7 +33,7 @@ namespace CGAL {
 
 // Single
 // With Traits
-template <typename Pgn1, class Pgn2, typename Traits>
+template <typename Pgn1, typename Pgn2, typename Traits>
 inline bool s_do_intersect(const Pgn1& pgn1, const Pgn2& pgn2, Traits& traits) {
   General_polygon_set_2<Traits> gps(pgn1, traits);
   return gps.do_intersect(pgn2);
@@ -52,7 +52,7 @@ inline bool s_do_intersect(const Pgn1& pgn1, const Pgn2& pgn2) {
 // With Traits
 template <typename InputIterator, typename Traits>
 inline bool r_do_intersect(InputIterator begin, InputIterator end,
-                           Traits& traits, unsigned int k=5) {
+                           Traits& traits, std::size_t k = 5) {
   if (begin == end) return false;
   General_polygon_set_2<Traits> gps(*begin, traits);
   return gps.do_intersect(std::next(begin), end, k);
@@ -61,8 +61,8 @@ inline bool r_do_intersect(InputIterator begin, InputIterator end,
 // Without Traits
 template <typename InputIterator>
 inline bool r_do_intersect(InputIterator begin, InputIterator end,
-                           unsigned int k=5) {
-  typedef typename std::iterator_traits<InputIterator>::value_type Pgn;
+                           std::size_t k = 5) {
+  using Pgn = typename std::iterator_traits<InputIterator>::value_type;
   typename Gps_polyline_traits<Pgn>::Traits traits;
   const typename Gps_polyline_traits<Pgn>::Polyline_traits& ptraits(traits);
   return r_do_intersect(convert_polygon_iterator(begin, ptraits),
@@ -74,7 +74,7 @@ inline bool r_do_intersect(InputIterator begin, InputIterator end,
 template <typename InputIterator1, typename InputIterator2, typename Traits>
 inline bool r_do_intersect(InputIterator1 begin1, InputIterator1 end1,
                            InputIterator2 begin2, InputIterator2 end2,
-                           Traits& traits, unsigned int k=5) {
+                           Traits& traits, std::size_t k = 5) {
   if (begin1 == end1) return do_intersect(begin2, end2, traits, k);
   General_polygon_set_2<Traits> gps(*begin1, traits);
   return gps.do_intersect(std::next(begin1), end1, begin2, end2, k);
@@ -84,8 +84,8 @@ inline bool r_do_intersect(InputIterator1 begin1, InputIterator1 end1,
 template <typename InputIterator1, typename InputIterator2>
 inline bool r_do_intersect (InputIterator1 begin1, InputIterator1 end1,
                             InputIterator2 begin2, InputIterator2 end2,
-                            unsigned int k=5) {
-  typedef typename std::iterator_traits<InputIterator1>::value_type Pgn;
+                            std::size_t k = 5) {
+  using Pgn = typename std::iterator_traits<InputIterator1>::value_type;
   typename Gps_polyline_traits<Pgn>::Traits traits;
   const typename Gps_polyline_traits<Pgn>::Polyline_traits& ptraits(traits);
   return r_do_intersect(convert_polygon_iterator(begin1, ptraits),
@@ -119,8 +119,7 @@ inline Oriented_side _oriented_side(const Point_2<Kernel>& point,
 
 // Without Traits (polygon, polygon)
 template <typename Pgn1, typename Pgn2>
-inline Oriented_side _oriented_side(const Pgn1& pgn1, const Pgn2& pgn2)
-{
+inline Oriented_side _oriented_side(const Pgn1& pgn1, const Pgn2& pgn2) {
   // Use the first polygon to determine the (default) traits
   typename Gps_polyline_traits<Pgn1>::Traits traits;
   const typename Gps_polyline_traits<Pgn1>::Polyline_traits& ptraits(traits);
@@ -149,7 +148,7 @@ template <typename Kernel, typename Container,
 inline OutputIterator s_intersection(const Pgn1& pgn1, const Pgn2& pgn2,
                                      OutputIterator oi) {
   // Use the first polygon to determine the (default) traits
-  typedef typename Gps_polyline_traits<Pgn1>::Polyline_traits   Polyline_traits;
+  using Polyline_traits = typename Gps_polyline_traits<Pgn1>::Polyline_traits;
 
   typename Gps_polyline_traits<Pgn1>::Traits traits;
   const Polyline_traits& ptraits(traits);
@@ -163,7 +162,7 @@ inline OutputIterator s_intersection(const Pgn1& pgn1, const Pgn2& pgn2,
 template <typename InputIterator, typename OutputIterator, typename Traits>
 inline OutputIterator r_intersection(InputIterator begin, InputIterator end,
                                      OutputIterator oi, Traits& traits,
-                                     unsigned int k=5) {
+                                     std::size_t k = 5) {
   if (begin == end) return (oi);
   General_polygon_set_2<Traits> gps(*begin, traits);
   gps.intersection(std::next(begin), end, k);
@@ -173,8 +172,8 @@ inline OutputIterator r_intersection(InputIterator begin, InputIterator end,
 // Without Traits
 template <typename InputIterator, typename OutputIterator>
 inline OutputIterator r_intersection(InputIterator begin, InputIterator end,
-                                     OutputIterator oi, unsigned int k=5) {
-  typedef typename std::iterator_traits<InputIterator>::value_type Pgn;
+                                     OutputIterator oi, std::size_t k = 5) {
+  using Pgn = typename std::iterator_traits<InputIterator>::value_type;
   typename Gps_polyline_traits<Pgn>::Traits traits;
   const typename Gps_polyline_traits<Pgn>::Polyline_traits& ptraits(traits);
   if (begin == end) return (oi);
@@ -190,7 +189,7 @@ template <typename InputIterator1, typename InputIterator2,
 inline OutputIterator r_intersection(InputIterator1 begin1, InputIterator1 end1,
                                      InputIterator2 begin2, InputIterator2 end2,
                                      OutputIterator oi, Traits& traits,
-                                     unsigned int k=5) {
+                                     std::size_t k = 5) {
   if (begin1 == end1) return r_intersection(begin2, end2, oi, traits, k);
   General_polygon_set_2<Traits> gps(*begin1, traits);
   gps.intersection(std::next(begin1), end1, begin2, end2, k);
@@ -203,8 +202,8 @@ template <typename InputIterator1, typename InputIterator2,
 inline OutputIterator
 r_intersection(InputIterator1 begin1, InputIterator1 end1,
                InputIterator2 begin2, InputIterator2 end2,
-               OutputIterator oi, unsigned int k=5) {
-  typedef typename std::iterator_traits<InputIterator1>::value_type Pgn;
+               OutputIterator oi, std::size_t k = 5) {
+  using Pgn = typename std::iterator_traits<InputIterator1>::value_type;
   typename Gps_polyline_traits<Pgn>::Traits traits;
   const typename Gps_polyline_traits<Pgn>::Polyline_traits& ptraits(traits);
   if (begin1 == end1) {
@@ -228,7 +227,7 @@ r_intersection(InputIterator1 begin1, InputIterator1 end1,
 // Polygon_2
 template <typename Traits>
 inline bool _is_empty(const typename Traits::Polygon_2& pgn, Traits& traits) {
-  typedef typename Traits::Curve_const_iterator Curve_const_iterator;
+  using Curve_const_iterator = typename Traits::Curve_const_iterator;
   const std::pair<Curve_const_iterator, Curve_const_iterator>& itr_pair =
     traits.construct_curves_2_object()(pgn);
   return (itr_pair.first == itr_pair.second);
@@ -268,9 +267,9 @@ template <typename Kernel, typename Container,
           typename Pgn1, typename Pgn2, typename Pwh>
 inline bool s_join(const Pgn1& pgn1, const Pgn2& pgn2, Pwh& pwh) {
   // Use the first polygon to determine the (default) traits
-  typedef typename Gps_polyline_traits<Pgn1>::Polyline_traits   Polyline_traits;
-  typedef General_polygon_2<Polyline_traits>                    General_pgn;
-  typedef General_polygon_with_holes_2<General_pgn>             General_pwh;
+  using Polyline_traits = typename Gps_polyline_traits<Pgn1>::Polyline_traits;
+  using General_pgn = General_polygon_2<Polyline_traits>;
+  using General_pwh = General_polygon_with_holes_2<General_pgn>;
 
   General_pwh general_pwh;
   typename Gps_polyline_traits<Pgn1>::Traits traits;
@@ -287,7 +286,7 @@ inline bool s_join(const Pgn1& pgn1, const Pgn2& pgn2, Pwh& pwh) {
 template <typename InputIterator, typename OutputIterator, typename Traits>
 inline OutputIterator r_join(InputIterator begin, InputIterator end,
                              OutputIterator oi, Traits& traits,
-                             unsigned int k=5) {
+                             std::size_t k = 5) {
   if (begin == end) return oi;
   General_polygon_set_2<Traits> gps(*begin, traits);
   gps.join(std::next(begin), end, k);
@@ -297,8 +296,8 @@ inline OutputIterator r_join(InputIterator begin, InputIterator end,
 // Without traits
 template <typename InputIterator, typename OutputIterator>
 inline OutputIterator r_join(InputIterator begin, InputIterator end,
-                             OutputIterator oi, unsigned int k=5) {
-  typedef typename std::iterator_traits<InputIterator>::value_type Pgn;
+                             OutputIterator oi, std::size_t k = 5) {
+  using Pgn = typename std::iterator_traits<InputIterator>::value_type;
   typename Gps_polyline_traits<Pgn>::Traits traits;
   const typename Gps_polyline_traits<Pgn>::Polyline_traits& ptraits(traits);
 
@@ -316,7 +315,7 @@ template <typename InputIterator1, typename InputIterator2,
 inline OutputIterator r_join(InputIterator1 begin1, InputIterator1 end1,
                              InputIterator2 begin2, InputIterator2 end2,
                              OutputIterator oi, Traits& traits,
-                             unsigned int k=5) {
+                             std::size_t k = 5) {
   if (begin1 == end1) return r_join(begin2, end2, oi, traits, k);
   General_polygon_set_2<Traits> gps(*begin1, traits);
   gps.join(std::next(begin1), end1, begin2, end2, k);
@@ -328,8 +327,8 @@ template <typename InputIterator1, typename InputIterator2,
           typename OutputIterator>
 inline OutputIterator r_join(InputIterator1 begin1, InputIterator1 end1,
                              InputIterator2 begin2, InputIterator2 end2,
-                             OutputIterator oi, unsigned int k=5) {
-  typedef typename std::iterator_traits<InputIterator1>::value_type Pgn;
+                             OutputIterator oi, std::size_t k = 5) {
+  using Pgn = typename std::iterator_traits<InputIterator1>::value_type;
   typename Gps_polyline_traits<Pgn>::Traits traits;
   const typename Gps_polyline_traits<Pgn>::Polyline_traits& ptraits(traits);
   if (begin1 == end1) {
@@ -361,10 +360,9 @@ inline OutputIterator _difference(const Pgn1& pgn1, const Pgn2& pgn2,
 template <typename Kernel, typename Container,
           typename Pgn1, typename Pgn2, typename OutputIterator>
 inline OutputIterator _difference(const Pgn1& pgn1, const Pgn2& pgn2,
-                                  OutputIterator oi)
-{
+                                  OutputIterator oi) {
   // Use the first polygon to determine the (default) traits
-  typedef typename Gps_polyline_traits<Pgn1>::Polyline_traits   Polyline_traits;
+  using Polyline_traits = typename Gps_polyline_traits<Pgn1>::Polyline_traits;
 
   typename Gps_polyline_traits<Pgn1>::Traits traits;
   const Polyline_traits& ptraits(traits);
@@ -394,7 +392,7 @@ template <typename Kernel, typename Container,
 inline OutputIterator s_symmetric_difference(const Pgn1& pgn1, const Pgn2& pgn2,
                                              OutputIterator oi) {
   // Use the first polygon to determine the (default) traits
-  typedef typename Gps_polyline_traits<Pgn1>::Polyline_traits   Polyline_traits;
+  using Polyline_traits = typename Gps_polyline_traits<Pgn1>::Polyline_traits;
   typename Gps_polyline_traits<Pgn1>::Traits traits;
   const Polyline_traits& ptraits(traits);
   s_symmetric_difference(convert_polygon(pgn1, ptraits),
@@ -409,7 +407,7 @@ template <typename InputIterator, typename OutputIterator, typename Traits>
 inline
 OutputIterator r_symmetric_difference(InputIterator begin, InputIterator end,
                                       OutputIterator oi, Traits& traits,
-                                      unsigned int k=5) {
+                                      std::size_t k = 5) {
   if (begin == end) return (oi);
   General_polygon_set_2<Traits> gps(*begin, traits);
   gps.symmetric_difference(std::next(begin), end, k);
@@ -421,9 +419,8 @@ template <typename InputIterator, typename OutputIterator>
 inline OutputIterator r_symmetric_difference(InputIterator begin,
                                              InputIterator end,
                                              OutputIterator oi,
-                                             unsigned int k=5)
-{
-  typedef typename std::iterator_traits<InputIterator>::value_type Pgn;
+                                             std::size_t k = 5) {
+  using Pgn = typename std::iterator_traits<InputIterator>::value_type;
   typename Gps_polyline_traits<Pgn>::Traits traits;
   const typename Gps_polyline_traits<Pgn>::Polyline_traits& ptraits(traits);
   if (begin == end) return (oi);
@@ -441,8 +438,7 @@ inline OutputIterator r_symmetric_difference(InputIterator1 begin1,
                                              InputIterator2 begin2,
                                              InputIterator2 end2,
                                              OutputIterator oi, Traits& traits,
-                                             unsigned int k=5)
-{
+                                             std::size_t k = 5) {
   if (begin1 == end1) return r_symmetric_difference(begin2, end2, oi, traits, k);
   General_polygon_set_2<Traits> gps(*begin1, traits);
   gps.symmetric_difference(std::next(begin1), end1, begin2, end2, k);
@@ -457,8 +453,8 @@ inline OutputIterator r_symmetric_difference(InputIterator1 begin1,
                                              InputIterator2 begin2,
                                              InputIterator2 end2,
                                              OutputIterator oi,
-                                             unsigned int k=5) {
-  typedef typename std::iterator_traits<InputIterator1>::value_type Pgn;
+                                             std::size_t k = 5) {
+  using Pgn = typename std::iterator_traits<InputIterator1>::value_type;
   typename Gps_polyline_traits<Pgn>::Traits traits;
   const typename Gps_polyline_traits<Pgn>::Polyline_traits& ptraits(traits);
   if (begin1 == end1){
@@ -522,10 +518,10 @@ OutputIterator _complement(const General_polygon_with_holes_2<Pgn>& pgn,
 template <typename Kernel, typename Container, typename Pwh>
 void _complement(const Polygon_2<Kernel, Container>& pgn, Pwh& pwh) {
   // Use the polygon to determine the (default) traits
-  typedef Polygon_2<Kernel, Container>                          Pgn;
-  typedef typename Gps_polyline_traits<Pgn>::Polyline_traits    Polyline_traits;
-  typedef General_polygon_2<Polyline_traits>                    General_pgn;
-  typedef General_polygon_with_holes_2<General_pgn>             General_pwh;
+  using Pgn = Polygon_2<Kernel, Container>;
+  using Polyline_traits = typename Gps_polyline_traits<Pgn>::Polyline_traits;
+  using General_pgn = General_polygon_2<Polyline_traits>;
+  using General_pwh = General_polygon_with_holes_2<General_pgn>;
 
   General_pwh general_pwh;
   typename Gps_polyline_traits<Pgn>::Traits traits;
@@ -539,8 +535,8 @@ template <typename Kernel, typename Container, typename OutputIterator>
 OutputIterator _complement(const Polygon_with_holes_2<Kernel, Container>& pgn,
                            OutputIterator oi) {
   // Use the polygon with holes to determine the (default) traits
-  typedef Polygon_with_holes_2<Kernel, Container>               Pgn;
-  typedef typename Gps_polyline_traits<Pgn>::Polyline_traits    Polyline_traits;
+  using Pgn = Polygon_with_holes_2<Kernel, Container>;
+  using Polyline_traits = typename Gps_polyline_traits<Pgn>::Polyline_traits;
 
   typename Gps_polyline_traits<Pgn>::Traits traits;
   const Polyline_traits& ptraits(traits);

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_agg_meta_traits.h

@@ -7,12 +7,11 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
-// Author(s): Baruch Zukerman <baruchzu@post.tau.ac.il>
-//            Efi Fogel       <efifogel@gmail.com>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Efi Fogel       <efifogel@gmail.com>
 
-#ifndef CGAL_BSO_2_GPS_AGG_META_TRAITS_H
-#define CGAL_BSO_2_GPS_AGG_META_TRAITS_H
+#ifndef CGAL_GPS_AGG_META_TRAITS_H
+#define CGAL_GPS_AGG_META_TRAITS_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
@@ -24,18 +23,17 @@
 namespace CGAL {
 
 template <typename Arrangement_>
-class Gps_agg_curve_data : public Curve_with_halfedge<Arrangement_>
-{
+class Gps_agg_curve_data : public Curve_with_halfedge<Arrangement_> {
 protected:
-  typedef Arrangement_                             Arrangement;
-  typedef typename Arrangement::Halfedge_handle    Halfedge_handle;
-  typedef Curve_with_halfedge<Arrangement_>        Base;
+  using Arrangement = Arrangement_;
+  using Halfedge_handle = typename Arrangement::Halfedge_handle;
+  using Base = Curve_with_halfedge<Arrangement_>;
 
   const Arrangement* m_arr; // pointer to the arrangement containing the edge.
-  unsigned int m_bc;        // the boundary counter of the halfedge with the same
+  std::size_t m_bc;         // the boundary counter of the halfedge with the same
                             // direction as the curve
 
-  unsigned int m_twin_bc;   // the boundary counter of the halfedge with the same
+  std::size_t m_twin_bc;    // the boundary counter of the halfedge with the same
                             // direction as the curve
 
 public:
@@ -47,24 +45,24 @@ public:
   {}
 
   Gps_agg_curve_data(const Arrangement* arr, Halfedge_handle he,
-                     unsigned int bc, unsigned int twin_bc) :
+                     std::size_t bc, std::size_t twin_bc) :
     Base(he),
     m_arr(arr),
     m_bc(bc),
     m_twin_bc(twin_bc)
   {}
 
-  unsigned int bc() const { return m_bc; }
+  std::size_t bc() const { return m_bc; }
 
-  unsigned int twin_bc() const { return m_twin_bc; }
+  std::size_t twin_bc() const { return m_twin_bc; }
 
-  unsigned int& bc() { return m_bc; }
+  std::size_t& bc() { return m_bc; }
 
-  unsigned int& twin_bc() { return m_twin_bc; }
+  std::size_t& twin_bc() { return m_twin_bc; }
 
-  void set_bc(unsigned int bc) { m_bc = bc; }
+  void set_bc(std::size_t bc) { m_bc = bc; }
 
-  void set_twin_bc(unsigned int twin_bc) { m_twin_bc = twin_bc; }
+  void set_twin_bc(std::size_t twin_bc) { m_twin_bc = twin_bc; }
 
   const Arrangement* arr() const { return m_arr; }
 };
@@ -73,54 +71,50 @@ template <typename Arrangement_>
 class Gps_agg_meta_traits :
   public Gps_traits_decorator<typename Arrangement_::Traits_adaptor_2,
                               Gps_agg_curve_data<Arrangement_>,
-                              Point_with_vertex<Arrangement_> >
-{
-  typedef Arrangement_                          Arrangement;
-  typedef Arrangement                           Arr;
+                              Point_with_vertex<Arrangement_>> {
+  using Arrangement = Arrangement_;
+  using Arr = Arrangement;
 
-  typedef typename Arr::Traits_adaptor_2        Traits;
-  typedef Traits                                Gt2;
+  using Traits = typename Arr::Traits_adaptor_2;
+  using Gt2 = Traits;
 
-  typedef typename Gt2::X_monotone_curve_2      Base_x_monotone_curve_2;
-  typedef typename Gt2::Point_2                 Base_point_2;
-  typedef typename Gt2::Construct_min_vertex_2  Base_Construct_min_vertex_2;
-  typedef typename Gt2::Construct_max_vertex_2  Base_Construct_max_vertex_2;
-  typedef typename Gt2::Compare_endpoints_xy_2  Base_Compare_endpoints_xy_2;
-  typedef typename Gt2::Compare_xy_2            Base_Compare_xy_2;
-  typedef typename Gt2::Compare_y_at_x_right_2  Base_Compare_y_at_x_right_2;
-  typedef typename Gt2::Compare_y_at_x_2        Base_Compare_y_at_x_2;
-  typedef typename Gt2::Intersect_2             Base_Intersect_2;
-  typedef typename Gt2::Split_2                 Base_Split_2;
+  using Base_x_monotone_curve_2 = typename Gt2::X_monotone_curve_2;
+  using Base_point_2 = typename Gt2::Point_2;
+  using Base_Construct_min_vertex_2 = typename Gt2::Construct_min_vertex_2;
+  using Base_Construct_max_vertex_2 = typename Gt2::Construct_max_vertex_2;
+  using Base_Compare_endpoints_xy_2 = typename Gt2::Compare_endpoints_xy_2;
+  using Base_Compare_xy_2 = typename Gt2::Compare_xy_2;
+  using Base_Compare_y_at_x_right_2 = typename Gt2::Compare_y_at_x_right_2;
+  using Base_Compare_y_at_x_2 = typename Gt2::Compare_y_at_x_2;
+  using Base_Intersect_2 = typename Gt2::Intersect_2;
+  using Base_Split_2 = typename Gt2::Split_2;
 
-  typedef typename Gt2::Parameter_space_in_x_2  Base_Parameter_space_in_x_2;
-  typedef typename Gt2::Compare_y_near_boundary_2
-                                                Base_Compare_y_near_boundary_2;
+  using Base_Parameter_space_in_x_2 = typename Gt2::Parameter_space_in_x_2;
+  using Base_Compare_y_near_boundary_2 = typename Gt2::Compare_y_near_boundary_2;
 
-  typedef typename Gt2::Parameter_space_in_y_2  Base_Parameter_space_in_y_2;
-  typedef typename Gt2::Compare_x_near_boundary_2
-                                                Base_Compare_x_near_boundary_2;
+  using Base_Parameter_space_in_y_2 = typename Gt2::Parameter_space_in_y_2;
+  using Base_Compare_x_near_boundary_2 = typename Gt2::Compare_x_near_boundary_2;
 
 public:
-  typedef typename Gt2::Multiplicity            Multiplicity;
-  typedef Gps_agg_curve_data<Arr>               Curve_data;
-  typedef Point_with_vertex<Arr>                Point_data;
+  using Multiplicity = typename Gt2::Multiplicity;
+  using Curve_data = Gps_agg_curve_data<Arr>;
+  using Point_data = Point_with_vertex<Arr>;
 
 private:
-  typedef Gps_agg_meta_traits<Arrangement>                      Self;
-  typedef Gps_traits_decorator<Gt2, Curve_data, Point_data>     Base;
+  using Self = Gps_agg_meta_traits<Arrangement>;
+  using Base = Gps_traits_decorator<Gt2, Curve_data, Point_data>;
 
 public:
-  typedef typename Base::X_monotone_curve_2     X_monotone_curve_2;
-  typedef typename Base::Point_2                Point_2;
-  typedef typename Gt2::Has_left_category       Has_left_category;
-  typedef typename Gt2::Has_merge_category      Has_merge_category;
-  typedef typename Gt2::Has_do_intersect_category
-    Has_do_intersect_category;
+  using X_monotone_curve_2 = typename Base::X_monotone_curve_2;
+  using Point_2 = typename Base::Point_2;
+  using Has_left_category = typename Gt2::Has_left_category;
+  using Has_merge_category = typename Gt2::Has_merge_category;
+  using Has_do_intersect_category = typename Gt2::Has_do_intersect_category;
 
-  typedef typename Arr::Left_side_category      Left_side_category;
-  typedef typename Arr::Bottom_side_category    Bottom_side_category;
-  typedef typename Arr::Top_side_category       Top_side_category;
-  typedef typename Arr::Right_side_category     Right_side_category;
+  using Left_side_category = typename Arr::Left_side_category;
+  using Bottom_side_category = typename Arr::Bottom_side_category;
+  using Top_side_category = typename Arr::Top_side_category;
+  using Right_side_category = typename Arr::Right_side_category;
 
   // a side is either oblivious or open (unbounded)
   static_assert(std::is_same<Left_side_category, Arr_oblivious_side_tag>::value ||
@@ -132,8 +126,8 @@ public:
   static_assert(std::is_same<Right_side_category, Arr_oblivious_side_tag>::value ||
                          std::is_same<Right_side_category, Arr_open_side_tag>::value);
 
-  typedef typename Arr::Halfedge_handle         Halfedge_handle;
-  typedef typename Arr::Vertex_handle           Vertex_handle;
+  using Halfedge_handle = typename Arr::Halfedge_handle;
+  using Vertex_handle = typename Arr::Vertex_handle;
 
   Gps_agg_meta_traits() {}
 
@@ -152,16 +146,13 @@ public:
     template <typename OutputIterator>
     OutputIterator operator()(const X_monotone_curve_2& cv1,
                               const X_monotone_curve_2& cv2,
-                              OutputIterator oi) const
-    {
+                              OutputIterator oi) const {
       // Check whether the curves are already in the same arrangement, and thus
       // must be interior-disjoint
       if (cv1.data().arr() == cv2.data().arr()) return oi;
 
-      typedef const std::pair<Base_point_2, Multiplicity>
-        Intersection_base_point;
-      typedef std::variant<Intersection_base_point, Base_x_monotone_curve_2>
-                                                        Intersection_base_result;
+      using Intersection_base_point = const std::pair<Base_point_2, Multiplicity>;
+      using Intersection_base_result = std::variant<Intersection_base_point, Base_x_monotone_curve_2>;
 
       const auto* base_traits = m_traits.m_base_traits;
       auto base_cmp_xy = base_traits->compare_xy_2_object();
@@ -191,8 +182,8 @@ public:
         const Base_x_monotone_curve_2* overlap_cv =
           std::get_if<Base_x_monotone_curve_2>(&xection);
         CGAL_assertion(overlap_cv != nullptr);
-        unsigned int ov_bc;
-        unsigned int ov_twin_bc;
+        std::size_t ov_bc;
+        std::size_t ov_twin_bc;
         if (base_cmp_endpoints(cv1) == base_cmp_endpoints(cv2)) {
           // cv1 and cv2 have the same directions
           ov_bc = cv1.data().bc() + cv2.data().bc();
@@ -230,8 +221,7 @@ public:
     Split_2(const Base_Split_2& base) : m_base_split(base) {}
 
     void operator()(const X_monotone_curve_2& cv, const Point_2 & p,
-                    X_monotone_curve_2& c1, X_monotone_curve_2& c2) const
-    {
+                    X_monotone_curve_2& c1, X_monotone_curve_2& c2) const {
       m_base_split(cv.base(), p.base(), c1.base(), c2.base());
       const Curve_data& cv_data = cv.data();
       c1.set_data(Curve_data(cv_data.arr(), Halfedge_handle(), cv_data.bc(),
@@ -259,8 +249,7 @@ public:
      * \param cv The curve.
      * \return The left endpoint.
      */
-    Point_2 operator()(const X_monotone_curve_2 & cv) const
-    {
+    Point_2 operator()(const X_monotone_curve_2 & cv) const {
       if (cv.data().halfedge() == Halfedge_handle())
         return (Point_2(m_base(cv.base())));
 
@@ -272,8 +261,7 @@ public:
   };
 
   /*! Get a Construct_min_vertex_2 functor object. */
-  Construct_min_vertex_2 construct_min_vertex_2_object() const
-  {
+  Construct_min_vertex_2 construct_min_vertex_2_object() const {
     return Construct_min_vertex_2(this->m_base_traits->
                                   construct_min_vertex_2_object());
   }
@@ -285,15 +273,14 @@ public:
 
   public:
     Construct_max_vertex_2(const Base_Construct_max_vertex_2& base) :
-        m_base(base)
+      m_base(base)
     {}
 
     /*! Obtain the right endpoint of the x-monotone curve (segment).
      * \param cv The curve.
      * \return The right endpoint.
      */
-    Point_2 operator()(const X_monotone_curve_2& cv) const
-    {
+    Point_2 operator()(const X_monotone_curve_2& cv) const {
       if (cv.data().halfedge() == Halfedge_handle())
         return (Point_2(m_base(cv.base())));
 
@@ -304,8 +291,7 @@ public:
   };
 
   /*! Get a Construct_min_vertex_2 functor object. */
-  Construct_max_vertex_2 construct_max_vertex_2_object() const
-  {
+  Construct_max_vertex_2 construct_max_vertex_2_object() const {
     return Construct_max_vertex_2(this->m_base_traits->
                                   construct_max_vertex_2_object());
   }
@@ -321,8 +307,7 @@ public:
      * \param cv The curve.
      * \return The left endpoint.
      */
-    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const
-    {
+    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const {
       const Point_data& inf1 = p1.data();
       const Point_data& inf2 = p2.data();
 
@@ -390,8 +375,7 @@ public:
   };
 
   /*! Obtain a Construct_min_vertex_2 functor object. */
-  Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const
-  {
+  Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const {
     return Compare_y_near_boundary_2(this->m_base_traits->
                                      compare_y_near_boundary_2_object()
     );
@@ -429,8 +413,7 @@ public:
   };
 
   /*! Obtain a Construct_min_vertex_2 functor object. */
-  Parameter_space_in_y_2 parameter_space_in_y_2_object() const
-  {
+  Parameter_space_in_y_2 parameter_space_in_y_2_object() const {
     return Parameter_space_in_y_2(this->m_base_traits->
                                   parameter_space_in_y_2_object());
   }
@@ -462,8 +445,7 @@ public:
   };
 
   /*! Obtain a Construct_min_vertex_2 functor object. */
-  Compare_x_near_boundary_2 compare_x_near_boundary_2_object() const
-  {
+  Compare_x_near_boundary_2 compare_x_near_boundary_2_object() const {
     return Compare_x_near_boundary_2(this->m_base_traits->
                                      compare_x_near_boundary_2_object());
   }

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_agg_op.h

@@ -7,11 +7,12 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Ophir Setter    <ophir.setter@cs.tau.ac.il>
+// Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
+//             Ophir Setter     <ophir.setter@cs.tau.ac.il>
+//             Efi Fogel        <efifogel@gmail.com>
 
-#ifndef CGAL_BSO_2_GPS_AGG_OP_H
-#define CGAL_BSO_2_GPS_AGG_OP_H
+#ifndef CGAL_GPS_AGG_OP_H
+#define CGAL_GPS_AGG_OP_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
@@ -19,8 +20,8 @@
  *
  * The class Gps_agg_op is responsible for aggregated Boolean set operations
  * depending on a visitor template parameter.  It uses the surface-sweep
- * algorithm from the arrangement packages to overlay all the polygon sets, and
- * then it uses a BFS that determines which of the faces is contained in the
+ * algorithm from the surface-sweep package to overlay all the polygon sets, and
+ * then it uses a BFS that determines which of the faces are contained in the
  * result using the visitor.
  */
 
@@ -37,31 +38,31 @@
 
 namespace CGAL {
 
-template <typename Arrangement_, typename BfsVisitor>
+template <typename Arrangement_, typename BfsVisitor, template <typename, typename, typename> class SweepVisitor>
 class Gps_agg_op {
-  typedef Arrangement_                                  Arrangement_2;
-  typedef BfsVisitor                                    Bfs_visitor;
+  using Arrangement_2 = Arrangement_;
+  using Bfs_visitor = BfsVisitor;
 
-  typedef typename Arrangement_2::Traits_adaptor_2      Geometry_traits_2;
-  typedef typename Arrangement_2::Topology_traits       Topology_traits;
+  using Geometry_traits_2 = typename Arrangement_2::Traits_adaptor_2;
+  using Topology_traits = typename Arrangement_2::Topology_traits;
 
-  typedef Arrangement_2                                 Arr;
-  typedef Geometry_traits_2                             Gt2;
-  typedef Topology_traits                               Tt;
+  using Arr = Arrangement_2;
+  using Gt2 = Geometry_traits_2;
+  using Tt = Topology_traits;
 
-  typedef typename Gt2::Curve_const_iterator            Curve_const_iterator;
-  typedef Gps_agg_meta_traits<Arr>                      Mgt2;
-  typedef typename Mgt2::Curve_data                     Curve_data;
-  typedef typename Mgt2::X_monotone_curve_2             Meta_X_monotone_curve_2;
+  using Curve_const_iterator = typename Gt2::Curve_const_iterator;
+  using Mgt2 = Gps_agg_meta_traits<Arr>;
+  using Curve_data = typename Mgt2::Curve_data;
+  using Meta_X_monotone_curve_2 = typename Mgt2::X_monotone_curve_2;
 
-  typedef typename Arr::Halfedge_handle                 Halfedge_handle;
-  typedef typename Arr::Halfedge_iterator               Halfedge_iterator;
-  typedef typename Arr::Face_handle                     Face_handle;
-  typedef typename Arr::Edge_iterator                   Edge_iterator;
-  typedef typename Arr::Vertex_handle                   Vertex_handle;
-  typedef typename Arr::Allocator                       Allocator;
+  using Halfedge_handle = typename Arr::Halfedge_handle;
+  using Halfedge_iterator = typename Arr::Halfedge_iterator;
+  using Face_handle = typename Arr::Face_handle;
+  using Edge_iterator = typename Arr::Edge_iterator;
+  using Vertex_handle = typename Arr::Vertex_handle;
+  using Allocator = typename Arr::Allocator;
 
-  typedef std::pair<Arr*, std::vector<Vertex_handle> *> Arr_entry;
+  using Arr_entry = std::pair<Arr*, std::vector<Vertex_handle> *>;
 
   // We obtain a proper helper type from the topology traits of the arrangement.
   // However, the arrangement is parametrized with the Gt2 geometry traits,
@@ -70,21 +71,16 @@ class Gps_agg_op {
   // We cannot parameterized the arrangement with the Mgt2 geometry
   // traits to start with, because it extends the curve type with arrangement
   // dependent types. (It is parameterized with the arrangement type.)
-  typedef Indexed_event<Mgt2, Arr, Allocator>           Event;
-  typedef Arr_construction_subcurve<Mgt2, Event, Allocator>
-                                                        Subcurve;
-  typedef typename Tt::template Construction_helper<Event, Subcurve>
-                                                        Helper_tmp;
-  typedef typename Helper_tmp::template rebind<Mgt2, Arr, Event, Subcurve>::other
-                                                        Helper;
-  typedef Gps_agg_op_visitor<Helper, Arr>               Visitor;
-  typedef Gps_agg_op_surface_sweep_2<Arr, Visitor>      Surface_sweep_2;
+  using Event = Indexed_event<Mgt2, Arr, Allocator>;
+  using Subcurve = Arr_construction_subcurve<Mgt2, Event, Allocator>;
+  using Helper_tmp = typename Tt::template Construction_helper<Event, Subcurve>;
+  using Helper = typename Helper_tmp::template rebind<Mgt2, Arr, Event, Subcurve>::other;
+  using Visitor = SweepVisitor<Helper, Arr, Default>;
+  using Surface_sweep_2 = Gps_agg_op_surface_sweep_2<Arr, Visitor>;
 
-  typedef Unique_hash_map<Halfedge_handle, unsigned int>
-                                                        Edges_hash;
-
-  typedef Unique_hash_map<Face_handle, unsigned int>    Faces_hash;
-  typedef Gps_bfs_scanner<Arr, Bfs_visitor>             Bfs_scanner;
+  using Edges_hash = Unique_hash_map<Halfedge_handle, std::size_t>;
+  using Faces_hash = Unique_hash_map<Face_handle, std::size_t>;
+  using Bfs_scanner = Gps_bfs_scanner<Arr, Bfs_visitor>;
 
 protected:
   Arr* m_arr;
@@ -95,7 +91,7 @@ protected:
   Faces_hash m_faces_hash;      // maps face to its IC (inside count)
 
 public:
-  /*! Constructor. */
+  /*! constructs. */
   Gps_agg_op(Arr& arr, std::vector<Vertex_handle>& vert_vec, const Gt2& tr) :
     m_arr(&arr),
     m_traits(new Mgt2(tr)),
@@ -103,40 +99,40 @@ public:
     m_surface_sweep(m_traits, &m_visitor)
   {}
 
-  void sweep_arrangements(unsigned int lower, unsigned int upper,
-                          unsigned int jump, std::vector<Arr_entry>& arr_vec)
-  {
-    std::list<Meta_X_monotone_curve_2> curves_list;
-
-    unsigned int n_inf_pgn = 0; // number of infinite polygons (arrangement
+  std::pair<std::size_t, std::size_t>
+  prepare(std::size_t lower, std::size_t upper, std::size_t jump,
+          std::vector<Arr_entry>& arr_vec, std::list<Meta_X_monotone_curve_2>& curves_list) {
+    std::size_t n_inf_pgn = 0;  // number of infinite polygons (arrangement
                                 // with a contained unbounded face
-    unsigned int n_pgn = 0;     // number of polygons (arrangements)
-    unsigned int i;
-
-    for (i = lower; i <= upper; i += jump, ++n_pgn) {
+    std::size_t n_pgn = 0;      // number of polygons (arrangements)
+    for (auto i = lower; i <= upper; i += jump, ++n_pgn) {
       // The BFS scan (after the loop) starts in the reference face,
       // so we count the number of polygons that contain the reference face.
       Arr* arr = (arr_vec[i]).first;
       if (arr->reference_face()->contained()) ++n_inf_pgn;
 
-      Edge_iterator  itr = arr->edges_begin();
-      for(; itr != arr->edges_end(); ++itr) {
+      for (auto itr = arr->edges_begin(); itr != arr->edges_end(); ++itr) {
         // take only relevant edges (which separate between contained and
         // non-contained faces.
-        Halfedge_iterator he = itr;
-        if(he->face()->contained() == he->twin()->face()->contained())
-          continue;
-        if ((Arr_halfedge_direction)he->direction() == ARR_RIGHT_TO_LEFT)
-          he = he->twin();
+        Halfedge_handle he = itr;
+        if (he->face()->contained() == he->twin()->face()->contained()) continue;
+        if ((Arr_halfedge_direction)he->direction() == ARR_RIGHT_TO_LEFT) he = he->twin();
 
         Curve_data cv_data(arr, he, 1, 0);
         curves_list.push_back(Meta_X_monotone_curve_2(he->curve(), cv_data));
       }
     }
+    return std::make_pair(n_inf_pgn, n_pgn);
+  }
 
-    m_surface_sweep.sweep(curves_list.begin(), curves_list.end(),
-                          lower, upper, jump, arr_vec);
-
+  /*! sweeps the plane without interceptions.
+   */
+  void sweep_arrangements(std::size_t lower, std::size_t upper, std::size_t jump,
+                          std::vector<Arr_entry>& arr_vec) {
+    std::size_t n_inf_pgn, n_pgn;
+    std::list<Meta_X_monotone_curve_2> curves_list;
+    std::tie(n_inf_pgn, n_pgn) = prepare(lower, upper, jump, arr_vec, curves_list);
+    m_surface_sweep.sweep(curves_list.begin(), curves_list.end(), lower, upper, jump, arr_vec);
     m_faces_hash[m_arr->reference_face()] = n_inf_pgn;
     Bfs_visitor visitor(&m_edges_hash, &m_faces_hash, n_pgn);
     visitor.visit_ubf(m_arr->faces_begin(), n_inf_pgn);
@@ -145,7 +141,69 @@ public:
     visitor.after_scan(*m_arr);
   }
 
-  /*! Destruct.
+  /*! sweeps the plane without interceptions, but stop when an intersection occurs.
+   */
+  bool sweep_intercept_arrangements(std::size_t lower, std::size_t upper, std::size_t jump,
+                                    std::vector<Arr_entry>& arr_vec) {
+    std::size_t n_inf_pgn, n_pgn;
+    std::list<Meta_X_monotone_curve_2> curves_list;
+    std::tie(n_inf_pgn, n_pgn) = prepare(lower, upper, jump, arr_vec, curves_list);
+    auto res = m_surface_sweep.sweep_intercept(curves_list.begin(), curves_list.end(), lower, upper, jump, arr_vec);
+    if (res) return true;
+
+    m_faces_hash[m_arr->reference_face()] = n_inf_pgn;
+    Bfs_visitor visitor(&m_edges_hash, &m_faces_hash, n_pgn);
+    visitor.visit_ubf(m_arr->faces_begin(), n_inf_pgn);
+    Bfs_scanner scanner(visitor);
+    scanner.scan(*m_arr);
+    visitor.after_scan(*m_arr);
+    return false;
+  }
+
+  template <typename InputIterator>
+  std::size_t prepare2(InputIterator begin, InputIterator end, std::list<Meta_X_monotone_curve_2>& curves_list) {
+    std::size_t n_inf_pgn = 0;  // number of infinite polygons (arrangement
+                                // with a contained unbounded face
+    for (auto it = begin; it != end; ++it) {
+      // The BFS scan (after the loop) starts in the reference face,
+      // so we count the number of polygons that contain the reference face.
+      Arr* arr = it->first;
+      if (arr->reference_face()->contained()) ++n_inf_pgn;
+
+      for (auto ite = arr->edges_begin(); ite != arr->edges_end(); ++ite) {
+        // take only relevant edges (which separate between contained and
+        // non-contained faces.
+        Halfedge_handle he = ite;
+        if (he->face()->contained() == he->twin()->face()->contained()) continue;
+        if ((Arr_halfedge_direction)he->direction() == ARR_RIGHT_TO_LEFT) he = he->twin();
+
+        Curve_data cv_data(arr, he, 1, 0);
+        curves_list.push_back(Meta_X_monotone_curve_2(he->curve(), cv_data));
+      }
+    }
+    return n_inf_pgn;
+  }
+
+  /*! sweeps the plane without interceptions, but stop when an intersection occurs.
+   */
+  template <typename InputIterator>
+  bool sweep_intercept_arrangements2(InputIterator begin, InputIterator end) {
+    std::list<Meta_X_monotone_curve_2> curves_list;
+    auto n_inf_pgn = prepare2(begin, end, curves_list);
+    auto res = m_surface_sweep.sweep_intercept2(curves_list.begin(), curves_list.end(), begin, end);
+    if (res) return true;
+
+    m_faces_hash[m_arr->reference_face()] = n_inf_pgn;
+    std::size_t n_pgn = std::distance(begin, end);      // number of polygons (arrangements)
+    Bfs_visitor visitor(&m_edges_hash, &m_faces_hash, n_pgn);
+    visitor.visit_ubf(m_arr->faces_begin(), n_inf_pgn);
+    Bfs_scanner scanner(visitor);
+    scanner.scan(*m_arr);
+    visitor.after_scan(*m_arr);
+    return false;
+  }
+
+  /*! destructs.
    */
   ~Gps_agg_op() { delete m_traits; }
 };

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_agg_op_surface_sweep_2.h

@@ -7,11 +7,12 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Ron Wein        <wein@post.tau.ac.il>
+// Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
+//             Ron Wein         <wein@post.tau.ac.il>
+//             Efi Fogel        <efifogel@gmail.com>
 
-#ifndef CGAL_BSO_2_GSP_AGG_OP_SURFACE_SWEEP_2_H
-#define CGAL_BSO_2_GSP_AGG_OP_SURFACE_SWEEP_2_H
+#ifndef CGAL_GSP_AGG_OP_SURFACE_SWEEP_2_H
+#define CGAL_GSP_AGG_OP_SURFACE_SWEEP_2_H
 
 #include <vector>
 
@@ -27,34 +28,34 @@ namespace Ss2 = Surface_sweep_2;
 template <typename Arrangement_, typename Visitor_>
 class Gps_agg_op_surface_sweep_2 : public Ss2::Surface_sweep_2<Visitor_> {
 public:
-  typedef Arrangement_                                  Arrangement_2;
-  typedef Visitor_                                      Visitor;
+  using Arrangement_2 = Arrangement_;
+  using Visitor = Visitor_;
 
-  typedef typename Visitor::Geometry_traits_2           Geometry_traits_2;
+  using Geometry_traits_2 = typename Visitor::Geometry_traits_2;
 
-  typedef Arrangement_2                                 Arr;
-  typedef Geometry_traits_2                             Gt2;
+  using Arr = Arrangement_2;
+  using Gt2 = Geometry_traits_2;
 
-  typedef typename Gt2::Point_2                         Point_2;
-  typedef typename Gt2::X_monotone_curve_2              X_monotone_curve_2;
+  using Point_2 = typename Gt2::Point_2;
+  using X_monotone_curve_2 = typename Gt2::X_monotone_curve_2;
 
-  typedef typename Arr::Vertex_handle                   Vertex_handle;
-  typedef typename Arr::Halfedge_handle                 Halfedge_handle;
+  using Vertex_handle = typename Arr::Vertex_handle;
+  using Halfedge_handle = typename Arr::Halfedge_handle;
 
-  typedef std::pair<Arr*, std::vector<Vertex_handle> *> Arr_entry;
+  using Arr_entry = std::pair<Arr*, std::vector<Vertex_handle> *>;
 
-  typedef Ss2::Surface_sweep_2<Visitor>                 Base;
+  using Base = Ss2::Surface_sweep_2<Visitor>;
 
-  typedef typename Visitor::Event                       Event;
-  typedef typename Visitor::Subcurve                    Subcurve;
+  using Event = typename Visitor::Event;
+  using Subcurve = typename Visitor::Subcurve;
 
-  typedef typename Base::Event_queue_iterator           EventQueueIter;
-  typedef typename Event::Subcurve_iterator             EventCurveIter;
+  using EventQueueIter = typename Base::Event_queue_iterator;
+  using EventCurveIter = typename Event::Subcurve_iterator;
 
-  typedef typename Event::Attribute                     Attribute;
+  using Attribute = typename Event::Attribute;
 
-  typedef std::list<Subcurve*>                          SubCurveList;
-  typedef typename SubCurveList::iterator               SubCurveListIter;
+  using SubCurveList = std::list<Subcurve*>;
+  using SubCurveListIter = typename SubCurveList::iterator;
 
 public:
   /*! Constructor.
@@ -70,21 +71,17 @@ public:
     Base(traits, visitor)
   {}
 
-  /*! Perform the sweep. */
-  template <class CurveInputIterator>
-  void sweep(CurveInputIterator curves_begin, CurveInputIterator curves_end,
-             unsigned int lower, unsigned int upper, unsigned int jump,
-             std::vector<Arr_entry>& arr_vec)
-  {
+  template <typename CurveInputIterator>
+  void pre_process(CurveInputIterator curves_begin, CurveInputIterator curves_end,
+                   std::size_t lower, std::size_t upper, std::size_t jump,
+                   std::vector<Arr_entry>& arr_vec) {
     CGAL_assertion(this->m_queue->empty() && this->m_statusLine.size() == 0);
 
-    typedef Unique_hash_map<Vertex_handle, Event*>      Vertices_map;
-    typedef typename Gt2::Compare_xy_2                  Compare_xy_2;
+    using Vertices_map = Unique_hash_map<Vertex_handle, Event*>;
+    using Compare_xy_2 = typename Gt2::Compare_xy_2;
 
-    this->m_visitor->before_sweep();
     // Allocate all of the Subcurve objects as one block.
-    this->m_num_of_subCurves =
-      static_cast<unsigned int>(std::distance(curves_begin, curves_end));
+    this->m_num_of_subCurves = static_cast<unsigned int>(std::distance(curves_begin, curves_end));
     if (this->m_num_of_subCurves > 0)
       this->m_subCurves =
         this->m_subCurveAlloc.allocate(this->m_num_of_subCurves);
@@ -95,9 +92,9 @@ public:
     Vertices_map vert_map;
     Vertex_handle vh;
     Vertex_handle invalid_v;
-    unsigned int i = lower;
-    unsigned int n = static_cast<unsigned int>((arr_vec[i].second)->size());
-    unsigned int j;
+    std::size_t i = lower;
+    auto n = (arr_vec[i].second)->size();
+    std::size_t j;
     EventQueueIter q_iter;
     bool first = true;
     Attribute event_type;
@@ -135,7 +132,7 @@ public:
     for (i += jump; i <= upper; i += jump) {
       // Merge the vertices of the other vectors into the existing queue.
       q_iter = this->m_queue->begin();
-      n = static_cast<unsigned int>((arr_vec[i].second)->size());
+      n = (arr_vec[i].second)->size();
 
       for (j = 0; j < n && (vh = (*(arr_vec[i].second))[j]) != invalid_v; j++) {
         event_type = _type_of_vertex(vh);
@@ -170,7 +167,7 @@ public:
 
     // Go over all curves (which are associated with halfedges) and associate
     // them with the events we have just created.
-    unsigned int index = 0;
+    std::size_t index = 0;
     CurveInputIterator iter;
     Halfedge_handle he;
     Event* e_left;
@@ -194,9 +191,10 @@ public:
       }
 
       // Create the subcurve object.
-      typedef decltype(this->m_subCurveAlloc) Subcurve_alloc;
-      std::allocator_traits<Subcurve_alloc>::construct(this->m_subCurveAlloc, this->m_subCurves + index,
-                                      this->m_masterSubcurve);
+      using Subcurve_alloc = decltype(this->m_subCurveAlloc);
+      std::allocator_traits<Subcurve_alloc>::construct(this->m_subCurveAlloc,
+                                                       this->m_subCurves + index,
+                                                       this->m_masterSubcurve);
       (this->m_subCurves + index)->init(*iter);
       (this->m_subCurves + index)->set_left_event(e_left);
       (this->m_subCurves + index)->set_right_event(e_right);
@@ -204,13 +202,174 @@ public:
       e_right->add_curve_to_left(this->m_subCurves + index);
       this->_add_curve_to_right(e_left, this->m_subCurves + index);
     }
+  }
 
-    // Perform the sweep:
+  template <typename CurveInputIterator, typename InputIterator>
+  void pre_process2(CurveInputIterator curves_begin, CurveInputIterator curves_end,
+                    InputIterator begin, InputIterator end) {
+    CGAL_assertion(this->m_queue->empty() && this->m_statusLine.size() == 0);
+
+    using Vertices_map = Unique_hash_map<Vertex_handle, Event*>;
+    using Compare_xy_2 = typename Gt2::Compare_xy_2;
+
+    // Allocate all of the Subcurve objects as one block.
+    this->m_num_of_subCurves = std::distance(curves_begin, curves_end);
+    if (this->m_num_of_subCurves > 0)
+      this->m_subCurves =
+        this->m_subCurveAlloc.allocate(this->m_num_of_subCurves);
+
+
+    // Initialize the event queue using the vertices vectors. Note that these
+    // vertices are already sorted, we simply have to merge them
+    Vertices_map vert_map;
+    Vertex_handle vh;
+    Vertex_handle invalid_v;
+    // std::size_t i = lower;
+    auto it = begin;
+    auto n = it->second->size();
+    std::size_t j;
+    EventQueueIter q_iter;
+    bool first = true;
+    Attribute event_type;
+    Event* event;
+
+    for (j = 0; j < n && (vh = (*(it->second))[j]) != invalid_v; j++) {
+      // Insert the vertices of the first vector one after the other.
+      event_type = _type_of_vertex(vh);
+      if (event_type == Event::DEFAULT) continue;
+
+      event = this->_allocate_event(vh->point(), event_type,
+                                    ARR_INTERIOR, ARR_INTERIOR);
+      // \todo When the boolean set operations are extended to support
+      //       unbounded curves, we will need here a special treatment.
+
+      #ifndef CGAL_ARRANGEMENT_ON_SURFACE_2_H
+        event->set_finite();
+      #endif
+
+      if (! first) {
+        q_iter = this->m_queue->insert_after(q_iter, event);
+      }
+      else {
+        q_iter = this->m_queue->insert(event);
+        first = false;
+      }
+
+      vert_map[vh] = event;
+    }
+
+    Comparison_result res = LARGER;
+    Compare_xy_2 comp_xy = this->m_traits->compare_xy_2_object();
+    EventQueueIter q_end = this->m_queue->end();
+
+    for (++it; it != end; ++it) {
+      // Merge the vertices of the other vectors into the existing queue.
+      q_iter = this->m_queue->begin();
+      n = it->second->size();
+
+      for (j = 0; j < n && (vh = (*(it->second))[j]) != invalid_v; j++) {
+        event_type = _type_of_vertex(vh);
+        if (event_type == Event::DEFAULT) continue;
+
+        while ((q_iter != q_end) &&
+               (res = comp_xy(vh->point(), (*q_iter)->point())) == LARGER)
+        {
+          ++q_iter;
+        }
+
+        if (res == SMALLER || q_iter == q_end) {
+          event = this->_allocate_event(vh->point(), event_type,
+                                        ARR_INTERIOR, ARR_INTERIOR);
+          // \todo When the boolean set operations are extended to support
+          //       unbounded curves, we will need here a special treatment.
+
+#ifndef CGAL_ARRANGEMENT_ON_SURFACE_2_H
+          event->set_finite();
+#endif
+
+          this->m_queue->insert_before(q_iter, event);
+          vert_map[vh] = event;
+        }
+        else if (res == EQUAL) {
+          // In this case q_iter points to an event already associated with
+          // the vertex, so we just update the map:
+          vert_map[vh] = *q_iter;
+        }
+      }
+    }
+
+    // Go over all curves (which are associated with halfedges) and associate
+    // them with the events we have just created.
+    std::size_t index = 0;
+    CurveInputIterator iter;
+    Halfedge_handle he;
+    Event* e_left;
+    Event* e_right;
+
+    for (iter = curves_begin; iter != curves_end; ++iter, index++) {
+      // Get the events associated with the end-vertices of the current
+      // halfedge.
+      he = iter->data().halfedge();
+
+      CGAL_assertion(vert_map.is_defined(he->source()));
+      CGAL_assertion(vert_map.is_defined(he->target()));
+
+      if ((Arr_halfedge_direction)he->direction() == ARR_LEFT_TO_RIGHT) {
+        e_left = vert_map[he->source()];
+        e_right = vert_map[he->target()];
+      }
+      else {
+        e_left = vert_map[he->target()];
+        e_right = vert_map[he->source()];
+      }
+
+      // Create the subcurve object.
+      using Subcurve_alloc = decltype(this->m_subCurveAlloc);
+      std::allocator_traits<Subcurve_alloc>::construct(this->m_subCurveAlloc,
+                                                       this->m_subCurves + index,
+                                                       this->m_masterSubcurve);
+      (this->m_subCurves + index)->init(*iter);
+      (this->m_subCurves + index)->set_left_event(e_left);
+      (this->m_subCurves + index)->set_right_event(e_right);
+
+      e_right->add_curve_to_left(this->m_subCurves + index);
+      this->_add_curve_to_right(e_left, this->m_subCurves + index);
+    }
+  }
+
+  /*! Perform the sweep. */
+  template <typename CurveInputIterator>
+  void sweep(CurveInputIterator curves_begin, CurveInputIterator curves_end,
+             std::size_t lower, std::size_t upper, std::size_t jump, std::vector<Arr_entry>& arr_vec) {
+    this->m_visitor->before_sweep();
+    pre_process(curves_begin, curves_end,lower, upper, jump, arr_vec);
     this->_sweep();
     this->_complete_sweep();
     this->m_visitor->after_sweep();
+  }
 
-    return;
+  /*! Perform the sweep. */
+  template <typename CurveInputIterator>
+  bool sweep_intercept(CurveInputIterator curves_begin, CurveInputIterator curves_end,
+                       std::size_t lower, std::size_t upper, std::size_t jump, std::vector<Arr_entry>& arr_vec) {
+    this->m_visitor->before_sweep();
+    pre_process(curves_begin, curves_end,lower, upper, jump, arr_vec);
+    this->_sweep();
+    this->_complete_sweep();
+    this->m_visitor->after_sweep();
+    return this->m_visitor->found_intersection();
+  }
+
+  /*! Perform the sweep. */
+  template <typename CurveInputIterator, typename InputIterator>
+  bool sweep_intercept2(CurveInputIterator curves_begin, CurveInputIterator curves_end,
+                        InputIterator begin, InputIterator end) {
+    this->m_visitor->before_sweep();
+    pre_process2(curves_begin, curves_end, begin, end);
+    this->_sweep();
+    this->_complete_sweep();
+    this->m_visitor->after_sweep();
+    return this->m_visitor->found_intersection();
   }
 
 private:
@@ -218,8 +377,7 @@ private:
    * Check if the given vertex is an endpoint of an edge we are going
    * to use in the sweep.
    */
-  Attribute _type_of_vertex(Vertex_handle v)
-  {
+  Attribute _type_of_vertex(Vertex_handle v) {
     typename Arr::Halfedge_around_vertex_circulator first, circ;
 
     circ = first = v->incident_halfedges();
@@ -232,7 +390,6 @@ private:
         else return (Event::LEFT_END);
       }
       ++circ;
-
     } while (circ != first);
 
     // If we reached here, we should not keep this vertex.

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_agg_op_visitor.h

@@ -7,12 +7,12 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Ron Wein        <wein@post.tau.ac.il>
+// Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
+//             Ron Wein         <wein@post.tau.ac.il>
+//             Efi Fogel        <efifogel@gmail.com>
 
-#ifndef CGAL_BSO_2_GSP_AGG_OP_VISITOR_H
-#define CGAL_BSO_2_GSP_AGG_OP_VISITOR_H
+#ifndef CGAL_GSP_AGG_OP_VISITOR_H
+#define CGAL_GSP_AGG_OP_VISITOR_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
@@ -31,33 +31,29 @@ class Gps_agg_op_base_visitor :
     Helper_,
     typename Default::Get<Visitor_, Gps_agg_op_base_visitor<Helper_,
                                                             Arrangement_,
-                                                            Visitor_> >::type>
-{
+                                                            Visitor_>>::type> {
 public:
-  typedef Helper_                                       Helper;
-  typedef Arrangement_                                  Arrangement_2;
+  using Helper = Helper_;
+  using Arrangement_2 = Arrangement_;
 
-  typedef typename Helper::Geometry_traits_2            Geometry_traits_2;
-  typedef typename Helper::Event                        Event;
-  typedef typename Helper::Subcurve                     Subcurve;
+  using Geometry_traits_2 = typename Helper::Geometry_traits_2;
+  using Event = typename Helper::Event;
+  using Subcurve = typename Helper::Subcurve;
 
 private:
-  typedef Geometry_traits_2                             Gt2;
-  typedef Arrangement_2                                 Arr;
-
-  typedef Gps_agg_op_base_visitor<Helper, Arr, Visitor_>
-                                                        Self;
-  typedef typename Default::Get<Visitor_, Self>::type   Visitor;
-  typedef Arr_construction_ss_visitor<Helper, Visitor>  Base;
+  using Gt2 = Geometry_traits_2;
+  using Arr = Arrangement_2;
+  using Self = Gps_agg_op_base_visitor<Helper, Arr, Visitor_>;
+  using Visitor = typename Default::Get<Visitor_, Self>::type;
+  using Base = Arr_construction_ss_visitor<Helper, Visitor>;
 
 public:
-  typedef typename Arr::Halfedge_handle                 Halfedge_handle;
-  typedef typename Arr::Vertex_handle                   Vertex_handle;
-  typedef typename Gt2::X_monotone_curve_2              X_monotone_curve_2;
-  typedef typename Gt2::Point_2                         Point_2;
+  using Halfedge_handle = typename Arr::Halfedge_handle;
+  using Vertex_handle = typename Arr::Vertex_handle;
+  using X_monotone_curve_2 = typename Gt2::X_monotone_curve_2;
+  using Point_2 = typename Gt2::Point_2;
 
-  typedef Unique_hash_map<Halfedge_handle, unsigned int>
-                                                        Edges_hash;
+  using Edges_hash = Unique_hash_map<Halfedge_handle, std::size_t>;
 
 protected:
   Edges_hash* m_edges_hash; // maps halfedges to their BC (coundary counter)
@@ -72,8 +68,7 @@ public:
   // TODO add mpl-warning
 
   virtual Halfedge_handle insert_in_face_interior(const X_monotone_curve_2& cv,
-                                                  Subcurve* sc)
-  {
+                                                  Subcurve* sc) {
     Halfedge_handle he = Base::insert_in_face_interior(cv, sc);
     insert_edge_to_hash(he, cv);
     return he;
@@ -83,8 +78,7 @@ public:
                                              Halfedge_handle hhandle,
                                              Halfedge_handle prev,
                                              Subcurve* sc,
-                                             bool& new_face_created)
-  {
+                                             bool& new_face_created) {
     Halfedge_handle res_he =
       Base::insert_at_vertices(cv, hhandle, prev, sc, new_face_created);
     insert_edge_to_hash(res_he, cv);
@@ -93,8 +87,7 @@ public:
 
   virtual Halfedge_handle insert_from_right_vertex(const X_monotone_curve_2& cv,
                                                    Halfedge_handle he,
-                                                   Subcurve* sc)
-  {
+                                                   Subcurve* sc) {
     Halfedge_handle res_he = Base::insert_from_right_vertex(cv, he, sc);
     insert_edge_to_hash(res_he, cv);
     return res_he;
@@ -102,16 +95,14 @@ public:
 
   virtual Halfedge_handle insert_from_left_vertex(const X_monotone_curve_2& cv,
                                                   Halfedge_handle he,
-                                                  Subcurve* sc)
-  {
+                                                  Subcurve* sc) {
     Halfedge_handle res_he = Base::insert_from_left_vertex(cv, he, sc);
     insert_edge_to_hash(res_he, cv);
     return res_he;
   }
 
 private:
-  void insert_edge_to_hash(Halfedge_handle he, const X_monotone_curve_2& cv)
-  {
+  void insert_edge_to_hash(Halfedge_handle he, const X_monotone_curve_2& cv) {
     const Comparison_result he_dir =
       ((Arr_halfedge_direction)he->direction() == ARR_LEFT_TO_RIGHT) ?
       SMALLER : LARGER;
@@ -133,54 +124,53 @@ private:
 
 template <typename Helper_, typename Arrangement_, typename Visitor_ = Default>
 class Gps_agg_op_visitor :
-  public Gps_agg_op_base_visitor<Helper_, Arrangement_,
-                                 Gps_agg_op_visitor<Helper_, Arrangement_,
-                                                    Visitor_> >
-{
+  public Gps_agg_op_base_visitor<
+    Helper_, Arrangement_,
+    typename Default::Get<Visitor_,
+                          Gps_agg_op_visitor<Helper_, Arrangement_, Visitor_>>::type> {
 public:
-  typedef Helper_                                       Helper;
-  typedef Arrangement_                                  Arrangement_2;
+  using Helper = Helper_;
+  using Arrangement_2 = Arrangement_;
 
-  typedef typename Helper::Geometry_traits_2            Geometry_traits_2;
-  typedef typename Helper::Event                        Event;
-  typedef typename Helper::Subcurve                     Subcurve;
+  using Geometry_traits_2 = typename Helper::Geometry_traits_2;
+  using Event = typename Helper::Event;
+  using Subcurve = typename Helper::Subcurve;
 
 private:
-  typedef Geometry_traits_2                             Gt2;
-  typedef Arrangement_2                                 Arr;
+  using Gt2 = Geometry_traits_2;
+  using Arr = Arrangement_2;
 
-  typedef Gps_agg_op_visitor<Helper, Arr, Visitor_>     Self;
-  typedef typename Default::Get<Visitor_, Self>::type   Visitor;
-  typedef Gps_agg_op_base_visitor<Helper, Arr, Visitor> Base;
+  using Self = Gps_agg_op_visitor<Helper, Arr, Visitor_>;
+  using Visitor = typename Default::Get<Visitor_, Self>::type;
+  using Base = Gps_agg_op_base_visitor<Helper, Arr, Visitor>;
 
 public:
-  typedef typename Base::Halfedge_handle                Halfedge_handle;
-  typedef typename Base::Vertex_handle                  Vertex_handle;
-  typedef typename Gt2::X_monotone_curve_2              X_monotone_curve_2;
-  typedef typename Gt2::Point_2                         Point_2;
+  using Edges_hash = typename Base::Edges_hash;
+  using Halfedge_handle = typename Base::Halfedge_handle;
+  using Vertex_handle = typename Base::Vertex_handle;
+  using X_monotone_curve_2 = typename Gt2::X_monotone_curve_2;
+  using Point_2 = typename Gt2::Point_2;
 
 protected:
-  unsigned int m_event_count;                   // The number of events so far.
+  std::size_t m_event_count;                    // The number of events so far.
   std::vector<Vertex_handle>* m_vertices_vec;   // The vertices, sorted in
                                                 // ascending order.
 
 public:
-  Gps_agg_op_visitor(Arr* arr, typename Base::Edges_hash* hash,
+  Gps_agg_op_visitor(Arr* arr, Edges_hash* hash,
                      std::vector<Vertex_handle>* vertices_vec) :
     Base(arr, hash),
     m_event_count(0),
     m_vertices_vec(vertices_vec)
   {}
 
-  void before_handle_event(Event* event)
-  {
+  void before_handle_event(Event* event) {
     event->set_index(m_event_count);
     m_event_count++;
   }
 
   virtual Halfedge_handle
-  insert_in_face_interior(const X_monotone_curve_2& cv, Subcurve* sc)
-  {
+  insert_in_face_interior(const X_monotone_curve_2& cv, Subcurve* sc) {
     Halfedge_handle res_he = Base::insert_in_face_interior(cv, sc);
 
     // We now have a halfedge whose source vertex is associated with the
@@ -198,8 +188,7 @@ public:
 
   virtual Halfedge_handle insert_from_right_vertex(const X_monotone_curve_2& cv,
                                                    Halfedge_handle he,
-                                                   Subcurve* sc)
-  {
+                                                   Subcurve* sc) {
     Halfedge_handle res_he = Base::insert_from_right_vertex(cv, he, sc);
 
     // We now have a halfedge whose target vertex is associated with the
@@ -213,9 +202,8 @@ public:
 
   virtual Halfedge_handle insert_from_left_vertex(const X_monotone_curve_2& cv,
                                                   Halfedge_handle he,
-                                                  Subcurve* sc)
-  {
-    Halfedge_handle  res_he = Base::insert_from_left_vertex(cv, he, sc);
+                                                  Subcurve* sc) {
+    Halfedge_handle res_he = Base::insert_from_left_vertex(cv, he, sc);
 
     // We now have a halfedge whose target vertex is associated with the
     // current event(we have already dealt with its source vertex).
@@ -223,18 +211,16 @@ public:
 
     CGAL_assertion((Arr_halfedge_direction)res_he->direction() ==
                     ARR_LEFT_TO_RIGHT);
-    _insert_vertex (curr_event, res_he->target());
+    _insert_vertex(curr_event, res_he->target());
     return res_he;
   }
 
 private:
-  void _insert_vertex(const Event* event, Vertex_handle v)
-  {
-    const unsigned int index = event->index();
+  void _insert_vertex(const Event* event, Vertex_handle v) {
+    const auto index = event->index();
     if (index >= m_vertices_vec->size()) m_vertices_vec->resize(2 * (index + 1));
     (*m_vertices_vec)[index] = v;
   }
-
 };
 
 } // namespace CGAL

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_bfs_base_visitor.h

@@ -8,90 +8,83 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Ophir Setter    <ophir.setter@cs.tau.ac.il>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Ophir Setter    <ophir.setter@cs.tau.ac.il>
 
 #ifndef CGAL_GPS_BPS_BASE_VISITOR_H
 #define CGAL_GPS_BPS_BASE_VISITOR_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
-
 #include <CGAL/Unique_hash_map.h>
 
 namespace CGAL {
 
 //! Gps_bfs_base_visitor
 /*! This is a base class for all visitors that are responsible for merging
-    polygon sets.
-    We use DerivedVisitor for static polymorphism for using contained_criteria
-    which determines if we should mark the face as contained given the inside
-    count of the face.
-*/
-template <class Arrangement_, class DerivedVisitor>
-class Gps_bfs_base_visitor
-{
-  typedef  Arrangement_                                  Arrangement;
-  typedef typename Arrangement::Face_iterator            Face_iterator;
-  typedef typename Arrangement::Halfedge_iterator        Halfedge_iterator;
+ * polygon sets.
+ * We use DerivedVisitor for static polymorphism for using contained_criteria
+ * which determines if we should mark the face as contained given the inside
+ * count of the face.
+ */
+template <typename Arrangement_, typename DerivedVisitor>
+class Gps_bfs_base_visitor {
+  using Arrangement = Arrangement_;
+  using Face_iterator = typename Arrangement::Face_iterator;
+  using Halfedge_iterator = typename Arrangement::Halfedge_iterator;
+
 public:
-  typedef Unique_hash_map<Halfedge_iterator, unsigned int> Edges_hash;
-  typedef Unique_hash_map<Face_iterator, unsigned int>     Faces_hash;
+  using Edges_hash = Unique_hash_map<Halfedge_iterator, std::size_t>;
+  using Faces_hash = Unique_hash_map<Face_iterator, std::size_t>;
 
 protected:
-  Edges_hash*    m_edges_hash;
-  Faces_hash*    m_faces_hash;
-  unsigned int   m_num_of_polygons; // number of polygons
+  Edges_hash* m_edges_hash;
+  Faces_hash* m_faces_hash;
+  std::size_t m_num_of_polygons; // number of polygons
 
 public:
-
   Gps_bfs_base_visitor(Edges_hash* edges_hash,
                        Faces_hash* faces_hash,
-                       unsigned int n_pgn):
+                       std::size_t n_pgn):
     m_edges_hash(edges_hash),
     m_faces_hash(faces_hash),
     m_num_of_polygons(n_pgn)
   {}
 
-
-    //! discovered_face
-/*! discovered_face is called by Gps_bfs_scanner when it reveals a new face
-    during a BFS scan. In the BFS traversal we are going from old_face to
-    new_face through the half-edge he.
-  \param old_face The face that was already revealed
-  \param new_face The face that we have just now revealed
-  \param he The half-edge that is used to traverse between them.
-*/
+  //! discovered_face
+  /*! discovered_face is called by Gps_bfs_scanner when it reveals a new face
+   * during a BFS scan. In the BFS traversal we are going from old_face to
+   * new_face through the half-edge he.
+   * \param old_face The face that was already revealed
+   * \param new_face The face that we have just now revealed
+   * \param he The half-edge that is used to traverse between them.
+   */
   void discovered_face(Face_iterator old_face,
                        Face_iterator new_face,
-                       Halfedge_iterator he)
-  {
-    unsigned int ic = compute_ic(old_face, new_face, he);
+                       Halfedge_iterator he) {
+    std::size_t ic = compute_ic(old_face, new_face, he);
 
     if (static_cast<DerivedVisitor*>(this)->contained_criteria(ic))
       new_face->set_contained(true);
   }
 
   // mark the unbounded_face (true iff contained)
-  void visit_ubf(Face_iterator ubf, unsigned int ubf_ic)
-  {
+  void visit_ubf(Face_iterator ubf, std::size_t ubf_ic) {
     CGAL_assertion(ubf->is_unbounded());
-    if(static_cast<DerivedVisitor*>(this)->contained_criteria(ubf_ic))
+    if (static_cast<DerivedVisitor*>(this)->contained_criteria(ubf_ic))
       ubf->set_contained(true);
   }
 
 protected:
-
   // compute the inside count of a face
-  unsigned int compute_ic(Face_iterator f1,
-                          Face_iterator f2,
-                          Halfedge_iterator he)
-  {
+  std::size_t compute_ic(Face_iterator f1,
+                         Face_iterator f2,
+                         Halfedge_iterator he) {
     CGAL_assertion(m_edges_hash->is_defined(he) &&
                    m_edges_hash->is_defined(he->twin()) &&
                    m_faces_hash->is_defined(f1) &&
-                   !m_faces_hash->is_defined(f2));
-    unsigned int ic_f2 =
+                   ! m_faces_hash->is_defined(f2));
+    std::size_t ic_f2 =
       (*m_faces_hash)[f1] - (*m_edges_hash)[he] + (*m_edges_hash)[he->twin()];
     (*m_faces_hash)[f2] = ic_f2;
 

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_bfs_intersection_visitor.h

@@ -7,59 +7,50 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
-
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Ophir Setter    <ophir.setter@cs.tau.ac.il>
-
+// Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
+//             Ophir Setter     <ophir.setter@cs.tau.ac.il>
+//             Efi Fogel        <efifogel@gmail.com>
 
 #ifndef CGAL_GPS_BFS_INTERSECTION_VISITOR_H
 #define CGAL_GPS_BFS_INTERSECTION_VISITOR_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
-
 #include <CGAL/Boolean_set_operations_2/Gps_bfs_base_visitor.h>
 
 namespace CGAL {
 
-template <class Arrangement_>
+template <typename Arrangement_>
 class Gps_bfs_intersection_visitor :
-public Gps_bfs_base_visitor<Arrangement_, Gps_bfs_intersection_visitor<Arrangement_> >
-{
-  typedef  Arrangement_                                  Arrangement;
-  typedef typename Arrangement::Face_iterator            Face_iterator;
-  typedef typename Arrangement::Halfedge_iterator        Halfedge_iterator;
-  typedef Gps_bfs_intersection_visitor<Arrangement>      Self;
-  typedef Gps_bfs_base_visitor<Arrangement, Self>        Base;
-  typedef typename Base::Edges_hash                      Edges_hash;
-  typedef typename Base::Faces_hash                      Faces_hash;
-
+    public Gps_bfs_base_visitor<Arrangement_, Gps_bfs_intersection_visitor<Arrangement_>> {
+  using Arrangement = Arrangement_;
+  using Face_iterator = typename Arrangement::Face_iterator;
+  using Halfedge_iterator = typename Arrangement::Halfedge_iterator;
+  using Self = Gps_bfs_intersection_visitor<Arrangement>;
+  using Base = Gps_bfs_base_visitor<Arrangement, Self>;
+  using Edges_hash = typename Base::Edges_hash;
+  using Faces_hash = typename Base::Faces_hash;
 
 public:
-
   Gps_bfs_intersection_visitor(Edges_hash* edges_hash,
                                Faces_hash* faces_hash,
-                               unsigned int n_polygons):
+                               std::size_t n_polygons):
     Base(edges_hash, faces_hash, n_polygons)
   {}
 
-
-    //! contained_criteria
-/*! contained_criteria is used to the determine if the face which has
-  inside count should be marked as contained.
-  \param ic the inner count of the talked-about face.
-  \return true if the face of ic, otherwise false.
-*/
-  bool contained_criteria(unsigned int ic)
-  {
+  //! contained_criteria
+  /*! contained_criteria is used to the determine if the face which has
+   * inside count should be marked as contained.
+   * \param ic the inner count of the talked-about face.
+   * \return true if the face of ic, otherwise false.
+   */
+  bool contained_criteria(std::size_t ic) {
     // intersection means that all polygons contain the face.
     CGAL_assertion(ic <= this->m_num_of_polygons);
     return (ic == this->m_num_of_polygons);
   }
 
-  void after_scan(Arrangement&)
-  {}
+  void after_scan(Arrangement&) {}
 };
 
 } //namespace CGAL

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_bfs_join_visitor.h

@@ -8,52 +8,46 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Ophir Setter    <ophir.setter@cs.tau.ac.il>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Ophir Setter    <ophir.setter@cs.tau.ac.il>
 
 #ifndef CGAL_GPS_BFS_JOIN_VISITOR_H
 #define CGAL_GPS_BFS_JOIN_VISITOR_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
-
 #include <CGAL/Boolean_set_operations_2/Gps_bfs_base_visitor.h>
 
 namespace CGAL {
 
-template <class Arrangement_>
+template <typename Arrangement_>
 class Gps_bfs_join_visitor :
-public Gps_bfs_base_visitor<Arrangement_, Gps_bfs_join_visitor<Arrangement_> >
-{
-  typedef  Arrangement_                                  Arrangement;
-  typedef typename Arrangement::Face_iterator            Face_iterator;
-  typedef typename Arrangement::Halfedge_iterator        Halfedge_iterator;
-  typedef Gps_bfs_join_visitor<Arrangement>              Self;
-  typedef Gps_bfs_base_visitor<Arrangement, Self>        Base;
-  typedef typename Base::Edges_hash                      Edges_hash;
-  typedef typename Base::Faces_hash                      Faces_hash;
+public Gps_bfs_base_visitor<Arrangement_, Gps_bfs_join_visitor<Arrangement_>> {
+  using Arrangement = Arrangement_;
+  using Face_iterator = typename Arrangement::Face_iterator;
+  using Halfedge_iterator = typename Arrangement::Halfedge_iterator;
+  using Self = Gps_bfs_join_visitor<Arrangement>;
+  using Base = Gps_bfs_base_visitor<Arrangement, Self>;
+  using Edges_hash = typename Base::Edges_hash;
+  using Faces_hash = typename Base::Faces_hash;
 
 public:
-
-  Gps_bfs_join_visitor(Edges_hash* edges_hash, Faces_hash* faces_hash, unsigned int n_pgn):
+  Gps_bfs_join_visitor(Edges_hash* edges_hash, Faces_hash* faces_hash, std::size_t n_pgn):
     Base(edges_hash, faces_hash, n_pgn)
   {}
 
-    //! contained_criteria
-/*! contained_criteria is used to the determine if the face which has
-  inside count should be marked as contained.
-  \param ic the inner count of the talked-about face.
-  \return true if the face of ic, otherwise false.
-*/
-  bool contained_criteria(unsigned int ic)
-  {
+  //! contained_criteria
+  /*! contained_criteria is used to the determine if the face which has
+   * inside count should be marked as contained.
+   * \param ic the inner count of the talked-about face.
+   * \return true if the face of ic, otherwise false.
+   */
+  bool contained_criteria(std::size_t ic) {
     // at least one polygon contains the face.
     return (ic > 0);
   }
 
-  void after_scan(Arrangement&)
-  {}
-
+  void after_scan(Arrangement&) {}
 };
 
 } //namespace CGAL

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_bfs_xor_visitor.h

@@ -8,8 +8,8 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Ophir Setter    <ophir.setter@cs.tau.ac.il>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Ophir Setter    <ophir.setter@cs.tau.ac.il>
 
 #ifndef CGAL_GPS_BFS_XOR_VISITOR_H
 #define CGAL_GPS_BFS_XOR_VISITOR_H
@@ -21,73 +21,61 @@
 
 namespace CGAL {
 
-template <class Arrangement_>
+template <typename Arrangement_>
 class Gps_bfs_xor_visitor :
-public Gps_bfs_base_visitor<Arrangement_, Gps_bfs_xor_visitor<Arrangement_> >
-{
-  typedef  Arrangement_                                  Arrangement;
-  typedef typename Arrangement::Face_iterator            Face_iterator;
-  typedef typename Arrangement::Halfedge_iterator        Halfedge_iterator;
-  typedef Gps_bfs_xor_visitor<Arrangement>               Self;
-  typedef Gps_bfs_base_visitor<Arrangement, Self>        Base;
-  typedef typename Base::Edges_hash                      Edges_hash;
-  typedef typename Base::Faces_hash                      Faces_hash;
+    public Gps_bfs_base_visitor<Arrangement_, Gps_bfs_xor_visitor<Arrangement_>> {
+  using Arrangement = Arrangement_;
+  using Face_iterator = typename Arrangement::Face_iterator;
+  using Halfedge_iterator = typename Arrangement::Halfedge_iterator;
+  using Self = Gps_bfs_xor_visitor<Arrangement>;
+  using Base = Gps_bfs_base_visitor<Arrangement, Self>;
+  using Edges_hash = typename Base::Edges_hash;
+  using Faces_hash = typename Base::Faces_hash;
 
 public:
-
   Gps_bfs_xor_visitor(Edges_hash* edges_hash, Faces_hash* faces_hash,
-                      unsigned int n_pgn) :
+                      std::size_t n_pgn) :
     Base(edges_hash, faces_hash, n_pgn)
   {}
 
-    //! contained_criteria
+  //! contained_criteria
 /*! contained_criteria is used to the determine if the face which has
   inside count should be marked as contained.
   \param ic the inner count of the talked-about face.
   \return true if the face of ic, otherwise false.
 */
-  bool contained_criteria(unsigned int ic)
-  {
+  bool contained_criteria(std::size_t ic) {
     // xor means odd number of polygons.
     return (ic % 2) == 1;
   }
 
   //! after_scan postprocessing after bfs scan.
-/*! The function fixes some of the curves, to be in the same direction as the
-    half-edges.
-
-  \param arr The given arrangement.
-*/
-  void after_scan(Arrangement& arr)
-  {
-    typedef typename Arrangement::Geometry_traits_2 Traits;
-    typedef typename Traits::Compare_endpoints_xy_2 Compare_endpoints_xy_2;
-    typedef typename Traits::Construct_opposite_2   Construct_opposite_2;
-    typedef typename Traits::X_monotone_curve_2     X_monotone_curve_2;
-    typedef typename Arrangement::Edge_iterator     Edge_iterator;
+  /*! The function fixes some of the curves, to be in the same direction as the
+   * half-edges.
+   *
+   * \param arr The given arrangement.
+   */
+  void after_scan(Arrangement& arr) {
+    using Traits = typename Arrangement::Geometry_traits_2;
+    using X_monotone_curve_2 = typename Traits::X_monotone_curve_2;
 
     Traits tr;
-    Compare_endpoints_xy_2 cmp_endpoints =
-      tr.compare_endpoints_xy_2_object();
-    Construct_opposite_2 ctr_opp = tr.construct_opposite_2_object();
+    auto cmp_endpoints = tr.compare_endpoints_xy_2_object();
+    auto ctr_opp = tr.construct_opposite_2_object();
 
-    for(Edge_iterator eit = arr.edges_begin();
-        eit != arr.edges_end();
-        ++eit)
-    {
-      Halfedge_iterator         he = eit;
+    for (auto eit = arr.edges_begin(); eit != arr.edges_end(); ++eit) {
+      Halfedge_iterator he = eit;
       const X_monotone_curve_2& cv = he->curve();
-      const bool                is_cont = he->face()->contained();
-      const Comparison_result   he_res =
+      const bool is_cont = he->face()->contained();
+      const Comparison_result he_res =
         ((Arr_halfedge_direction)he->direction() == ARR_LEFT_TO_RIGHT) ?
-                                         SMALLER : LARGER;
+        SMALLER : LARGER;
       const bool has_same_dir = (cmp_endpoints(cv) == he_res);
 
       if ((is_cont && !has_same_dir) || (!is_cont && has_same_dir))
         arr.modify_edge(he, ctr_opp(cv));
     }
   }
-
 };
 
 } //namespace CGAL

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_do_intersect_agg_op_visitor.h

@@ -0,0 +1,93 @@
+// Copyright (c) 2005  Tel-Aviv University (Israel).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
+//
+// Author(s) : Efi Fogel        <efifogel@gmail.com>
+
+#ifndef CGAL_GSP_DO_INTERSECT_AGG_OP_VISITOR_H
+#define CGAL_GSP_DO_INTERSECT_AGG_OP_VISITOR_H
+
+#include <vector>
+
+#include <CGAL/license/Boolean_set_operations_2.h>
+#include <CGAL/Boolean_set_operations_2/Gps_agg_op_visitor.h>
+#include <CGAL/Default.h>
+
+namespace CGAL {
+
+template <typename Helper_, typename Arrangement_, typename Visitor_ = Default>
+class Gps_do_intersect_agg_op_visitor :
+  public Gps_agg_op_visitor<
+    Helper_, Arrangement_,
+    typename Default::Get<Visitor_, Gps_do_intersect_agg_op_visitor<Helper_, Arrangement_, Visitor_>>::type> {
+public:
+  using Helper = Helper_;
+  using Arrangement_2 = Arrangement_;
+  using Geometry_traits_2 = typename Helper::Geometry_traits_2;
+  using Event = typename Helper::Event;
+  using Subcurve = typename Helper::Subcurve;
+
+private:
+  using Gt2 = Geometry_traits_2;
+  using Arr = Arrangement_2;
+  using Self = Gps_do_intersect_agg_op_visitor<Helper, Arr, Visitor_>;
+  using Visitor = typename Default::Get<Visitor_, Self>::type;
+  using Base = Gps_agg_op_visitor<Helper, Arr, Visitor>;
+
+protected:
+  bool m_found_x;
+
+public:
+  using Edges_hash = typename Base::Edges_hash;
+  using Vertex_handle = typename Base::Vertex_handle;
+  using Status_line_iterator = typename Base::Status_line_iterator;
+  using X_monotone_curve_2 = typename Base::X_monotone_curve_2;
+  using Point_2 = typename Base::Point_2;
+  using Multiplicity = typename Base::Multiplicity;
+
+  Gps_do_intersect_agg_op_visitor(Arr* arr, Edges_hash* hash,
+                                  std::vector<Vertex_handle>* vertices_vec) :
+    Base(arr, hash, vertices_vec),
+    m_found_x(false)
+  {}
+
+  /*! Update an event that corresponds to a curve endpoint. */
+  void update_event(Event* e, const Point_2& end_point, const X_monotone_curve_2& cv, Arr_curve_end cv_end, bool is_new)
+  { Base::update_event(e, end_point, cv, cv_end, is_new); }
+
+  /*! Update an event that corresponds to a curve endpoint */
+  void update_event(Event* e, const X_monotone_curve_2& cv, Arr_curve_end cv_end, bool is_new )
+  { Base::update_event(e, cv, cv_end, is_new); }
+
+  /*! Update an event that corresponds to a curve endpoint */
+  void update_event(Event* e, const Point_2& p, bool is_new)
+  { Base::update_event(e, p, is_new); }
+
+  /*! Update an event that corresponds to an intersection */
+  void update_event(Event* e, Subcurve* sc) { Base::update_event(e, sc); }
+
+  /*! Update an event that corresponds to an intersection between curves */
+  void update_event(Event* e, Subcurve* sc1, Subcurve* sc2, bool is_new, Multiplicity multiplicity) {
+    if ((multiplicity % 2) == 1) m_found_x = true;
+    Base::update_event(e, sc1, sc2, is_new, multiplicity);
+  }
+
+  //!
+  bool after_handle_event(Event* e, Status_line_iterator iter, bool flag) {
+    auto res = Base::after_handle_event(e, iter, flag);
+    if (m_found_x) this->surface_sweep()->stop_sweep();
+    return res;
+  }
+
+  /*! Getter */
+  bool found_intersection() { return m_found_x; }
+};
+
+} // namespace CGAL
+
+#endif

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_do_intersect_functor.h

@@ -15,112 +15,61 @@
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
-
 namespace CGAL {
 
-template <class Arrangement_>
-class Gps_do_intersect_functor
-{
+template <typename Arrangement_>
+class Gps_do_intersect_functor {
 public:
+  using Arrangement_2 = Arrangement_;
 
-  typedef Arrangement_                                    Arrangement_2;
+  using Face_const_handle = typename Arrangement_2::Face_const_handle;
+  using Vertex_const_handle = typename Arrangement_2::Vertex_const_handle;
+  using Halfedge_const_handle = typename Arrangement_2::Halfedge_const_handle;
 
-  typedef typename Arrangement_2::Face_const_handle       Face_const_handle;
-  typedef typename Arrangement_2::Vertex_const_handle     Vertex_const_handle;
-  typedef typename Arrangement_2::Halfedge_const_handle   Halfedge_const_handle;
-
-  typedef typename Arrangement_2::Face_handle        Face_handle;
-  typedef typename Arrangement_2::Halfedge_handle    Halfedge_handle;
-  typedef typename Arrangement_2::Vertex_handle      Vertex_handle;
+  using Face_handle = typename Arrangement_2::Face_handle;
+  using Halfedge_handle = typename Arrangement_2::Halfedge_handle;
+  using Vertex_handle = typename Arrangement_2::Vertex_handle;
 
   // default constructor
-  Gps_do_intersect_functor() : m_found_reg_intersection(false),
-                               m_found_boudary_intersection(false)
-
+  Gps_do_intersect_functor() :
+    m_found_reg_intersection(false),
+    m_found_boudary_intersection(false)
   {}
 
-   void create_face (Face_const_handle f1,
-                     Face_const_handle f2,
-                     Face_handle )
-  {
-    if(f1->contained() && f2->contained())
-      // found intersection
-      m_found_reg_intersection = true;
-  }
+  void create_face(Face_const_handle f1, Face_const_handle f2, Face_handle)
+  { if (f1->contained() && f2->contained()) m_found_reg_intersection = true; }
 
+  void create_vertex(Vertex_const_handle, Vertex_const_handle, Vertex_handle)
+  { m_found_boudary_intersection = true; }
 
-  void create_vertex(Vertex_const_handle ,
-                     Vertex_const_handle ,
-                     Vertex_handle  )
-  {
-    m_found_boudary_intersection = true;
-  }
+  void create_vertex(Vertex_const_handle, Halfedge_const_handle, Vertex_handle)
+  { m_found_boudary_intersection = true; }
 
-  void create_vertex(Vertex_const_handle ,
-                     Halfedge_const_handle ,
-                     Vertex_handle )
-  {
-    m_found_boudary_intersection = true;
-  }
+  void create_vertex(Halfedge_const_handle, Vertex_const_handle, Vertex_handle)
+  { m_found_boudary_intersection = true; }
 
-  void create_vertex(Halfedge_const_handle ,
-                     Vertex_const_handle ,
-                     Vertex_handle )
-  {
-    m_found_boudary_intersection = true;
-  }
+  void create_vertex(Halfedge_const_handle, Halfedge_const_handle, Vertex_handle) {}
 
-  void create_vertex(Halfedge_const_handle ,
-                     Halfedge_const_handle ,
-                     Vertex_handle )
-  {}
+  void create_vertex(Face_const_handle, Vertex_const_handle, Vertex_handle) {}
 
+  void create_vertex(Vertex_const_handle, Face_const_handle, Vertex_handle) {}
 
-  void create_vertex(Face_const_handle ,
-                     Vertex_const_handle ,
-                     Vertex_handle )
-  {}
+  void create_edge(Halfedge_const_handle, Halfedge_const_handle, Halfedge_handle)
+  { m_found_boudary_intersection = true; }
 
-  void create_vertex(Vertex_const_handle ,
-                     Face_const_handle ,
-                     Vertex_handle )
-  {}
+  void create_edge(Halfedge_const_handle, Face_const_handle, Halfedge_handle) {}
 
-  void create_edge(Halfedge_const_handle ,
-                   Halfedge_const_handle ,
-                   Halfedge_handle )
-  {
-    m_found_boudary_intersection = true;
-  }
+  void create_edge(Face_const_handle, Halfedge_const_handle, Halfedge_handle) {}
 
-  void create_edge(Halfedge_const_handle ,
-                   Face_const_handle ,
-                   Halfedge_handle )
-  {}
+  bool found_reg_intersection() const { return m_found_reg_intersection; }
 
-  void create_edge(Face_const_handle ,
-                   Halfedge_const_handle ,
-                   Halfedge_handle )
-  {}
+  bool found_boundary_intersection() const { return m_found_boudary_intersection; }
 
-
-  bool found_reg_intersection() const
-  {
-    return m_found_reg_intersection;
-  }
-
-  bool found_boundary_intersection() const
-  {
-    return m_found_boudary_intersection;
-  }
-
-  protected:
-
-    bool m_found_reg_intersection;
-    bool m_found_boudary_intersection;
+protected:
+  bool m_found_reg_intersection;
+  bool m_found_boudary_intersection;
 };
 
-
 } //namespace CGAL
 
 #endif

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_merge.h

@@ -7,15 +7,17 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
+// Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
+//             Efi Fogel        <efifogel@gmail.com>
 
 #ifndef CGAL_GPS_MERGE_H
 #define CGAL_GPS_MERGE_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
-
 #include <CGAL/Boolean_set_operations_2/Gps_agg_op.h>
+#include <CGAL/Boolean_set_operations_2/Gps_agg_op_visitor.h>
+#include <CGAL/Boolean_set_operations_2/Gps_do_intersect_agg_op_visitor.h>
 #include <CGAL/Boolean_set_operations_2/Gps_bfs_join_visitor.h>
 #include <CGAL/Boolean_set_operations_2/Gps_bfs_xor_visitor.h>
 #include <CGAL/Boolean_set_operations_2/Gps_bfs_intersection_visitor.h>
@@ -23,50 +25,40 @@
 
 namespace CGAL {
 
-/*!
-  \file   Gps_merge.h
-  \brief  This file contains classes that are responsible for merging
-          two sets of polygons in the divide-and-conquer algorithm.
-          The file contains 3 mergers: Join_merge, Intersection_merge and
-          Xor_merge. Join_merge is used when we want to merge the two sets,
-          Intersection_merge is used for intersection, and Xor_merge is used
-          for symmetric difference.
-*/
-
-//! Base_merge
-/*! Base_merge is the base class for all merger classes.
-    All merges used BFS algorithm with a different visitor when discovering
-    a new face.
+/*! \file Gps_merge.h
+ *
+ * This file contains classes that are responsible for merging two sets of
+ * polygons in the divide-and-conquer algorithm.  The file contains 3 mergers:
+ * Join_merge, Intersection_merge and Xor_merge. Join_merge is used when we want
+ * to merge the two sets, Intersection_merge is used for intersection, and
+ * Xor_merge is used for symmetric difference.
  */
-template <class Arrangement_, class Visitor_>
-class Base_merge
-{
-  typedef Arrangement_                                Arrangement_2;
-  typedef Visitor_                                    Visitor;
-  typedef typename Arrangement_2::Vertex_handle       Vertex_handle;
-  typedef std::pair<Arrangement_2 *,
-                    std::vector<Vertex_handle> *>     Arr_entry;
+
+/*! Base_merge
+ * Base_merge is the base class for all merger classes.
+ * All merges used BFS algorithm with a different visitor when discovering
+ * a new face.
+ */
+template <typename Arrangement_, typename Visitor_>
+class Base_merge {
+  using Arrangement_2 = Arrangement_;
+  using Visitor = Visitor_;
+  using Vertex_handle = typename Arrangement_2::Vertex_handle;
+  using Arr_entry = std::pair<Arrangement_2*, std::vector<Vertex_handle>*>;
 
 public:
-   void operator()(unsigned int i,
-                   unsigned int j,
-                   unsigned int jump,
-                   std::vector<Arr_entry>& arr_vec)
-  {
-    if(i==j)
-      return;
+  void operator()(std::size_t i, std::size_t j, std::size_t jump, std::vector<Arr_entry>& arr_vec) {
+    if (i == j) return;
 
-    const typename Arrangement_2::Geometry_traits_2 * tr =
-      arr_vec[i].first->geometry_traits();
-    Arrangement_2              *res = new Arrangement_2(tr);
-    std::vector<Vertex_handle> *verts = new std::vector<Vertex_handle>;
+    const auto* tr = arr_vec[i].first->geometry_traits();
+    Arrangement_2* res = new Arrangement_2(tr);
+    std::vector<Vertex_handle>* verts = new std::vector<Vertex_handle>;
 
-    Gps_agg_op<Arrangement_2, Visitor>
-      agg_op(*res, *verts, *(res->traits_adaptor()));
+    using Agg_op = Gps_agg_op<Arrangement_2, Visitor, Gps_agg_op_visitor>;
+    Agg_op agg_op(*res, *verts, *(res->traits_adaptor()));
     agg_op.sweep_arrangements(i, j, jump, arr_vec);
 
-    for(unsigned int count=i; count<=j; count+=jump)
-    {
+    for (std::size_t count = i; count <= j; count += jump) {
       delete (arr_vec[count].first);
       delete (arr_vec[count].second);
     }
@@ -74,38 +66,92 @@ public:
     arr_vec[i].first = res;
     arr_vec[i].second = verts;
   }
-
 };
 
-//! Join_merge
-/*! Join_merge is used to join two sets of polygons together in the D&C
-    algorithm. It is a base merge with a visitor that joins faces.
+/*! Base_intercepted_merge
+ * Base_intercepted_merge is the base class for all merger classes that can be
+ * interceted (e.g., when an intersection is detected).  All merges used BFS
+ * algorithm with a different visitor when discovering a new face.
  */
-template <class Arrangement_>
-class Join_merge : public Base_merge<Arrangement_,
-  Gps_bfs_join_visitor<Arrangement_> >
-{};
+template <typename Arrangement_, typename Visitor_>
+class Base_intercepted_merge {
+  using Arrangement_2 = Arrangement_;
+  using Visitor = Visitor_;
+  using Vertex_handle = typename Arrangement_2::Vertex_handle;
+  using Arr_entry = std::pair<Arrangement_2*, std::vector<Vertex_handle>*>;
 
+public:
+  template <typename InputIterator>
+  bool operator()(InputIterator begin, InputIterator end) {
+    CGAL_assertion(begin != end);
 
-//! Intersection_merge
-/*! Intersection_merge is used to merge two sets of polygons creating their
-    intersection.
- */
-template <class Arrangement_>
-class Intersection_merge : public Base_merge<Arrangement_,
-  Gps_bfs_intersection_visitor<Arrangement_> >
-{};
+    const auto* tr = begin->first->geometry_traits();
+    Arrangement_2* arr = new Arrangement_2(tr);
+    std::vector<Vertex_handle>* verts = new std::vector<Vertex_handle>;
 
-//! Xor_merge
-/*! Xor_merge is used to merge two sets of polygons creating their
-    symmetric difference.
- */
-template <class Arrangement_>
-class Xor_merge : public Base_merge<Arrangement_,
-  Gps_bfs_xor_visitor<Arrangement_> >
-{
+    using Agg_op = Gps_agg_op<Arrangement_2, Visitor, Gps_do_intersect_agg_op_visitor>;
+    Agg_op agg_op(*arr, *verts, *(arr->traits_adaptor()));
+    auto res = agg_op.sweep_intercept_arrangements2(begin, end);
+
+    begin->first = arr;
+    begin->second = verts;
+
+    return res;
+  }
+
+  bool operator()(std::size_t i, std::size_t j, std::size_t jump, std::vector<Arr_entry>& arr_vec) {
+    if (i == j) return false;
+
+    const auto* tr = arr_vec[i].first->geometry_traits();
+    Arrangement_2* arr = new Arrangement_2(tr);
+    std::vector<Vertex_handle>* verts = new std::vector<Vertex_handle>;
+
+    using Agg_op = Gps_agg_op<Arrangement_2, Visitor, Gps_do_intersect_agg_op_visitor>;
+    Agg_op agg_op(*arr, *verts, *(arr->traits_adaptor()));
+    auto res = agg_op.sweep_intercept_arrangements(i, j, jump, arr_vec);
+
+    for (auto count = i; count <= j; count += jump) {
+      delete (arr_vec[count].first);
+      arr_vec[count].first = nullptr;
+      delete (arr_vec[count].second);
+      arr_vec[count].second = nullptr;
+    }
+
+    arr_vec[i].first = arr;
+    arr_vec[i].second = verts;
+    return res;
+  }
 };
 
+/*! Join_merge
+ * Join_merge is used to join two sets of polygons together in the D&C
+ * algorithm. It is a base merge with a visitor that joins faces.
+ */
+template <typename Arrangement_>
+class Join_merge : public Base_merge<Arrangement_, Gps_bfs_join_visitor<Arrangement_>>{};
+
+/*! Intersection_merge
+ * Intersection_merge is used to merge two sets of polygons creating their
+ * intersection.
+ */
+template <typename Arrangement_>
+class Intersection_merge : public Base_merge<Arrangement_, Gps_bfs_intersection_visitor<Arrangement_>>{};
+
+/*! Do_intersect_merge
+ * Do_intersect_merge is used to merge two sets of polygons creating their
+ * intersection. When an intersection in the interior of the boundary curves
+ * is detected, the sweep is intercepted.
+ */
+template <typename Arrangement_>
+class Do_intersect_merge : public Base_intercepted_merge<Arrangement_, Gps_bfs_intersection_visitor<Arrangement_>>{};
+
+/*! Xor_merge
+ * Xor_merge is used to merge two sets of polygons creating their
+ * symmetric difference.
+ */
+template <typename Arrangement_>
+class Xor_merge : public Base_merge<Arrangement_, Gps_bfs_xor_visitor<Arrangement_>>{};
+
 } //namespace CGAL
 
 #endif

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_polygon_simplifier.h

@@ -7,11 +7,10 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
 
-#ifndef CGAL_BSO_2_GPS_POLYGON_SIMPILFIER_H
-#define CGAL_BSO_2_GPS_POLYGON_SIMPILFIER_H
+#ifndef CGAL_GPS_POLYGON_SIMPILFIER_H
+#define CGAL_GPS_POLYGON_SIMPILFIER_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
@@ -31,34 +30,33 @@ namespace Ss2 = Surface_sweep_2;
 
 template <typename Arrangement_>
 class Gps_polygon_simplifier {
-  typedef Arrangement_                                  Arrangement_2;
+  using Arrangement_2 = Arrangement_;
 
-  typedef typename Arrangement_2::Geometry_traits_2     Geometry_traits_2;
-  typedef typename Arrangement_2::Topology_traits       Topology_traits;
+  using Geometry_traits_2 = typename Arrangement_2::Geometry_traits_2;
+  using Topology_traits = typename Arrangement_2::Topology_traits;
 
-  typedef Arrangement_2                                 Arr;
-  typedef Geometry_traits_2                             Gt2;
-  typedef Topology_traits                               Tt;
+  using Arr = Arrangement_2;
+  using Gt2 = Geometry_traits_2;
+  using Tt = Topology_traits;
 
-  typedef typename Gt2::Curve_const_iterator            Curve_const_iterator;
-  typedef typename Gt2::Polygon_2                       Polygon_2;
-  typedef typename Gt2::Polygon_with_holes_2            Polygon_with_holes_2;
-  typedef typename Gt2::Construct_curves_2              Construct_curves_2;
+  using Curve_const_iterator = typename Gt2::Curve_const_iterator;
+  using Polygon_2 = typename Gt2::Polygon_2;
+  using Polygon_with_holes_2 = typename Gt2::Polygon_with_holes_2;
+  using Construct_curves_2 = typename Gt2::Construct_curves_2;
 
-  typedef Gps_simplifier_traits<Gt2>                    Mgt2;
-  typedef typename Mgt2::Curve_data                     Curve_data;
-  typedef typename Mgt2::X_monotone_curve_2             Meta_X_monotone_curve_2;
+  using Mgt2 = Gps_simplifier_traits<Gt2>;
+  using Curve_data = typename Mgt2::Curve_data;
+  using Meta_X_monotone_curve_2 = typename Mgt2::X_monotone_curve_2;
 
-  typedef typename Arr::Halfedge_handle                 Halfedge_handle;
-  typedef typename Arr::Halfedge_iterator               Halfedge_iterator;
-  typedef typename Arr::Face_handle                     Face_handle;
-  typedef typename Arr::Face_iterator                   Face_iterator;
-  typedef typename Arr::Edge_iterator                   Edge_iterator;
-  typedef typename Arr::Vertex_handle                   Vertex_handle;
-  typedef typename Arr::Ccb_halfedge_const_circulator
-    Ccb_halfedge_const_circulator;
-  typedef typename Arr::Ccb_halfedge_circulator         Ccb_halfedge_circulator;
-  typedef typename Arr::Allocator                       Allocator;
+  using Halfedge_handle = typename Arr::Halfedge_handle;
+  using Halfedge_iterator = typename Arr::Halfedge_iterator;
+  using Face_handle = typename Arr::Face_handle;
+  using Face_iterator = typename Arr::Face_iterator;
+  using Edge_iterator = typename Arr::Edge_iterator;
+  using Vertex_handle = typename Arr::Vertex_handle;
+  using Ccb_halfedge_const_circulator = typename Arr::Ccb_halfedge_const_circulator;
+  using Ccb_halfedge_circulator = typename Arr::Ccb_halfedge_circulator;
+  using Allocator = typename Arr::Allocator;
 
   // We obtain a proper helper type from the topology traits of the arrangement.
   // However, the arrangement is parametrized with the Gt2 geometry traits,
@@ -67,22 +65,18 @@ class Gps_polygon_simplifier {
   // We cannot parameterized the arrangement with the Mgt2 geometry
   // traits to start with, because it extends the curve type with arrangement
   // dependent types. (It is parameterized with the arrangement type.)
-  typedef Indexed_event<Mgt2, Arr, Allocator>           Event;
-  typedef Arr_construction_subcurve<Mgt2, Event, Allocator>
-                                                        Subcurve;
-  typedef typename Tt::template Construction_helper<Event, Subcurve>
-                                                        Helper_tmp;
-  typedef typename Helper_tmp::template rebind<Mgt2, Arr, Event, Subcurve>::other
-                                                        Helper;
-  typedef Gps_agg_op_base_visitor<Helper, Arr>          Visitor;
-  typedef Ss2::Surface_sweep_2<Visitor>                 Surface_sweep_2;
+  using Event = Indexed_event<Mgt2, Arr, Allocator>;
+  using Subcurve = Arr_construction_subcurve<Mgt2, Event, Allocator>;
+  using Helper_tmp = typename Tt::template Construction_helper<Event, Subcurve>;
+  using Helper = typename Helper_tmp::template rebind<Mgt2, Arr, Event, Subcurve>::other;
+  using Visitor = Gps_agg_op_base_visitor<Helper, Arr>;
+  using Surface_sweep_2 = Ss2::Surface_sweep_2<Visitor>;
 
-  typedef Unique_hash_map<Halfedge_handle, unsigned int>
-                                                        Edges_hash;
+  using Edges_hash = Unique_hash_map<Halfedge_handle, std::size_t>;
 
-  typedef Unique_hash_map<Face_handle, unsigned int>    Faces_hash;
-  typedef Gps_bfs_join_visitor<Arr>                     Bfs_visitor;
-  typedef Gps_bfs_scanner<Arr, Bfs_visitor>             Bfs_scanner;
+  using Faces_hash = Unique_hash_map<Face_handle, std::size_t>;
+  using Bfs_visitor = Gps_bfs_join_visitor<Arr>;
+  using Bfs_scanner = Gps_bfs_scanner<Arr, Bfs_visitor>;
 
 protected:
   Arr* m_arr;
@@ -104,16 +98,14 @@ public:
   {}
 
   /*! Destructor. */
-  ~Gps_polygon_simplifier()
-  {
+  ~Gps_polygon_simplifier() {
     if (m_own_traits && (m_traits != nullptr)) {
       delete m_traits;
       m_traits = nullptr;
     }
   }
 
-  void simplify(const Polygon_2& pgn)
-  {
+  void simplify(const Polygon_2& pgn) {
     Construct_curves_2 ctr_curves =
       reinterpret_cast<const Gt2*>(m_traits)->construct_curves_2_object();
 
@@ -122,14 +114,13 @@ public:
     std::pair<Curve_const_iterator, Curve_const_iterator> itr_pair =
       ctr_curves(pgn);
 
-    unsigned int index = 0;
+    std::size_t index = 0;
     for (Curve_const_iterator itr = itr_pair.first; itr != itr_pair.second;
-         ++itr, ++index)
-    {
+         ++itr, ++index) {
       Curve_data cv_data(1, 0, index);
       curves_list.push_back(Meta_X_monotone_curve_2(*itr, cv_data));
     }
-    m_traits->set_polygon_size(static_cast<unsigned int>(curves_list.size()));
+    m_traits->set_polygon_size(curves_list.size());
 
     m_surface_sweep.sweep(curves_list.begin(), curves_list.end());
 

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_polygon_validation.h

@@ -7,14 +7,13 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
-// Author(s): Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Ron Wein        <wein@post.tau.ac.il>
-//                 Boris Kozorovitzky <boriskoz@post.tau.ac.il>
-//                 Guy Zucker <guyzucke@post.tau.ac.il>
+// Author(s) : Baruch Zukerman    <baruchzu@post.tau.ac.il>
+//             Ron Wein           <wein@post.tau.ac.il>
+//             Boris Kozorovitzky <boriskoz@post.tau.ac.il>
+//             Guy Zucker         <guyzucke@post.tau.ac.il>
 
-#ifndef CGAL_BSO_2_GPS_POLYGON_VALIDATION_2_H
-#define CGAL_BSO_2_GPS_POLYGON_VALIDATION_2_H
+#ifndef CGAL_GPS_POLYGON_VALIDATION_2_H
+#define CGAL_GPS_POLYGON_VALIDATION_2_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_simplifier_traits.h

@@ -7,9 +7,8 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
-// Author(s): Baruch Zukerman <baruchzu@post.tau.ac.il>
-//            Efi Fogel       <efifogel@gmail.com>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Efi Fogel       <efifogel@gmail.com>
 
 #ifndef CGAL_GPS_SIMPLIFIER_TRAITS_H
 #define CGAL_GPS_SIMPLIFIER_TRAITS_H
@@ -23,97 +22,94 @@ namespace CGAL {
 
 class Gps_simplifier_curve_data {
 protected:
-  unsigned int m_bc;
-  unsigned int m_twin_bc;
-  unsigned int m_index;
+  std::size_t m_bc;
+  std::size_t m_twin_bc;
+  std::size_t m_index;
 
 public:
   Gps_simplifier_curve_data() {}
 
-  Gps_simplifier_curve_data(unsigned int bc, unsigned int twin_bc,
-                            unsigned int index):
+  Gps_simplifier_curve_data(std::size_t bc, std::size_t twin_bc,
+                            std::size_t index):
     m_bc(bc),
     m_twin_bc(twin_bc),
     m_index(index)
   {}
 
-  unsigned int bc() const { return m_bc; }
+  std::size_t bc() const { return m_bc; }
 
-  unsigned int twin_bc() const { return m_twin_bc; }
+  std::size_t twin_bc() const { return m_twin_bc; }
 
-  unsigned int index() const { return m_index; }
+  std::size_t index() const { return m_index; }
 
-  unsigned int& index() { return m_index; }
+  std::size_t& index() { return m_index; }
 
-  unsigned int& twin_bc() { return m_twin_bc; }
+  std::size_t& twin_bc() { return m_twin_bc; }
 
-  void set_bc(unsigned int bc) { m_bc = bc; }
+  void set_bc(std::size_t bc) { m_bc = bc; }
 
-  void set_twin_bc(unsigned int twin_bc) { m_twin_bc = twin_bc; }
+  void set_twin_bc(std::size_t twin_bc) { m_twin_bc = twin_bc; }
 
-  void set_index(unsigned int index) { m_index = index; }
+  void set_index(std::size_t index) { m_index = index; }
 };
 
 struct Gps_simplifier_point_data {
 protected:
-  unsigned int m_index;
+  std::size_t m_index;
 
 public:
   Gps_simplifier_point_data() {}
 
-  Gps_simplifier_point_data(unsigned int index) : m_index(index) {}
+  Gps_simplifier_point_data(std::size_t index) : m_index(index) {}
 
-  unsigned int index() const { return m_index; }
+  std::size_t index() const { return m_index; }
 
-  void set_index(unsigned int index) { m_index = index; }
+  void set_index(std::size_t index) { m_index = index; }
 };
 
 template <typename Traits_>
 class Gps_simplifier_traits :
   public Gps_traits_decorator<Traits_,
                               Gps_simplifier_curve_data,
-                              Gps_simplifier_point_data>
-{
+                              Gps_simplifier_point_data> {
 public:
-  typedef Traits_                                           Traits;
-  typedef Gps_traits_decorator<Traits_,
-                               Gps_simplifier_curve_data,
-                               Gps_simplifier_point_data>   Base;
-  typedef Gps_simplifier_traits<Traits>                     Self;
-  typedef typename Traits::X_monotone_curve_2     Base_x_monotone_curve_2;
-  typedef typename Traits::Point_2                Base_point_2;
-  typedef typename Traits::Construct_min_vertex_2 Base_Construct_min_vertex_2;
-  typedef typename Traits::Construct_max_vertex_2 Base_Construct_max_vertex_2;
-  typedef typename Traits::Compare_endpoints_xy_2 Base_Compare_endpoints_xy_2;
-  typedef typename Traits::Compare_xy_2           Base_Compare_xy_2;
-  typedef typename Traits::Compare_y_at_x_right_2 Base_Compare_y_at_x_right_2;
-  typedef typename Traits::Compare_y_at_x_2       Base_Compare_y_at_x_2;
-  typedef typename Traits::Intersect_2            Base_Intersect_2;
-  typedef typename Traits::Split_2                Base_Split_2;
+  using Traits = Traits_;
+  using Base = Gps_traits_decorator<Traits_, Gps_simplifier_curve_data, Gps_simplifier_point_data>;
+  using Self = Gps_simplifier_traits<Traits>;
+  using Base_x_monotone_curve_2 = typename Traits::X_monotone_curve_2;
+  using Base_point_2 = typename Traits::Point_2;
+  using Base_Construct_min_vertex_2 = typename Traits::Construct_min_vertex_2;
+  using Base_Construct_max_vertex_2 = typename Traits::Construct_max_vertex_2;
+  using Base_Compare_endpoints_xy_2 = typename Traits::Compare_endpoints_xy_2;
+  using Base_Compare_xy_2 = typename Traits::Compare_xy_2;
+  using Base_Compare_y_at_x_right_2 = typename Traits::Compare_y_at_x_right_2;
+  using Base_Compare_y_at_x_2 = typename Traits::Compare_y_at_x_2;
+  using Base_Intersect_2 = typename Traits::Intersect_2;
+  using Base_Split_2 = typename Traits::Split_2;
 
 protected:
-  mutable unsigned int m_pgn_size;
+  mutable std::size_t m_pgn_size;
 
 public:
-  typedef typename Base::X_monotone_curve_2       X_monotone_curve_2;
-  typedef typename Base::Point_2                  Point_2;
-  typedef typename Base::Multiplicity             Multiplicity;
+  using X_monotone_curve_2 = typename Base::X_monotone_curve_2;
+  using Point_2 = typename Base::Point_2;
+  using Multiplicity = typename Base::Multiplicity;
 
-  typedef typename Base::Curve_data               Curve_data;
-  typedef typename Base::Point_data               Point_data;
+  using Curve_data = typename Base::Curve_data;
+  using Point_data = typename Base::Point_data;
 
   Gps_simplifier_traits() {}
 
   Gps_simplifier_traits(const Traits& tr) : Base(tr) {}
 
-  unsigned int polygon_size() const { return m_pgn_size; }
+  std::size_t polygon_size() const { return m_pgn_size; }
 
-  void set_polygon_size(unsigned int pgn_size) const { m_pgn_size = pgn_size; }
+  void set_polygon_size(std::size_t pgn_size) const { m_pgn_size = pgn_size; }
 
-  bool is_valid_index(unsigned int index) const
+  bool is_valid_index(std::size_t index) const
   { return (index < m_pgn_size); }
 
-  unsigned int invalid_index() const { return (m_pgn_size); }
+  std::size_t invalid_index() const { return (m_pgn_size); }
 
   class Intersect_2 {
   private:
@@ -129,12 +125,9 @@ public:
     template <typename OutputIterator>
     OutputIterator operator()(const X_monotone_curve_2& cv1,
                               const X_monotone_curve_2& cv2,
-                              OutputIterator oi) const
-    {
-      typedef const std::pair<Base_point_2, Multiplicity>
-        Intersection_base_point;
-      typedef std::variant<Intersection_base_point, Base_x_monotone_curve_2>
-                                                        Intersection_base_result;
+                              OutputIterator oi) const {
+      using Intersection_base_point = const std::pair<Base_point_2, Multiplicity>;
+      using Intersection_base_result = std::variant<Intersection_base_point, Base_x_monotone_curve_2>;
 
       const auto* base_traits = m_traits.m_base_traits;
       auto base_cmp_xy = base_traits->compare_xy_2_object();
@@ -146,7 +139,7 @@ public:
       //if (m_traits.is_valid_index(cv1.data().index()) &&
       //    m_traits.is_valid_index(cv2.data().index()))
       //{
-      //  unsigned int index_diff =
+      //  std::size_t index_diff =
       //    (cv1.data().index() > cv2.data().index()) ?
       //    (cv1.data().index() - cv2.data().index()):
       //    (cv2.data().index() - cv1.data().index());
@@ -180,8 +173,8 @@ public:
           std::get_if<Base_x_monotone_curve_2>(&xection);
 
         CGAL_assertion(overlap_cv != nullptr);
-        unsigned int ov_bc;
-        unsigned int ov_twin_bc;
+        std::size_t ov_bc;
+        std::size_t ov_twin_bc;
         if (base_cmp_endpoints(cv1) == base_cmp_endpoints(cv2)) {
           // cv1 and cv2 have the same directions
           ov_bc = cv1.data().bc() + cv2.data().bc();
@@ -207,7 +200,7 @@ public:
   };
 
   /*! Obtain an Intersect_2 functor object. */
-  Intersect_2 intersect_2_object () const { return Intersect_2(*this); }
+  Intersect_2 intersect_2_object() const { return Intersect_2(*this); }
 
   class Split_2 {
   private:
@@ -220,8 +213,7 @@ public:
 
   public:
     void operator()(const X_monotone_curve_2& cv, const Point_2 & p,
-                    X_monotone_curve_2& c1, X_monotone_curve_2& c2) const
-    {
+                    X_monotone_curve_2& c1, X_monotone_curve_2& c2) const {
       const auto* base_traits = m_traits.m_base_traits;
       auto base_split = base_traits->split_2_object();
       base_split(cv.base(), p.base(), c1.base(), c2.base());
@@ -250,8 +242,7 @@ public:
       * \param cv The curve.
       * \return The left endpoint.
       */
-    Point_2 operator()(const X_monotone_curve_2 & cv) const
-    {
+    Point_2 operator()(const X_monotone_curve_2 & cv) const {
       const auto* base_traits = m_traits.m_base_traits;
       auto base_ctr_min_vertex = base_traits->construct_min_vertex_2_object();
 
@@ -290,8 +281,7 @@ public:
       * \param cv The curve.
       * \return The left endpoint.
       */
-    Point_2 operator() (const X_monotone_curve_2 & cv) const
-    {
+    Point_2 operator() (const X_monotone_curve_2 & cv) const {
       const auto* base_traits = m_traits.m_base_traits;
       auto base_ctr_max_vertex = base_traits->construct_max_vertex_2_object();
       if (! m_traits.is_valid_index(cv.data().index()))
@@ -329,8 +319,7 @@ public:
       * \param cv The curve.
       * \return The left endpoint.
       */
-    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const
-    {
+    Comparison_result operator()(const Point_2& p1, const Point_2& p2) const {
       const auto* base_traits = m_traits.m_base_traits;
       auto base_cmp_xy = base_traits->compare_xy_2_object();
 

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Indexed_event.h

@@ -11,8 +11,8 @@
 //             Ron Wein <wein@post.tau.ac.il>
 //             Efi Fogel <efifogel@gmail.com>
 
-#ifndef CGAL_BSO_2_INDEXED_VISITOR_H
-#define CGAL_BSO_2_INDEXED_VISITOR_H
+#ifndef CGAL_INDEXED_VISITOR_H
+#define CGAL_INDEXED_VISITOR_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
@@ -32,17 +32,16 @@ class Indexed_event :
                                             Arrangement_,
                                             Allocator_>,
                               Allocator_>,
-    Arrangement_>
-{
+    Arrangement_> {
 private:
-  unsigned int m_index;
+  std::size_t m_index;
 
 public:
   Indexed_event() : m_index (0) {}
 
-  unsigned int index() const { return (m_index); }
+  std::size_t index() const { return (m_index); }
 
-  void set_index(unsigned int index) { m_index = index; }
+  void set_index(std::size_t index) { m_index = index; }
 };
 
 } // namespace CGAL

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Polygon_conversions.h

@@ -31,9 +31,9 @@ namespace CGAL {
 // Utility struct
 template <typename Polygon>
 struct Gps_polyline_traits {
-  typedef typename Gps_default_traits<Polygon>::Arr_traits      Segment_traits;
-  typedef Arr_polyline_traits_2<Segment_traits>                 Polyline_traits;
-  typedef Gps_traits_2<Polyline_traits>                         Traits;
+  using Segment_traits = typename Gps_default_traits<Polygon>::Arr_traits;
+  using Polyline_traits = Arr_polyline_traits_2<Segment_traits>;
+  using Traits = Gps_traits_2<Polyline_traits>;
 };
 
 // Helper to map Polygon_2 -> General_polygon_2 / PWH_2 -> General_PWH_2
@@ -85,9 +85,7 @@ using Disable_if_Polygon_2_iterator =
 // Convert Polygon_2 to General_polygon_2<Polyline_traits>
   template <typename Kernel, typename Container, typename ArrTraits>
 General_polygon_2<ArrTraits>
-convert_polygon(const Polygon_2<Kernel, Container>& polygon,
-                const ArrTraits& traits)
-{
+convert_polygon(const Polygon_2<Kernel, Container>& polygon, const ArrTraits& traits) {
   auto ctr = traits.construct_curve_2_object();
   if (polygon.is_empty()) return General_polygon_2<ArrTraits>();
   using Point = typename ArrTraits::Point_2;
@@ -99,22 +97,20 @@ convert_polygon(const Polygon_2<Kernel, Container>& polygon,
   General_polygon_2<ArrTraits> gpgn;
   auto make_x_mtn = traits.make_x_monotone_2_object();
   make_x_mtn(cv,
-             boost::make_function_output_iterator
-             ([&](const Make_x_monotone_result& obj)
-              { gpgn.push_back(*(std::get_if<X_monotone_curve>(&obj))); }));
+             boost::make_function_output_iterator([&](const Make_x_monotone_result& obj)
+             { gpgn.push_back(*(std::get_if<X_monotone_curve>(&obj))); }));
   return gpgn;
 }
 
 // Convert Polygon_with_holes_2 to General_polygon_with_holes_2<Polyline_traits>
   template <typename Kernel, typename Container, typename ArrTraits>
-General_polygon_with_holes_2<General_polygon_2<ArrTraits> >
+General_polygon_with_holes_2<General_polygon_2<ArrTraits>>
 convert_polygon(const Polygon_with_holes_2<Kernel, Container>& pwh,
                 const ArrTraits& traits) {
-  typedef General_polygon_2<ArrTraits>          General_pgn;
-  typedef Polygon_2<Kernel, Container>          Pgn;
-  auto converter = [&](const Pgn& pgn)->General_pgn {
-    return convert_polygon(pgn, traits);
-  };
+  using General_pgn = General_polygon_2<ArrTraits>;
+  using Pgn = Polygon_2<Kernel, Container>;
+  auto converter = [&](const Pgn& pgn)->General_pgn
+  { return convert_polygon(pgn, traits); };
   return General_polygon_with_holes_2<General_polygon_2<ArrTraits>>
     (convert_polygon(pwh.outer_boundary(), traits),
      boost::make_transform_iterator(pwh.holes().begin(), converter),
@@ -137,14 +133,11 @@ convert_polygon_back(const General_polygon_2<ArrTraits>& gpgn) {
 // Convert General_polygon_with_holes_2<Polyline_traits> to Polygon_with_holes_2
 template <typename Kernel, typename Container, typename ArrTraits>
 Polygon_with_holes_2<Kernel, Container>
-convert_polygon_back(const General_polygon_with_holes_2
-                       <General_polygon_2<ArrTraits> >& gpwh)
-{
+convert_polygon_back(const General_polygon_with_holes_2<General_polygon_2<ArrTraits>>& gpwh) {
   using Pgn = Polygon_2<Kernel, Container>;
   using General_pgn = General_polygon_2<ArrTraits>;
-  auto converter = [](const General_pgn& gpgn)->Pgn {
-    return convert_polygon_back<Kernel, Container>(gpgn);
-  };
+  auto converter = [](const General_pgn& gpgn)->Pgn
+  { return convert_polygon_back<Kernel, Container>(gpgn); };
   return Polygon_with_holes_2<Kernel, Container>
     (convert_polygon_back<Kernel, Container>(gpwh.outer_boundary()),
      boost::make_transform_iterator(gpwh.holes().begin(), converter),
@@ -155,21 +148,17 @@ convert_polygon_back(const General_polygon_with_holes_2
 // Polygon_2 to General_polygon_2<Polyline_traits>, or
 // Polygon_with_holes_2 to General_polygon_with_holes_2<Polyline_traits>
 template <typename InputIterator, typename Traits>
-boost::transform_iterator
-<std::function
- <typename General_polygon_of_polygon<typename std::iterator_traits
-                                      <InputIterator>::value_type>::type
-  (typename std::iterator_traits<InputIterator>::reference)>,
- InputIterator>
-convert_polygon_iterator(InputIterator it, const Traits& traits)
-{
+boost::transform_iterator<std::function<
+  typename General_polygon_of_polygon<typename std::iterator_traits<
+    InputIterator>::value_type>::type
+  (typename std::iterator_traits<InputIterator>::reference)>, InputIterator>
+convert_polygon_iterator(InputIterator it, const Traits& traits) {
   using Input_type = typename std::iterator_traits<InputIterator>::value_type;
   using Return_type = typename General_polygon_of_polygon<Input_type>::type;
   using Function_type = std::function<Return_type(Input_type)>;
 
-  Function_type func =
-    [&traits](const Input_type& p)->Return_type
-    { return convert_polygon(p, traits); };
+  Function_type func = [&traits](const Input_type& p)->Return_type
+  { return convert_polygon(p, traits); };
 
   return boost::transform_iterator<Function_type, InputIterator>(it, func);
 }
@@ -186,8 +175,7 @@ struct Polygon_converter {
 
   // Convert and export to output iterator.
   template <typename ArrTraits>
-  void operator()(const General_polygon_with_holes_2
-                  <General_polygon_2<ArrTraits> >& gpwh) const
+  void operator()(const General_polygon_with_holes_2<General_polygon_2<ArrTraits>>& gpwh) const
   { *m_output++ = convert_polygon_back<Kernel, Container>(gpwh); }
 };
 
@@ -195,9 +183,7 @@ struct Polygon_converter {
 // OutputIterator
 template <typename Kernel, typename Container, typename OutputIterator>
 struct Polygon_converter_output_iterator :
-  boost::function_output_iterator<Polygon_converter
-                                  <Kernel, Container, OutputIterator> >
-{
+  boost::function_output_iterator<Polygon_converter<Kernel, Container, OutputIterator>> {
   using Converter = Polygon_converter<Kernel, Container, OutputIterator>;
   using Base = boost::function_output_iterator<Converter>;
 
@@ -214,11 +200,8 @@ struct Polygon_converter_output_iterator :
 // (indirection with Polygon_2)
 template <typename OutputIterator, typename Kernel, typename Container>
 Polygon_converter_output_iterator<Kernel, Container, OutputIterator>
-convert_polygon_back(OutputIterator& output,
-                     const Polygon_2<Kernel, Container>&)
-{
-  return Polygon_converter_output_iterator
-    <Kernel, Container, OutputIterator>(output);
+convert_polygon_back(OutputIterator& output, const Polygon_2<Kernel, Container>&) {
+  return Polygon_converter_output_iterator<Kernel, Container, OutputIterator>(output);
 }
 
 // Converts General_polygon_with_holes_2<Polyline_traits> to Polygon_with_holes_2
@@ -226,10 +209,8 @@ convert_polygon_back(OutputIterator& output,
 template <typename OutputIterator, typename Kernel, typename Container>
 Polygon_converter_output_iterator<Kernel, Container, OutputIterator>
 convert_polygon_back(OutputIterator& output,
-                     const Polygon_with_holes_2<Kernel, Container>&)
-{
-  return Polygon_converter_output_iterator
-    <Kernel, Container, OutputIterator>(output);
+                     const Polygon_with_holes_2<Kernel, Container>&) {
+  return Polygon_converter_output_iterator<Kernel, Container, OutputIterator>(output);
 }
 
 template <typename InputIterator>
@@ -238,7 +219,6 @@ struct Iterator_to_gps_traits {
   typedef typename Gps_default_traits<InputPolygon>::Traits    Traits;
 };
 
-
 }
 
-#endif // CGAL_BSO_POLYGON_CONVERSIONS_H
+#endif

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/do_intersect.h

@@ -8,10 +8,10 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s): Baruch Zukerman <baruchzu@post.tau.ac.il>
-//            Ron Wein        <wein@post.tau.ac.il>
-//            Efi Fogel       <efif@post.tau.ac.il>
-//            Simon Giraudot  <simon.giraudot@geometryfactory.com>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Ron Wein        <wein@post.tau.ac.il>
+//             Efi Fogel       <efif@post.tau.ac.il>
+//             Simon Giraudot  <simon.giraudot@geometryfactory.com>
 
 #ifndef CGAL_BOOLEAN_SET_OPERATIONS_2_DO_INTERSECT_H
 #define CGAL_BOOLEAN_SET_OPERATIONS_2_DO_INTERSECT_H
@@ -33,12 +33,18 @@
 #include <CGAL/Boolean_set_operations_2/Polygon_conversions.h>
 #include <CGAL/type_traits/is_iterator.h>
 
-namespace CGAL
-{
+namespace CGAL {
 
 /// \name do_intersect() functions.
 //@{
 
+/*! We do not use polyline for do_intersect), as we rely on the overlay traits
+ * to only intercept intersections between the interiors of segments that
+ * comprise the boundary of polygons. Observe that The intersections between the
+ * interiors of polylines that comprise the boundary of polygons may include an
+ * endpoint of a segment, and we do not want that.
+ */
+
 // Polygon_2, Polygon_2 ========================================================
 // With Traits
 template <typename Kernel, typename Container, typename Traits>
@@ -47,24 +53,24 @@ inline bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
                          Traits& traits)
 { return s_do_intersect(pgn1, pgn2, traits); }
 
-// With Tag_true
+// without traits
 template <typename Kernel, typename Container>
 inline bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
-                         const Polygon_2<Kernel, Container>& pgn2,
-                         Tag_true = Tag_true())
-{ return s_do_intersect(pgn1, pgn2); }
-
-// With Tag_false
-template <typename Kernel, typename Container>
-inline bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
-                         const Polygon_2<Kernel, Container>& pgn2,
-                         Tag_false)
-{
-  typedef Polygon_2<Kernel, Container>                          Polygon;
+                         const Polygon_2<Kernel, Container>& pgn2) {
+  using Polygon = Polygon_2<Kernel, Container>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_do_intersect(pgn1, pgn2, traits);
 }
 
+#ifndef CGAL_NO_DEPRECATED_CODE
+template <typename Kernel, typename Container, bool b>
+inline bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
+                         const Polygon_2<Kernel, Container>& pgn2,
+                         std::bool_constant<b>) {
+  return do_intersect(pgn1, pgn2);
+}
+#endif
+
 // Polygon_2, Polygon_with_hole_2 ==============================================
 // With Traits
 template <typename Kernel, typename Container, typename Traits>
@@ -73,25 +79,25 @@ inline bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
                          Traits& traits)
 { return s_do_intersect(pgn1, pgn2, traits); }
 
-// With Tag_true
+// Without traits
 template <typename Kernel, typename Container>
 inline bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
-                         const Polygon_with_holes_2<Kernel, Container>& pgn2,
-                         Tag_true = Tag_true())
-{ return s_do_intersect(pgn1, pgn2); }
-
-// With Tag_false
-template <typename Kernel, typename Container>
-inline bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
-                         const Polygon_with_holes_2<Kernel, Container>& pgn2,
-                         Tag_false)
-{
+                         const Polygon_with_holes_2<Kernel, Container>& pgn2) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_2<Kernel, Container>                          Polygon;
+  using Polygon = Polygon_2<Kernel, Container>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_do_intersect(pgn1, pgn2, traits);
 }
 
+#ifndef CGAL_NO_DEPRECATED_CODE
+template <typename Kernel, typename Container, bool b>
+inline bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
+                         const Polygon_with_holes_2<Kernel, Container>& pgn2,
+                         std::bool_constant<b>) {
+  return do_intersect(pgn1, pgn2);
+}
+#endif
+
 // Polygon_with_hole_2, Polygon_2 ==============================================
 // With Traits
 template <typename Kernel, typename Container, typename Traits>
@@ -100,25 +106,25 @@ inline bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
                          Traits& traits)
 { return s_do_intersect(pgn1, pgn2, traits); }
 
-// With Tag_true
+// Without traits
 template <typename Kernel, typename Container>
 inline bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
-                         const Polygon_2<Kernel, Container>& pgn2,
-                         Tag_true = Tag_true())
-{ return s_do_intersect(pgn1, pgn2); }
-
-// With Tag_false
-template <typename Kernel, typename Container>
-inline bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
-                         const Polygon_2<Kernel, Container>& pgn2,
-                         Tag_false)
-{
+                         const Polygon_2<Kernel, Container>& pgn2) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_with_holes_2<Kernel, Container>       Polygon_with_holes;
+  using Polygon_with_holes = Polygon_with_holes_2<Kernel, Container>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_do_intersect(pgn1, pgn2, traits);
 }
 
+#ifndef CGAL_NO_DEPRECATED_CODE
+template <typename Kernel, typename Container, bool b>
+inline bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
+                         const Polygon_2<Kernel, Container>& pgn2,
+                         std::bool_constant<b>) {
+  return do_intersect(pgn1, pgn2);
+}
+#endif
+
 // Polygon_with_hole_2, Polygon_with_hole_2 ====================================
 // With Traits
 template <typename Kernel, typename Container, typename Traits>
@@ -127,25 +133,25 @@ inline bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
                          Traits& traits)
 { return s_do_intersect(pgn1, pgn2, traits); }
 
-// With Tag_true
+// Without traits
 template <typename Kernel, typename Container>
 inline bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
-                         const Polygon_with_holes_2<Kernel, Container>& pgn2,
-                         Tag_true = Tag_true())
-{ return s_do_intersect(pgn1, pgn2); }
-
-// With Tag_false
-template <typename Kernel, typename Container>
-inline bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
-                         const Polygon_with_holes_2<Kernel, Container>& pgn2,
-                         Tag_false)
-{
+                         const Polygon_with_holes_2<Kernel, Container>& pgn2) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_with_holes_2<Kernel, Container>       Polygon_with_holes;
+  using Polygon_with_holes = Polygon_with_holes_2<Kernel, Container>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_do_intersect(pgn1, pgn2, traits);
 }
 
+#ifndef CGAL_NO_DEPRECATED_CODE
+template <typename Kernel, typename Container, bool b>
+inline bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
+                         const Polygon_with_holes_2<Kernel, Container>& pgn2,
+                         std::bool_constant<b>) {
+  return do_intersect(pgn1, pgn2);
+}
+#endif
+
 // General_polygon_2, General_polygon_2 ========================================
 // With Traits
 template <typename ArrTraits, typename GpsTraits>
@@ -157,14 +163,22 @@ inline bool do_intersect(const General_polygon_2<ArrTraits>& pgn1,
 // Without Traits
 template <typename ArrTraits>
 inline bool do_intersect(const General_polygon_2<ArrTraits>& pgn1,
-                         const General_polygon_2<ArrTraits>& pgn2)
-{
+                         const General_polygon_2<ArrTraits>& pgn2) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
+  using Polygon = General_polygon_2<ArrTraits>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_do_intersect(pgn1, pgn2, traits);
 }
 
+#ifndef CGAL_NO_DEPRECATED_CODE
+template <typename ArrTraits, bool b>
+inline bool do_intersect(const General_polygon_2<ArrTraits>& pgn1,
+                         const General_polygon_2<ArrTraits>& pgn2,
+                         std::bool_constant<b>) {
+  return do_intersect(pgn1, pgn2);
+}
+#endif
+
 // General_polygon_2, General_polygon_with_holes_2 =============================
 // With Traits
 template <typename ArrTraits, typename GpsTraits>
@@ -178,14 +192,23 @@ inline bool do_intersect(const General_polygon_2<ArrTraits>& pgn1,
 template <typename ArrTraits>
 inline bool do_intersect(const General_polygon_2<ArrTraits>& pgn1,
                          const General_polygon_with_holes_2
-                           <General_polygon_2<ArrTraits> >& pgn2)
-{
+                           <General_polygon_2<ArrTraits> >& pgn2) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
+  using Polygon = General_polygon_2<ArrTraits>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_do_intersect(pgn1, pgn2, traits);
 }
 
+#ifndef CGAL_NO_DEPRECATED_CODE
+template <typename ArrTraits, bool b>
+inline bool do_intersect(const General_polygon_2<ArrTraits>& pgn1,
+                         const General_polygon_with_holes_2
+                           <General_polygon_2<ArrTraits> >& pgn2,
+                         std::bool_constant<b>) {
+  return do_intersect(pgn1, pgn2);
+}
+#endif
+
 // General_polygon_with_holes_2, General_polygon_2 =============================
 // With Traits
 template <typename ArrTraits, typename GpsTraits>
@@ -199,15 +222,25 @@ inline bool do_intersect(const General_polygon_with_holes_2
 template <typename ArrTraits>
 inline bool do_intersect(const General_polygon_with_holes_2
                            <General_polygon_2<ArrTraits> >& pgn1,
-                         const General_polygon_2<ArrTraits>& pgn2)
-{
+                         const General_polygon_2<ArrTraits>& pgn2) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
-  typedef General_polygon_with_holes_2<Polygon>         Polygon_with_holes;
+  using Polygon = General_polygon_2<ArrTraits>;
+  using Polygon_with_holes = General_polygon_with_holes_2<Polygon>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_do_intersect(pgn1, pgn2, traits);
 }
 
+#ifndef CGAL_NO_DEPRECATED_CODE
+template <typename ArrTraits, bool b>
+inline bool do_intersect(const General_polygon_with_holes_2
+                           <General_polygon_2<ArrTraits> >& pgn1,
+                         const General_polygon_2<ArrTraits>& pgn2,
+                         std::bool_constant<b>) {
+  return do_intersect(pgn1, pgn2);
+}
+#endif
+
+
 // General_polygon_with_holes_2, General_polygon_with_holes_2 ==================
 // With Traits
 template <typename Polygon_, typename Traits>
@@ -219,14 +252,22 @@ inline bool do_intersect(const General_polygon_with_holes_2<Polygon_>& pgn1,
 // Without Traits
 template <typename Polygon_>
 inline bool do_intersect(const General_polygon_with_holes_2<Polygon_>& pgn1,
-                         const General_polygon_with_holes_2<Polygon_>& pgn2)
-{
+                         const General_polygon_with_holes_2<Polygon_>& pgn2) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_with_holes_2<Polygon_>        Polygon_with_holes;
+  using Polygon_with_holes = General_polygon_with_holes_2<Polygon_>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_do_intersect(pgn1, pgn2, traits);
 }
 
+#ifndef CGAL_NO_DEPRECATED_CODE
+template <typename Polygon_, bool b>
+inline bool do_intersect(const General_polygon_with_holes_2<Polygon_>& pgn1,
+                         const General_polygon_with_holes_2<Polygon_>& pgn2,
+                         std::bool_constant<b>) {
+  return do_intersect(pgn1, pgn2);
+}
+#endif
+
 //@}
 
 /// \name Aggregated do_intersect() functions.
@@ -235,26 +276,15 @@ inline bool do_intersect(const General_polygon_with_holes_2<Polygon_>& pgn1,
 // With Traits
 template <typename InputIterator, typename Traits>
 inline bool do_intersect(InputIterator begin, InputIterator end, Traits& traits,
-                         unsigned int k=5,
+                         std::size_t k = 5,
                          std::enable_if_t<CGAL::is_iterator<InputIterator>::value>* = 0)
 { return r_do_intersect(begin, end, traits, k); }
 
 // Without Traits
-// Tag_true => convert to polylines
 template <typename InputIterator>
-inline bool do_intersect(InputIterator begin, InputIterator end,
-                         Tag_true = Tag_true(), unsigned int k=5,
+inline bool do_intersect(InputIterator begin, InputIterator end, std::size_t k = 5,
                          std::enable_if_t<CGAL::is_iterator<InputIterator>::value>* = 0,
-                         Enable_if_Polygon_2_iterator<InputIterator>* = 0)
-{ return r_do_intersect(begin, end, k); }
-
-// Tag_false => do not convert to polylines
-template <typename InputIterator>
-inline bool do_intersect(InputIterator begin, InputIterator end,
-                         Tag_false, unsigned int k=5,
-                         std::enable_if_t<CGAL::is_iterator<InputIterator>::value>* = 0,
-                         Enable_if_Polygon_2_iterator<InputIterator>* = 0)
-{
+                         Enable_if_Polygon_2_iterator<InputIterator>* = 0) {
   typename Iterator_to_gps_traits<InputIterator>::Traits traits;
   return r_do_intersect(begin, end, traits, k);
 }
@@ -262,49 +292,57 @@ inline bool do_intersect(InputIterator begin, InputIterator end,
 // General polygons or polygons with holes
 template <typename InputIterator>
 inline bool do_intersect(InputIterator begin, InputIterator end,
-                         unsigned int k=5,
+                         std::size_t k = 5,
                          std::enable_if_t<CGAL::is_iterator<InputIterator>::value>* = 0,
-                         Disable_if_Polygon_2_iterator<InputIterator>* = 0)
-{
+                         Disable_if_Polygon_2_iterator<InputIterator>* = 0) {
   typename Iterator_to_gps_traits<InputIterator>::Traits traits;
   return do_intersect(begin, end, traits, k);
 }
 
+#ifndef CGAL_NO_DEPRECATED_CODE
+template <typename InputIterator, bool b>
+inline bool do_intersect(InputIterator begin, InputIterator end, std::bool_constant<b>,
+                         std::enable_if_t<CGAL::is_iterator<InputIterator>::value>* = 0) {
+  return do_intersect(begin, end);
+}
+#endif
+
 // With Traits
 template <typename InputIterator1, typename InputIterator2, typename Traits>
 inline bool do_intersect(InputIterator1 begin1, InputIterator1 end1,
                          InputIterator2 begin2, InputIterator2 end2,
-                         Traits& traits, unsigned int k=5)
+                         Traits& traits, std::size_t k = 5)
 { return r_do_intersect(begin1, end1, begin2, end2, traits, k); }
 
 // Without Traits
-// Tag_true => convert to polylines
 template <typename InputIterator1, typename InputIterator2>
-inline bool do_intersect (InputIterator1 begin1, InputIterator1 end1,
-                          InputIterator2 begin2, InputIterator2 end2,
-                          Tag_true = Tag_true(), unsigned int k=5,
-                          Enable_if_Polygon_2_iterator<InputIterator1>* = 0)
-{ return r_do_intersect(begin1, end1, begin2, end2, k); }
-
-// Tag_false => do not convert to polylines
-template <typename InputIterator1, typename InputIterator2>
-inline bool do_intersect (InputIterator1 begin1, InputIterator1 end1,
-                          InputIterator2 begin2, InputIterator2 end2,
-                          Tag_false, unsigned int k=5,
-                          Enable_if_Polygon_2_iterator<InputIterator1>* = 0)
+inline bool do_intersect(InputIterator1 begin1, InputIterator1 end1,
+                         InputIterator2 begin2, InputIterator2 end2,
+                         std::size_t k = 5,
+                         Enable_if_Polygon_2_iterator<InputIterator1>* = 0)
 { return r_do_intersect(begin1, end1, begin2, end2, k); }
 
 // General polygons or polygons with holes
 template <typename InputIterator1, typename InputIterator2>
-inline bool do_intersect (InputIterator1 begin1, InputIterator1 end1,
-                          InputIterator2 begin2, InputIterator2 end2,
-                          unsigned int k=5,
-                          Disable_if_Polygon_2_iterator<InputIterator1>* = 0)
-{
+inline bool do_intersect(InputIterator1 begin1, InputIterator1 end1,
+                         InputIterator2 begin2, InputIterator2 end2,
+                         std::size_t k = 5,
+                         Disable_if_Polygon_2_iterator<InputIterator1>* = 0) {
   typename Iterator_to_gps_traits<InputIterator1>::Traits traits;
   return r_do_intersect(begin1, end1, begin2, end2, traits, k);
 }
 
+#ifndef CGAL_NO_DEPRECATED_CODE
+template <typename InputIterator1, typename InputIterator2, bool b>
+inline bool do_intersect(InputIterator1 begin1, InputIterator1 end1,
+                         InputIterator2 begin2, InputIterator2 end2,
+                         std::bool_constant<b>,
+                         std::enable_if_t<CGAL::is_iterator<InputIterator1>::value &&
+                                          CGAL::is_iterator<InputIterator2>::value >* = 0) {
+  return do_intersect(begin1, end1, begin2, end2);
+}
+#endif
+
 //@}
 
 } //namespace CGAL

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/intersection.h

@@ -7,11 +7,10 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
-// Author(s): Baruch Zukerman <baruchzu@post.tau.ac.il>
-//            Ron Wein        <wein@post.tau.ac.il>
-//            Efi Fogel       <efif@post.tau.ac.il>
-//            Simon Giraudot  <simon.giraudot@geometryfactory.com>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Ron Wein        <wein@post.tau.ac.il>
+//             Efi Fogel       <efif@post.tau.ac.il>
+//             Simon Giraudot  <simon.giraudot@geometryfactory.com>
 
 #ifndef CGAL_BOOLEAN_SET_OPERATIONS_2_INTERSECTION_H
 #define CGAL_BOOLEAN_SET_OPERATIONS_2_INTERSECTION_H
@@ -33,8 +32,7 @@
 #include <CGAL/Boolean_set_operations_2/Polygon_conversions.h>
 #include <CGAL/type_traits/is_iterator.h>
 
-namespace CGAL
-{
+namespace CGAL {
 
 /// \name intersection() functions.
 //@{
@@ -59,10 +57,9 @@ inline OutputIterator intersection(const Polygon_2<Kernel, Container>& pgn1,
 template <typename Kernel, typename Container, typename OutputIterator>
 inline OutputIterator intersection(const Polygon_2<Kernel, Container>& pgn1,
                                    const Polygon_2<Kernel, Container>& pgn2,
-                                   OutputIterator out, Tag_false)
-{
+                                   OutputIterator out, Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_2<Kernel, Container>                          Polygon;
+  using Polygon = Polygon_2<Kernel, Container>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_intersection(pgn1, pgn2, out, traits);
 }
@@ -90,10 +87,9 @@ template <typename Kernel, typename Container, typename OutputIterator>
 inline OutputIterator
 intersection(const Polygon_2<Kernel, Container>& pgn1,
              const Polygon_with_holes_2<Kernel, Container>& pgn2,
-             OutputIterator out, Tag_false)
-{
+             OutputIterator out, Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_2<Kernel, Container>                          Polygon;
+  using Polygon = Polygon_2<Kernel, Container>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_intersection(pgn1, pgn2, out, traits);
 }
@@ -121,10 +117,9 @@ template <typename Kernel, typename Container, typename OutputIterator>
 inline OutputIterator
 intersection(const Polygon_with_holes_2<Kernel, Container>& pgn1,
              const Polygon_2<Kernel, Container>& pgn2,
-             OutputIterator out, Tag_false)
-{
+             OutputIterator out, Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_with_holes_2<Kernel, Container>       Polygon_with_holes;
+  using Polygon_with_holes = Polygon_with_holes_2<Kernel, Container>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_intersection(pgn1, pgn2, out, traits);
 }
@@ -152,10 +147,9 @@ template <typename Kernel, typename Container, typename OutputIterator>
 inline OutputIterator
 intersection(const Polygon_with_holes_2<Kernel, Container>& pgn1,
              const Polygon_with_holes_2<Kernel, Container>& pgn2,
-             OutputIterator out, Tag_false)
-{
+             OutputIterator out, Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_with_holes_2<Kernel, Container>       Polygon_with_holes;
+  using Polygon_with_holes = Polygon_with_holes_2<Kernel, Container>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_intersection(pgn1, pgn2, out, traits);
 }
@@ -172,10 +166,9 @@ inline OutputIterator intersection(const General_polygon_2<ArrTraits>& pgn1,
 template <typename ArrTraits, typename OutputIterator>
 inline OutputIterator intersection(const General_polygon_2<ArrTraits>& pgn1,
                                    const General_polygon_2<ArrTraits>& pgn2,
-                                   OutputIterator out)
-{
+                                   OutputIterator out) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
+  using Polygon = General_polygon_2<ArrTraits>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_intersection(pgn1, pgn2, out, traits);
 }
@@ -194,10 +187,9 @@ template <typename ArrTraits, typename OutputIterator>
 inline OutputIterator intersection(const General_polygon_2<ArrTraits>& pgn1,
                                    const General_polygon_with_holes_2
                                      <General_polygon_2<ArrTraits> >& pgn2,
-                                   OutputIterator out)
-{
+                                   OutputIterator out) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
+  using Polygon = General_polygon_2<ArrTraits>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_intersection(pgn1, pgn2, out, traits);
 }
@@ -216,11 +208,10 @@ template <typename ArrTraits, typename OutputIterator>
 inline OutputIterator intersection(const General_polygon_with_holes_2
                                      <General_polygon_2<ArrTraits> >& pgn1,
                                    const General_polygon_2<ArrTraits>& pgn2,
-                                   OutputIterator out)
-{
+                                   OutputIterator out) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
-  typedef General_polygon_with_holes_2<Polygon>         Polygon_with_holes;
+  using Polygon = General_polygon_2<ArrTraits>;
+  using Polygon_with_holes = General_polygon_with_holes_2<Polygon>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_intersection(pgn1, pgn2, out, traits);
 }
@@ -239,10 +230,9 @@ template <typename Polygon_, typename OutputIterator>
 inline OutputIterator
 intersection(const General_polygon_with_holes_2<Polygon_>& pgn1,
              const General_polygon_with_holes_2<Polygon_>& pgn2,
-             OutputIterator out)
-{
+             OutputIterator out) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_with_holes_2<Polygon_>        Polygon_with_holes;
+  using Polygon_with_holes = General_polygon_with_holes_2<Polygon_>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_intersection(pgn1, pgn2, out, traits);
 }
@@ -256,7 +246,7 @@ intersection(const General_polygon_with_holes_2<Polygon_>& pgn1,
 template <typename InputIterator, typename OutputIterator, typename Traits>
 inline OutputIterator intersection(InputIterator begin, InputIterator end,
                                    OutputIterator oi, Traits& traits,
-                                   unsigned int k=5)
+                                   std::size_t k = 5)
 { return r_intersection(begin, end, oi, traits, k); }
 
 // Without Traits
@@ -265,7 +255,7 @@ template <typename InputIterator, typename OutputIterator>
 inline OutputIterator
 intersection(InputIterator begin, InputIterator end,
              OutputIterator oi, Tag_true = Tag_true(),
-             unsigned int k=5,
+             std::size_t k = 5,
              Enable_if_Polygon_2_iterator<InputIterator>* = 0)
 { return r_intersection(begin, end, oi, k); }
 
@@ -273,9 +263,8 @@ intersection(InputIterator begin, InputIterator end,
 template <typename InputIterator, typename OutputIterator>
 inline OutputIterator
 intersection(InputIterator begin, InputIterator end,
-             OutputIterator oi, Tag_false, unsigned int k=5,
-             Enable_if_Polygon_2_iterator<InputIterator>* = 0)
-{
+             OutputIterator oi, Tag_false, std::size_t k = 5,
+             Enable_if_Polygon_2_iterator<InputIterator>* = 0) {
   typename Iterator_to_gps_traits<InputIterator>::Traits traits;
   return r_intersection(begin, end, oi, traits, k);
 }
@@ -284,11 +273,10 @@ intersection(InputIterator begin, InputIterator end,
 template <typename InputIterator, typename OutputIterator>
 inline OutputIterator
 intersection(InputIterator begin, InputIterator end,
-             OutputIterator oi, unsigned int k=5,
+             OutputIterator oi, std::size_t k = 5,
              // workaround to avoid ambiguous calls with kernel functions
              std::enable_if_t<CGAL::is_iterator<InputIterator>::value>* = 0,
-             Disable_if_Polygon_2_iterator<InputIterator>* = 0)
-{
+             Disable_if_Polygon_2_iterator<InputIterator>* = 0) {
   typename Iterator_to_gps_traits<InputIterator>::Traits traits;
   return r_intersection(begin, end, oi, traits, k);
 }
@@ -300,7 +288,7 @@ template <typename InputIterator1, typename InputIterator2,
 inline OutputIterator intersection(InputIterator1 begin1, InputIterator1 end1,
                                    InputIterator2 begin2, InputIterator2 end2,
                                    OutputIterator oi, Traits& traits,
-                                   unsigned int k=5)
+                                   std::size_t k = 5)
 { return r_intersection(begin1, end1, begin2, end2, oi, traits, k); }
 
 // Without Traits
@@ -310,7 +298,7 @@ template <typename InputIterator1, typename InputIterator2,
 inline OutputIterator
 intersection(InputIterator1 begin1, InputIterator1 end1,
              InputIterator2 begin2, InputIterator2 end2,
-             OutputIterator oi, Tag_true = Tag_true(), unsigned int k=5,
+             OutputIterator oi, Tag_true = Tag_true(), std::size_t k = 5,
              Enable_if_Polygon_2_iterator<InputIterator1>* = 0)
 { return r_intersection(begin1, end1, begin2, end2, oi, k); }
 
@@ -320,9 +308,8 @@ template <typename InputIterator1, typename InputIterator2,
 inline OutputIterator
 intersection(InputIterator1 begin1, InputIterator1 end1,
              InputIterator2 begin2, InputIterator2 end2,
-             OutputIterator oi, Tag_false, unsigned int k=5,
-             Enable_if_Polygon_2_iterator<InputIterator1>* = 0)
-{
+             OutputIterator oi, Tag_false, std::size_t k = 5,
+             Enable_if_Polygon_2_iterator<InputIterator1>* = 0) {
   typename Iterator_to_gps_traits<InputIterator1>::Traits traits;
   return r_intersection(begin1, end1, begin2, end2, oi, traits, k);
 }
@@ -333,9 +320,8 @@ template <typename InputIterator1, typename InputIterator2,
 inline OutputIterator
 intersection(InputIterator1 begin1, InputIterator1 end1,
              InputIterator2 begin2, InputIterator2 end2,
-             OutputIterator oi, unsigned int k=5,
-             Disable_if_Polygon_2_iterator<InputIterator1>* = 0)
-{
+             OutputIterator oi, std::size_t k = 5,
+             Disable_if_Polygon_2_iterator<InputIterator1>* = 0) {
   typename Iterator_to_gps_traits<InputIterator1>::Traits traits;
   return r_intersection(begin1, end1, begin2, end2, oi, traits, k);
 }

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/join.h

@@ -7,11 +7,10 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
-// Author(s): Baruch Zukerman <baruchzu@post.tau.ac.il>
-//            Ron Wein        <wein@post.tau.ac.il>
-//            Efi Fogel       <efif@post.tau.ac.il>
-//            Simon Giraudot  <simon.giraudot@geometryfactory.com>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Ron Wein        <wein@post.tau.ac.il>
+//             Efi Fogel       <efif@post.tau.ac.il>
+//             Simon Giraudot  <simon.giraudot@geometryfactory.com>
 
 #ifndef CGAL_BOOLEAN_SET_OPERATIONS_2_JOIN_H
 #define CGAL_BOOLEAN_SET_OPERATIONS_2_JOIN_H
@@ -33,8 +32,7 @@
 #include <CGAL/Boolean_set_operations_2/Polygon_conversions.h>
 #include <CGAL/type_traits/is_iterator.h>
 
-namespace CGAL
-{
+namespace CGAL {
 
 /// \name join() functions.
 //@{
@@ -60,10 +58,9 @@ template <typename Kernel, typename Container>
 inline bool join(const Polygon_2<Kernel, Container>& pgn1,
                  const Polygon_2<Kernel, Container>& pgn2,
                  Polygon_with_holes_2<Kernel, Container>& res,
-                 Tag_false)
-{
+                 Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_2<Kernel, Container>                          Polygon;
+  using Polygon = Polygon_2<Kernel, Container>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_join(pgn1, pgn2, res, traits);
 }
@@ -89,10 +86,9 @@ template <typename Kernel, typename Container>
 inline bool join(const Polygon_2<Kernel, Container>& pgn1,
                  const Polygon_with_holes_2<Kernel, Container>& pgn2,
                  Polygon_with_holes_2<Kernel, Container>& res,
-                 Tag_false)
-{
+                 Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_2<Kernel, Container>                          Polygon;
+  using Polygon = Polygon_2<Kernel, Container>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_join(pgn1, pgn2, res, traits);
 }
@@ -118,10 +114,9 @@ template <typename Kernel, typename Container>
 inline bool join(const Polygon_with_holes_2<Kernel, Container>& pgn1,
                  const Polygon_2<Kernel, Container>& pgn2,
                  Polygon_with_holes_2<Kernel, Container>& res,
-                 Tag_false)
-{
+                 Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_with_holes_2<Kernel, Container>       Polygon_with_holes;
+  using Polygon_with_holes = Polygon_with_holes_2<Kernel, Container>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_join(pgn1, pgn2, res, traits);
 }
@@ -147,10 +142,9 @@ template <typename Kernel, typename Container>
 inline bool join(const Polygon_with_holes_2<Kernel, Container>& pgn1,
                  const Polygon_with_holes_2<Kernel, Container>& pgn2,
                  Polygon_with_holes_2<Kernel, Container>& res,
-                 Tag_false)
-{
+                 Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_with_holes_2<Kernel, Container>       Polygon_with_holes;
+  using Polygon_with_holes = Polygon_with_holes_2<Kernel, Container>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_join(pgn1, pgn2, res, traits);
 }
@@ -170,10 +164,9 @@ template <typename ArrTraits>
 inline bool
 join(const General_polygon_2<ArrTraits>& pgn1,
      const General_polygon_2<ArrTraits>& pgn2,
-     General_polygon_with_holes_2<General_polygon_2<ArrTraits> >& res)
-{
+     General_polygon_with_holes_2<General_polygon_2<ArrTraits> >& res) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
+  using Polygon = General_polygon_2<ArrTraits>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_join(pgn1, pgn2, res, traits);
 }
@@ -193,10 +186,9 @@ template <typename ArrTraits>
 inline bool
 join(const General_polygon_2<ArrTraits>& pgn1,
      const General_polygon_with_holes_2<General_polygon_2<ArrTraits> >& pgn2,
-     General_polygon_with_holes_2<General_polygon_2<ArrTraits> >& res)
-{
+     General_polygon_with_holes_2<General_polygon_2<ArrTraits> >& res) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
+  using Polygon = General_polygon_2<ArrTraits>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_join(pgn1, pgn2, res, traits);
 }
@@ -216,11 +208,10 @@ template <typename ArrTraits>
 inline bool
 join(const General_polygon_with_holes_2<General_polygon_2<ArrTraits> >& pgn1,
      const General_polygon_2<ArrTraits>& pgn2,
-     General_polygon_with_holes_2<General_polygon_2<ArrTraits> >& res)
-{
+     General_polygon_with_holes_2<General_polygon_2<ArrTraits> >& res) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
-  typedef General_polygon_with_holes_2<Polygon>         Polygon_with_holes;
+  using Polygon = General_polygon_2<ArrTraits>;
+  using Polygon_with_holes = General_polygon_with_holes_2<Polygon>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_join(pgn1, pgn2, res, traits);
 }
@@ -237,10 +228,9 @@ inline bool join(const General_polygon_with_holes_2<Polygon_>& pgn1,
 template <typename Polygon_>
 inline bool join(const General_polygon_with_holes_2<Polygon_>& pgn1,
                  const General_polygon_with_holes_2<Polygon_>& pgn2,
-                 General_polygon_with_holes_2<Polygon_>& res)
-{
+                 General_polygon_with_holes_2<Polygon_>& res) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_with_holes_2<Polygon_>        Polygon_with_holes;
+  using Polygon_with_holes = General_polygon_with_holes_2<Polygon_>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_join(pgn1, pgn2, res, traits);
 }
@@ -253,7 +243,7 @@ inline bool join(const General_polygon_with_holes_2<Polygon_>& pgn1,
 // With Traits
 template <typename InputIterator, typename OutputIterator, typename Traits>
 inline OutputIterator join(InputIterator begin, InputIterator end,
-                           OutputIterator oi, Traits& traits, unsigned int k=5)
+                           OutputIterator oi, Traits& traits, std::size_t k = 5)
 { return r_join(begin, end, oi, traits, k); }
 
 // Without Traits
@@ -261,16 +251,15 @@ inline OutputIterator join(InputIterator begin, InputIterator end,
 template <typename InputIterator, typename OutputIterator>
 inline OutputIterator join(InputIterator begin, InputIterator end,
                            OutputIterator oi, Tag_true = Tag_true(),
-                           unsigned int k=5,
+                           std::size_t k = 5,
                            Enable_if_Polygon_2_iterator<InputIterator>* = 0)
 { return r_join(begin, end, oi, k); }
 
 // Tag_false => do not convert to polylines
 template <typename InputIterator, typename OutputIterator>
 inline OutputIterator join(InputIterator begin, InputIterator end,
-                           OutputIterator oi, Tag_false, unsigned int k=5,
-                           Enable_if_Polygon_2_iterator<InputIterator>* = 0)
-{
+                           OutputIterator oi, Tag_false, std::size_t k = 5,
+                           Enable_if_Polygon_2_iterator<InputIterator>* = 0) {
   typename Iterator_to_gps_traits<InputIterator>::Traits traits;
   return r_join(begin, end, oi, traits, k);
 }
@@ -278,9 +267,8 @@ inline OutputIterator join(InputIterator begin, InputIterator end,
 // General polygons or polygons with holes
 template <typename InputIterator, typename OutputIterator>
 inline OutputIterator join(InputIterator begin, InputIterator end,
-                           OutputIterator oi, unsigned int k=5,
-                           Disable_if_Polygon_2_iterator<InputIterator>* = 0)
-{
+                           OutputIterator oi, std::size_t k = 5,
+                           Disable_if_Polygon_2_iterator<InputIterator>* = 0) {
   typename Iterator_to_gps_traits<InputIterator>::Traits traits;
   return r_join(begin, end, oi, traits, k);
 }
@@ -291,7 +279,7 @@ template <typename InputIterator1, typename InputIterator2,
           typename OutputIterator, typename Traits>
 inline OutputIterator join(InputIterator1 begin1, InputIterator1 end1,
                            InputIterator2 begin2, InputIterator2 end2,
-                           OutputIterator oi, Traits& traits, unsigned int k=5)
+                           OutputIterator oi, Traits& traits, std::size_t k = 5)
 { return r_join(begin1, end1, begin2, end2, oi, traits, k); }
 
 // Without Traits
@@ -301,7 +289,7 @@ template <typename InputIterator1, typename InputIterator2,
 inline OutputIterator join(InputIterator1 begin1, InputIterator1 end1,
                            InputIterator2 begin2, InputIterator2 end2,
                            OutputIterator oi, Tag_true = Tag_true(),
-                           unsigned int k=5,
+                           std::size_t k = 5,
                            Enable_if_Polygon_2_iterator<InputIterator1>* = 0)
 { return r_join(begin1, end1, begin2, end2, oi, k); }
 
@@ -310,9 +298,8 @@ template <typename InputIterator1, typename InputIterator2,
           typename OutputIterator>
 inline OutputIterator join(InputIterator1 begin1, InputIterator1 end1,
                            InputIterator2 begin2, InputIterator2 end2,
-                           OutputIterator oi, Tag_false, unsigned int k=5,
-                           Enable_if_Polygon_2_iterator<InputIterator1>* = 0)
-{
+                           OutputIterator oi, Tag_false, std::size_t k = 5,
+                           Enable_if_Polygon_2_iterator<InputIterator1>* = 0) {
   typename Iterator_to_gps_traits<InputIterator1>::Traits traits;
   return r_join(begin1, end1, begin2, end2, oi, traits, k);
 }
@@ -322,9 +309,8 @@ template <typename InputIterator1, typename InputIterator2,
           typename OutputIterator>
 inline OutputIterator join(InputIterator1 begin1, InputIterator1 end1,
                            InputIterator2 begin2, InputIterator2 end2,
-                           OutputIterator oi, unsigned int k=5,
-                           Disable_if_Polygon_2_iterator<InputIterator1>* = 0)
-{
+                           OutputIterator oi, std::size_t k = 5,
+                           Disable_if_Polygon_2_iterator<InputIterator1>* = 0) {
   typename Iterator_to_gps_traits<InputIterator1>::Traits traits;
   return r_join(begin1, end1, begin2, end2, oi, traits, k);
 }

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/symmetric_difference.h

@@ -7,11 +7,10 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
-// Author(s): Baruch Zukerman <baruchzu@post.tau.ac.il>
-//            Ron Wein        <wein@post.tau.ac.il>
-//            Efi Fogel       <efif@post.tau.ac.il>
-//            Simon Giraudot  <simon.giraudot@geometryfactory.com>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Ron Wein        <wein@post.tau.ac.il>
+//             Efi Fogel       <efif@post.tau.ac.il>
+//             Simon Giraudot  <simon.giraudot@geometryfactory.com>
 
 #ifndef CGAL_BOOLEAN_SET_OPERATIONS_SYMMETRIC_DIFFERENCE_H
 #define CGAL_BOOLEAN_SET_OPERATIONS_SYMMETRIC_DIFFERENCE_H
@@ -33,8 +32,7 @@
 #include <CGAL/Boolean_set_operations_2/Polygon_conversions.h>
 #include <CGAL/type_traits/is_iterator.h>
 
-namespace CGAL
-{
+namespace CGAL {
 
 /// \name symmetric_difference() functions.
 //@{
@@ -62,10 +60,9 @@ template <typename Kernel, typename Container, typename OutputIterator>
 inline OutputIterator
 symmetric_difference(const Polygon_2<Kernel, Container>& pgn1,
                      const Polygon_2<Kernel, Container>& pgn2,
-                     OutputIterator oi, Tag_false)
-{
+                     OutputIterator oi, Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_2<Kernel, Container>                          Polygon;
+  using Polygon = Polygon_2<Kernel, Container>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_symmetric_difference(pgn1, pgn2, oi, traits);
 }
@@ -93,10 +90,9 @@ template <typename Kernel, typename Container, typename OutputIterator>
 inline OutputIterator
 symmetric_difference(const Polygon_2<Kernel, Container>& pgn1,
                      const Polygon_with_holes_2<Kernel, Container>& pgn2,
-                     OutputIterator oi, Tag_false)
-{
+                     OutputIterator oi, Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_2<Kernel, Container>                          Polygon;
+  using Polygon = Polygon_2<Kernel, Container>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_symmetric_difference(pgn1, pgn2, oi, traits);
 }
@@ -124,10 +120,9 @@ template <typename Kernel, typename Container, typename OutputIterator>
 inline OutputIterator
 symmetric_difference(const Polygon_with_holes_2<Kernel, Container>& pgn1,
                      const Polygon_2<Kernel, Container>& pgn2,
-                     OutputIterator oi, Tag_false)
-{
+                     OutputIterator oi, Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_with_holes_2<Kernel, Container>       Polygon_with_holes;
+  using Polygon_with_holes = Polygon_with_holes_2<Kernel, Container>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_symmetric_difference(pgn1, pgn2, oi, traits);
 }
@@ -155,10 +150,9 @@ template <typename Kernel, typename Container, typename OutputIterator>
 inline OutputIterator
 symmetric_difference(const Polygon_with_holes_2<Kernel, Container>& pgn1,
                      const Polygon_with_holes_2<Kernel, Container>& pgn2,
-                     OutputIterator oi, Tag_false)
-{
+                     OutputIterator oi, Tag_false) {
   // Use the first polygon to determine the (default) traits
-  typedef Polygon_with_holes_2<Kernel, Container>       Polygon_with_holes;
+  using Polygon_with_holes = Polygon_with_holes_2<Kernel, Container>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_symmetric_difference(pgn1, pgn2, oi, traits);
 }
@@ -176,10 +170,9 @@ template <typename ArrTraits, typename OutputIterator>
 inline OutputIterator
 symmetric_difference(const General_polygon_2<ArrTraits>& pgn1,
                      const General_polygon_2<ArrTraits>& pgn2,
-                     OutputIterator oi)
-{
+                     OutputIterator oi) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
+  using Polygon = General_polygon_2<ArrTraits>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_symmetric_difference(pgn1, pgn2, oi, traits);
 }
@@ -200,10 +193,9 @@ inline OutputIterator
 symmetric_difference(const General_polygon_2<ArrTraits>& pgn1,
                      const General_polygon_with_holes_2
                            <General_polygon_2<ArrTraits> >& pgn2,
-                     OutputIterator oi)
-{
+                     OutputIterator oi) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
+  using Polygon = General_polygon_2<ArrTraits>;
   typename Gps_default_traits<Polygon>::Traits traits;
   return s_symmetric_difference(pgn1, pgn2, oi, traits);
 }
@@ -224,11 +216,10 @@ inline OutputIterator
 symmetric_difference(const General_polygon_with_holes_2
                        <General_polygon_2<ArrTraits> >& pgn1,
                      const General_polygon_2<ArrTraits>& pgn2,
-                     OutputIterator oi)
-{
+                     OutputIterator oi) {
   // Use the first polygon to determine the (default) traits
-  typedef General_polygon_2<ArrTraits>                  Polygon;
-  typedef General_polygon_with_holes_2<Polygon>         Polygon_with_holes;
+  using Polygon = General_polygon_2<ArrTraits>;
+  using Polygon_with_holes = General_polygon_with_holes_2<Polygon>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_symmetric_difference(pgn1, pgn2, oi, traits);
 }
@@ -247,9 +238,8 @@ template <typename Polygon_, typename OutputIterator>
 inline OutputIterator
 symmetric_difference(const General_polygon_with_holes_2<Polygon_>& pgn1,
                      const General_polygon_with_holes_2<Polygon_>& pgn2,
-                     OutputIterator oi)
-{
-  typedef General_polygon_with_holes_2<Polygon_>        Polygon_with_holes;
+                     OutputIterator oi) {
+  using Polygon_with_holes = General_polygon_with_holes_2<Polygon_>;
   typename Gps_default_traits<Polygon_with_holes>::Traits traits;
   return s_symmetric_difference(pgn1, pgn2, oi, traits);
 }
@@ -264,7 +254,7 @@ template <typename InputIterator, typename OutputIterator, typename Traits>
 inline
 OutputIterator symmetric_difference(InputIterator begin, InputIterator end,
                                     OutputIterator oi, Traits& traits,
-                                    unsigned int k=5)
+                                    std::size_t k = 5)
 { return r_symmetric_difference(begin, end, oi, traits, k); }
 
 // Without Traits
@@ -272,7 +262,7 @@ OutputIterator symmetric_difference(InputIterator begin, InputIterator end,
 template <typename InputIterator, typename OutputIterator>
 inline OutputIterator
 symmetric_difference(InputIterator begin, InputIterator end,
-                     OutputIterator oi, Tag_true = Tag_true(), unsigned int k=5,
+                     OutputIterator oi, Tag_true = Tag_true(), std::size_t k = 5,
                      Enable_if_Polygon_2_iterator<InputIterator>* = 0)
 { return r_symmetric_difference(begin, end, oi, k); }
 
@@ -280,9 +270,8 @@ symmetric_difference(InputIterator begin, InputIterator end,
 template <typename InputIterator, typename OutputIterator>
 inline OutputIterator
 symmetric_difference(InputIterator begin, InputIterator end,
-                     OutputIterator oi, Tag_false, unsigned int k=5,
-                     Enable_if_Polygon_2_iterator<InputIterator>* = 0)
-{
+                     OutputIterator oi, Tag_false, std::size_t k = 5,
+                     Enable_if_Polygon_2_iterator<InputIterator>* = 0) {
   typename Iterator_to_gps_traits<InputIterator>::Traits traits;
   return r_symmetric_difference(begin, end, oi, traits, k);
 }
@@ -291,9 +280,8 @@ symmetric_difference(InputIterator begin, InputIterator end,
 template <typename InputIterator, typename OutputIterator>
 inline OutputIterator
 symmetric_difference(InputIterator begin, InputIterator end,
-                     OutputIterator oi, unsigned int k=5,
-                     Disable_if_Polygon_2_iterator<InputIterator>* = 0)
-{
+                     OutputIterator oi, std::size_t k = 5,
+                     Disable_if_Polygon_2_iterator<InputIterator>* = 0) {
   typename Iterator_to_gps_traits<InputIterator>::Traits traits;
   return r_symmetric_difference(begin, end, oi, traits, k);
 }
@@ -306,7 +294,7 @@ inline
 OutputIterator symmetric_difference(InputIterator1 begin1, InputIterator1 end1,
                                     InputIterator2 begin2, InputIterator2 end2,
                                     OutputIterator oi, Traits& traits,
-                                    unsigned int k=5)
+                                    std::size_t k = 5)
 { return r_symmetric_difference(begin1, end1, begin2, end2, oi, traits, k); }
 
 // Without Traits
@@ -316,7 +304,7 @@ template <typename InputIterator1, typename InputIterator2,
 inline OutputIterator
 symmetric_difference(InputIterator1 begin1, InputIterator1 end1,
                      InputIterator2 begin2, InputIterator2 end2,
-                     OutputIterator oi, Tag_true = Tag_true(), unsigned int k=5,
+                     OutputIterator oi, Tag_true = Tag_true(), std::size_t k = 5,
                      Enable_if_Polygon_2_iterator<InputIterator1>* = 0)
 { return r_symmetric_difference(begin1, end1, begin2, end2, oi, k); }
 
@@ -326,9 +314,8 @@ template <typename InputIterator1, typename InputIterator2,
 inline OutputIterator
 symmetric_difference(InputIterator1 begin1, InputIterator1 end1,
                      InputIterator2 begin2, InputIterator2 end2,
-                     OutputIterator oi, Tag_false, unsigned int k=5,
-                     Enable_if_Polygon_2_iterator<InputIterator1>* = 0)
-{
+                     OutputIterator oi, Tag_false, std::size_t k = 5,
+                     Enable_if_Polygon_2_iterator<InputIterator1>* = 0) {
   typename Iterator_to_gps_traits<InputIterator1>::Traits traits;
   return r_symmetric_difference(begin1, end1, begin2, end2, oi, traits, k);
 }
@@ -339,9 +326,8 @@ template <typename InputIterator1, typename InputIterator2,
 inline OutputIterator
 symmetric_difference(InputIterator1 begin1, InputIterator1 end1,
                      InputIterator2 begin2, InputIterator2 end2,
-                     OutputIterator oi, unsigned int k=5,
-                     Disable_if_Polygon_2_iterator<InputIterator1>* = 0)
-{
+                     OutputIterator oi, std::size_t k = 5,
+                     Disable_if_Polygon_2_iterator<InputIterator1>* = 0) {
   typename Iterator_to_gps_traits<InputIterator1>::Traits traits;
   return r_symmetric_difference(begin1, end1, begin2, end2, oi, traits, k);
 }

Boolean_set_operations_2/include/CGAL/General_polygon_set_2.h

@@ -7,8 +7,8 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Efi Fogel <efif@post.tau.ac.il>
+// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
+//             Efi Fogel <efif@post.tau.ac.il>
 
 #ifndef CGAL_GENERAL_POLYGON_SET_2_H
 #define CGAL_GENERAL_POLYGON_SET_2_H
@@ -27,25 +27,20 @@
 namespace CGAL {
 
 // General_polygon_set_2
-template <class Traits_, class Dcel_ = Gps_default_dcel<Traits_> >
-class General_polygon_set_2 : public General_polygon_set_on_surface_2
-  <Traits_, typename Default_planar_topology<Traits_, Dcel_>::Traits>
-{
-protected:
-  typedef General_polygon_set_2<Traits_, Dcel_>           Self;
+template <typename Traits_, typename Dcel_ = Gps_default_dcel<Traits_>>
+class General_polygon_set_2 :
+  public General_polygon_set_on_surface_2<
+    Traits_, typename Default_planar_topology<Traits_, Dcel_>::Traits> {
 
 public:
-  typedef Traits_                                         Traits_2;
-  typedef Dcel_                                           Dcel;
-
-  typedef General_polygon_set_on_surface_2 <Traits_2,
-    typename Default_planar_topology<Traits_2, Dcel >::Traits>
-                                                          Base;
-
-  typedef CGAL::Arrangement_2<Traits_2, Dcel>             Arrangement_2;
-
-  typedef typename Base::Polygon_2                        Polygon_2;
-  typedef typename Base::Polygon_with_holes_2             Polygon_with_holes_2;
+  using Traits_2 = Traits_;
+  using Dcel = Dcel_;
+  using Self = General_polygon_set_2<Traits_2, Dcel>;
+  using Topology_traits = typename Default_planar_topology<Traits_2, Dcel>::Traits;
+  using Base = General_polygon_set_on_surface_2<Traits_2, Topology_traits>;
+  using Arrangement_2 = CGAL::Arrangement_2<Traits_2, Dcel>;
+  using Polygon_2 = typename Base::Polygon_2;
+  using Polygon_with_holes_2 = typename Base::Polygon_with_holes_2;
 
   // default constructor
   General_polygon_set_2() : Base() {}
@@ -80,19 +75,16 @@ public:
   using Base::join;
   using Base::symmetric_difference;
 
-  inline void intersection(const Self& ps1, const Self& ps2)
-  {
+  inline void intersection(const Self& ps1, const Self& ps2) {
     Base::intersection(static_cast<const Base&>(ps1),
                        static_cast<const Base&>(ps2));
   }
 
-  inline void join(const Self& ps1, const Self& ps2)
-  {
+  inline void join(const Self& ps1, const Self& ps2) {
     Base::join(static_cast<const Base&>(ps1), static_cast<const Base&>(ps2));
   }
 
-  inline void symmetric_difference(const Self& ps1, const Self& ps2)
-  {
+  inline void symmetric_difference(const Self& ps1, const Self& ps2) {
     Base::symmetric_difference(static_cast<const Base&>(ps1),
                                static_cast<const Base&>(ps2));
   }

Boolean_set_operations_2/include/CGAL/General_polygon_set_on_surface_2.h

@@ -7,8 +7,8 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-// Author(s)     : Baruch Zukerman <baruchzu@post.tau.ac.il>
-//                 Efi Fogel <efif@post.tau.ac.il>
+// Author(s):      Baruch Zukerman <baruchzu@post.tau.ac.il>
+//                 Efi Fogel       <efif@post.tau.ac.il>
 //                 Ophir Setter    <ophir.setter@cs.tau.ac.il>
 
 #ifndef CGAL_GENERAL_POLYGON_SET_ON_SURFACE_2_H
@@ -23,54 +23,48 @@
 
 namespace CGAL {
 
-namespace Boolean_set_operation_2_internal
-{
-  struct PreconditionValidationPolicy
-  {
-   /*! is_valid - Checks if a Traits::Polygon_2 OR
-       Traits::Polygon_with_holes_2 are valid.
-       This validation policy checks that polygons are valid in a
-       CGAL_precondition macro. We inherit from Gps_on_surface_base_2
-       and use preconditions to validate the input polygons.
+namespace Boolean_set_operation_2_internal {
+
+struct PreconditionValidationPolicy {
+  /*! Checks if a Traits::Polygon_2 or Traits::Polygon_with_holes_2 are valid.
+   * This validation policy checks that polygons are valid in a
+   * CGAL_precondition macro. We inherit from Gps_on_surface_base_2 and use
+   * preconditions to validate the input polygons.
    */
-    template <class Polygon, class Traits>
-    inline static void is_valid(const Polygon& p, const Traits& t)
-    {
-      CGAL_precondition(is_valid_unknown_polygon(p, t));
-      CGAL_USE(p); CGAL_USE(t);
-    }
-  };
+  template <typename Polygon, typename Traits>
+  inline static void is_valid(const Polygon& p, const Traits& t) {
+    CGAL_precondition(is_valid_unknown_polygon(p, t));
+    CGAL_USE(p); CGAL_USE(t);
+  }
+};
+
 }
 
-// General_polygon_set_on_surface_2
-/*
-  This class is derived from Gps_on_surface_base_2.
-  It enforces the validation conditions for general polygons, and is therefore
-  the basic implementation that should be used by the user
-*/
-template <class Traits_, class TopTraits_>
-  class General_polygon_set_on_surface_2 :
-  public Gps_on_surface_base_2<Traits_, TopTraits_,
-                 Boolean_set_operation_2_internal::PreconditionValidationPolicy>
-{
+/* `General_polygon_set_on_surface_2` class is derived from
+ * `Gps_on_surface_base_2`.  It enforces the validation conditions for general
+ * polygons, and is therefore the basic implementation that should be used by
+ * the user
+ */
+template <typename Traits_, typename TopTraits_>
+class General_polygon_set_on_surface_2 :
+    public Gps_on_surface_base_2<
+      Traits_, TopTraits_,
+      Boolean_set_operation_2_internal::PreconditionValidationPolicy> {
+
 protected:
-  typedef Traits_                                                   Traits_2;
-  typedef General_polygon_set_on_surface_2<Traits_2, TopTraits_>    Self;
-  typedef Gps_on_surface_base_2<Traits_2, TopTraits_,
-   Boolean_set_operation_2_internal::PreconditionValidationPolicy>  Base;
+  using Traits_2 = Traits_;
+  using Self = General_polygon_set_on_surface_2<Traits_2, TopTraits_>;
+  using Base = Gps_on_surface_base_2<Traits_2, TopTraits_,
+                                     Boolean_set_operation_2_internal::PreconditionValidationPolicy>;
 
 public:
-  typedef typename Base::Polygon_2                                  Polygon_2;
-  typedef typename Base::Polygon_with_holes_2
-    Polygon_with_holes_2;
-  typedef typename Base::Arrangement_on_surface_2
-    Arrangement_on_surface_2;
+  using Polygon_2 = typename Base::Polygon_2;
+  using Polygon_with_holes_2 = typename Base::Polygon_with_holes_2;
+  using Arrangement_on_surface_2 = typename Base::Arrangement_on_surface_2;
 
 public:
-
   // default constructor
-  General_polygon_set_on_surface_2() : Base()
-  {}
+  General_polygon_set_on_surface_2() : Base() {}
 
   // constructor from a traits object
   General_polygon_set_on_surface_2(const Traits_2& traits) : Base(traits) {}
@@ -79,8 +73,7 @@ public:
   General_polygon_set_on_surface_2(const Self& ps) : Base(ps) {}
 
   // assignment operator
-  General_polygon_set_on_surface_2& operator=(const Self& ps)
-  {
+  General_polygon_set_on_surface_2& operator=(const Self& ps) {
     Base::operator=(ps);
     return (*this);
   }
@@ -90,19 +83,15 @@ public:
 
   // constructor from a polygon with holes
   explicit
-  General_polygon_set_on_surface_2(const Polygon_with_holes_2& pwh) :
-    Base(pwh)
-  {}
+  General_polygon_set_on_surface_2(const Polygon_with_holes_2& pwh) : Base(pwh) {}
 
   // constructor from a polygon and a traits object
-  explicit General_polygon_set_on_surface_2(const Polygon_2& pgn,
-                                            const Traits_2& traits) :
+  explicit General_polygon_set_on_surface_2(const Polygon_2& pgn, const Traits_2& traits) :
     Base(pgn, traits) {}
 
   // constructor from a polygon with holes and a traits object
   explicit
-  General_polygon_set_on_surface_2(const Polygon_with_holes_2& pwh,
-                                   const Traits_2& traits) :
+  General_polygon_set_on_surface_2(const Polygon_with_holes_2& pwh, const Traits_2& traits) :
     Base(pwh, traits)
   {}
 
@@ -142,4 +131,4 @@ private:
 
 #include <CGAL/enable_warnings.h>
 
-#endif // CGAL_GENERAL_POLYGON_SET_ON_SURFACE_2_H
+#endif

Boolean_set_operations_2/test/Boolean_set_operations_2/bug_3989.cpp

@@ -1,48 +0,0 @@
-#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
-#include <CGAL/Boolean_set_operations_2.h>
-#include <CGAL/Polygon_set_2.h>
-#include <list>
-
-typedef CGAL::Exact_predicates_exact_constructions_kernel K;
-
-
-int main()
-{
-  CGAL::Polygon_2<K> ob;
-  ob.push_back(CGAL::Point_2<K>(1, 1));
-  ob.push_back(CGAL::Point_2<K>(1, 0));
-  ob.push_back(CGAL::Point_2<K>(6, 0));
-  ob.push_back(CGAL::Point_2<K>(6, 7));
-  ob.push_back(CGAL::Point_2<K>(0, 7));
-  ob.push_back(CGAL::Point_2<K>(0, 1));
-
-  CGAL::Polygon_2<K> h;
-  h.push_back(CGAL::Point_2<K>(2, 1));
-  h.push_back(CGAL::Point_2<K>(2, 2));
-  h.push_back(CGAL::Point_2<K>(3, 2));
-  h.push_back(CGAL::Point_2<K>(3, 3));
-  h.push_back(CGAL::Point_2<K>(2, 3));
-  h.push_back(CGAL::Point_2<K>(2, 4));
-  h.push_back(CGAL::Point_2<K>(3, 4));
-  h.push_back(CGAL::Point_2<K>(3, 5));
-  h.push_back(CGAL::Point_2<K>(4, 5));
-  h.push_back(CGAL::Point_2<K>(4, 1));
-
-  CGAL::Polygon_with_holes_2<K> ob_with_holes(ob);
-  ob_with_holes.add_hole(h);
-  CGAL::Polygon_set_2<K> inter(ob_with_holes);
-
-  CGAL::Polygon_2<K> new_poly;
-  new_poly.push_back(CGAL::Point_2<K>(1, 1));
-  new_poly.push_back(CGAL::Point_2<K>(2, 1));
-  new_poly.push_back(CGAL::Point_2<K>(2, 2));
-  new_poly.push_back(CGAL::Point_2<K>(2, 3));
-  new_poly.push_back(CGAL::Point_2<K>(2, 4));
-  new_poly.push_back(CGAL::Point_2<K>(2, 5));
-  new_poly.push_back(CGAL::Point_2<K>(3, 5));
-  new_poly.push_back(CGAL::Point_2<K>(4, 5));
-  new_poly.push_back(CGAL::Point_2<K>(4, 6));
-  new_poly.push_back(CGAL::Point_2<K>(1, 6));
-
-  inter.difference(new_poly);
-}

Boolean_set_operations_2/test/Boolean_set_operations_2/test_compilation.cpp

@@ -1,4 +1,3 @@
-
 #include <vector>
 
 #include <CGAL/Simple_cartesian.h>
@@ -13,35 +12,32 @@
 #include <CGAL/Polygon_set_2.h>
 
 //typedef CGAL::Quotient<CGAL::MP_Float>                Number_type;
-typedef int Number_type;
+using Number_type = int;
 
-typedef CGAL::Simple_cartesian<Number_type>             Kernel;
+using Kernel = CGAL::Simple_cartesian<Number_type>;
 
-typedef CGAL::Gps_segment_traits_2<Kernel>              Traits;
-typedef CGAL::Polygon_set_2<Kernel>                     Ps;
+using Traits = CGAL::Gps_segment_traits_2<Kernel>;
+using Ps = CGAL::Polygon_set_2<Kernel>;
 
-typedef CGAL::Arr_segment_traits_2<Kernel>              Arr_traits;
-typedef CGAL::Gps_traits_2<Arr_traits>                  General_traits;
-typedef CGAL::General_polygon_set_2<General_traits>     Gps;
+using Arr_traits = CGAL::Arr_segment_traits_2<Kernel>;
+using General_traits = CGAL::Gps_traits_2<Arr_traits>;
+using Gps = CGAL::General_polygon_set_2<General_traits>;
 
-typedef CGAL::Arr_non_caching_segment_traits_2<Kernel>  Nc_traits;
-typedef CGAL::Gps_segment_traits_2<Kernel,
-                                   std::vector<Kernel::Point_2>,
-                                   Nc_traits>           Traits_non_caching;
-typedef CGAL::General_polygon_set_2<Traits_non_caching> Gps_non_caching;
+using Nc_traits = CGAL::Arr_non_caching_segment_traits_2<Kernel>;
+using Traits_non_caching = CGAL::Gps_segment_traits_2<Kernel, std::vector<Kernel::Point_2>, Nc_traits>;
+using Gps_non_caching = CGAL::General_polygon_set_2<Traits_non_caching>;
 
-template <class GPS>
-void test()
-{
-  typedef typename GPS::Traits_2                        Traits;
-  typedef typename Traits::Point_2                      Point_2;
-  typedef typename Traits::Polygon_2                    Polygon_2;
-  typedef typename Traits::Polygon_with_holes_2         Polygon_with_holes_2;
+template <typename GPS>
+void test() {
+  using Traits = typename GPS::Traits_2;
+  using Point_2 = typename Traits::Point_2;
+  using Polygon_2 = typename Traits::Polygon_2;
+  using Polygon_with_holes_2 = typename Traits::Polygon_with_holes_2;
 
   Polygon_2 pgn1, pgn2;
-  Polygon_with_holes_2  pgn_with_holes1, pgn_with_holes2;
-  std::vector<Polygon_2>             polygons;
-  std::vector<Polygon_with_holes_2>  polygons_with_holes;
+  Polygon_with_holes_2 pgn_with_holes1, pgn_with_holes2;
+  std::vector<Polygon_2> polygons;
+  std::vector<Polygon_with_holes_2> polygons_with_holes;
   GPS gps;
   GPS other;
 
@@ -242,8 +238,7 @@ void test()
   GPS new_gps2 = gps;
 }
 
-void test_CGAL_Polygon_variants()
-{
+void test_CGAL_Polygon_variants() {
   typedef CGAL::Polygon_2<Kernel>               Polygon_2;
   typedef CGAL::Polygon_with_holes_2<Kernel>    Polygon_with_holes_2;
   typedef CGAL::Gps_default_traits<Polygon_2>::Traits Traits;
@@ -257,45 +252,25 @@ void test_CGAL_Polygon_variants()
   Traits tr;
 
   CGAL::do_intersect(pgn1, pgn2);
-  CGAL::do_intersect(pgn1, pgn2, CGAL::Tag_true());
-  CGAL::do_intersect(pgn1, pgn2, CGAL::Tag_false());
   CGAL::do_intersect(pgn1, pgn2, tr);
 
   CGAL::do_intersect(pgn1, pgn_with_holes2);
-  CGAL::do_intersect(pgn1, pgn_with_holes2, CGAL::Tag_true());
-  CGAL::do_intersect(pgn1, pgn_with_holes2, CGAL::Tag_false());
   CGAL::do_intersect(pgn1, pgn_with_holes2, tr);
 
   CGAL::do_intersect(pgn_with_holes1, pgn2);
-  CGAL::do_intersect(pgn_with_holes1, pgn2, CGAL::Tag_true());
-  CGAL::do_intersect(pgn_with_holes1, pgn2, CGAL::Tag_false());
   CGAL::do_intersect(pgn_with_holes1, pgn2, tr);
 
   CGAL::do_intersect(pgn_with_holes1, pgn_with_holes2);
-  CGAL::do_intersect(pgn_with_holes1, pgn_with_holes2, CGAL::Tag_true());
-  CGAL::do_intersect(pgn_with_holes1, pgn_with_holes2, CGAL::Tag_false());
   CGAL::do_intersect(pgn_with_holes1, pgn_with_holes2, tr);
 
   CGAL::do_intersect(polygons.begin(), polygons.end());
-  CGAL::do_intersect(polygons.begin(), polygons.end(), CGAL::Tag_true());
-  CGAL::do_intersect(polygons.begin(), polygons.end(), CGAL::Tag_false());
   CGAL::do_intersect(polygons.begin(), polygons.end(), tr);
 
   CGAL::do_intersect(polygons_with_holes.begin(), polygons_with_holes.end());
-  CGAL::do_intersect(polygons_with_holes.begin(), polygons_with_holes.end(),
-                     CGAL::Tag_true());
-  CGAL::do_intersect(polygons_with_holes.begin(), polygons_with_holes.end(),
-                     CGAL::Tag_false());
   CGAL::do_intersect(polygons_with_holes.begin(), polygons_with_holes.end(), tr);
 
   CGAL::do_intersect(polygons.begin(), polygons.end(),
                      polygons_with_holes.begin(), polygons_with_holes.end());
-  CGAL::do_intersect(polygons.begin(), polygons.end(),
-                     polygons_with_holes.begin(), polygons_with_holes.end(),
-                     CGAL::Tag_true());
-  CGAL::do_intersect(polygons.begin(), polygons.end(),
-                     polygons_with_holes.begin(), polygons_with_holes.end(),
-                     CGAL::Tag_false());
   CGAL::do_intersect(polygons.begin(), polygons.end(),
                      polygons_with_holes.begin(), polygons_with_holes.end(), tr);
 
@@ -519,8 +494,7 @@ void test_CGAL_Polygon_variants()
   CGAL::complement(pgn_with_holes1, std::back_inserter(result), tr);
 }
 
-int main()
-{
+int main() {
   test<Gps>();
   test<Ps>();
   test<Gps_non_caching>();

Boolean_set_operations_2/test/Boolean_set_operations_2/test_do_intersect_circles.cpp

@@ -0,0 +1,94 @@
+#include <iostream>
+
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Boolean_set_operations_2.h>
+#include <CGAL/Arr_circle_segment_traits_2.h>
+#include <CGAL/General_polygon_2.h>
+#include <CGAL/Boolean_set_operations_2.h>
+// #include <CGAL/draw_arrangement_2.h>
+
+using Kernel = CGAL::Exact_predicates_exact_constructions_kernel;
+using Point_2 = Kernel::Point_2;
+using Polygon_2 = CGAL::Polygon_2<Kernel>;
+using Circle_2 = Kernel::Circle_2;
+
+int main() {
+  Kernel kernel;
+  auto ctr_circle = kernel.construct_circle_2_object();
+  auto circle1 = ctr_circle(Point_2(0, 1), 1);
+  auto circle2 = ctr_circle(Point_2(0, -1), 1);
+  auto circle3 = ctr_circle(Point_2(0, 2), 4);
+
+  // 1. Circular arcs and linear segments
+  using Circle_segment_arr_traits_2 = CGAL::Arr_circle_segment_traits_2<Kernel>;
+  using Circle_segment_xcv_2 = Circle_segment_arr_traits_2::X_monotone_curve_2;
+  using Circle_segment_pnt_2 = Circle_segment_arr_traits_2::Point_2;
+  using Circle_segment_gps_traits_2 = CGAL::Gps_traits_2<Circle_segment_arr_traits_2>;
+  using Circle_segment_polygon = Circle_segment_gps_traits_2::General_polygon_2;
+
+  Circle_segment_arr_traits_2 circle_segment_traits;
+
+  Circle_segment_pnt_2 cs_pnt11(1, 1);
+  Circle_segment_pnt_2 cs_pnt12(-1, 1);
+  Circle_segment_xcv_2 xcv11(circle1, cs_pnt11, cs_pnt12, CGAL::COUNTERCLOCKWISE);
+  Circle_segment_xcv_2 xcv12(circle1, cs_pnt12, cs_pnt11, CGAL::COUNTERCLOCKWISE);
+  Circle_segment_polygon pgn1;
+  pgn1.push_back(xcv11);
+  pgn1.push_back(xcv12);
+
+  Circle_segment_pnt_2 cs_pnt21(1, -1);
+  Circle_segment_pnt_2 cs_pnt22(-1, -1);
+  Circle_segment_xcv_2 xcv21(circle2, cs_pnt21, cs_pnt22, CGAL::COUNTERCLOCKWISE);
+  Circle_segment_xcv_2 xcv22(circle2, cs_pnt22, cs_pnt21, CGAL::COUNTERCLOCKWISE);
+  Circle_segment_polygon pgn2;
+  pgn2.push_back(xcv21);
+  pgn2.push_back(xcv22);
+
+  Circle_segment_pnt_2 cs_pnt31(2, 2);
+  Circle_segment_pnt_2 cs_pnt32(-2, 2);
+  Circle_segment_xcv_2 xcv31(circle3, cs_pnt31, cs_pnt32, CGAL::COUNTERCLOCKWISE);
+  Circle_segment_xcv_2 xcv32(circle3, cs_pnt32, cs_pnt31, CGAL::COUNTERCLOCKWISE);
+  Circle_segment_polygon pgn3;
+  pgn3.push_back(xcv31);
+  pgn3.push_back(xcv32);
+
+  // 1.1.
+  auto do_intersect = CGAL::do_intersect(pgn1, pgn2);
+  if (do_intersect) {
+    std::cerr << "The circles intersect (case 1)\n" << std::endl;
+    return 1;
+  }
+
+  // 1.2.
+  std::vector<Circle_segment_polygon> pgns1 = { pgn1, pgn2 };
+  do_intersect = CGAL::do_intersect(pgns1.begin(), pgns1.end());
+  if (do_intersect) {
+    std::cerr << "The circles intersect (case 2)\n" << std::endl;
+    return 1;
+  }
+
+  // 2.1.
+  do_intersect = CGAL::do_intersect(pgn1, pgn3);
+  if (! do_intersect) {
+    std::cerr << "The circles do not intersect (case 1)\n" << std::endl;
+    return 1;
+  }
+
+  // 2.2.
+  std::vector<Circle_segment_polygon> pgns2 = { pgn1, pgn3 };
+  do_intersect = CGAL::do_intersect(pgns2.begin(), pgns2.end());
+  if (! do_intersect) {
+    std::cerr << "The circles do not intersect (case 2)\n" << std::endl;
+    return 1;
+  }
+
+  // using Circle_segment_arr = CGAL::Arrangement_2<Circle_segment_arr_traits_2>;
+  // Circle_segment_arr arr;
+  // CGAL::insert_non_intersecting_curve(arr, xcv11);
+  // CGAL::insert_non_intersecting_curve(arr, xcv12);
+  // CGAL::insert_non_intersecting_curve(arr, xcv21);
+  // CGAL::insert_non_intersecting_curve(arr, xcv22);
+  // CGAL::draw(arr);
+
+  return 0;
+}

Classification/examples/Classification/example_classification.cpp

@@ -8,7 +8,7 @@
 #include <CGAL/bounding_box.h>
 #include <CGAL/tags.h>
 #include <CGAL/IO/read_points.h>
-#include <CGAL/IO/write_ply_points.h>
+#include <CGAL/IO/PLY.h>
 
 #include <CGAL/Real_timer.h>
 

Combinatorial_map/doc/Combinatorial_map/Concepts/GenericMap.h

@@ -1068,8 +1068,18 @@ If \link GenericMap::are_attributes_automatically_managed `are_attributes_automa
 template <unsigned int i>
 size_type remove_cell(Dart_descriptor d);
 
+/*!
+\ingroup PkgCombinatorialMapsRefIO
+  Writes `amap` in `os`, using our own internal file format in XML. Writes both the topology of the combinatorial map and its enabled attributes.
+ */
+friend std::ostream& operator<< (std::ostream& os, const GenericMap& amap);
+
+/*!
+  \ingroup PkgCombinatorialMapsRefIO
+  Reads `amap` from `is`, using our own internal file format in XML. Reads both the topology of the combinatorial map and its enabled attributes which are present in `is`. Note that if `amap` is not empty before the reading, the new map is added in the previous one.
+ */
+friend std::ifstream& operator>> (std::ifstream& is, GenericMap& amap);
+
 /// @}
 
 }; /* end GenericMap */
-
-

Combinatorial_map/doc/Combinatorial_map/PackageDescription.txt

@@ -6,6 +6,9 @@
 /// \defgroup PkgCombinatorialMapsClasses Classes
 /// \ingroup PkgCombinatorialMapsRef
 
+/// \defgroup PkgCombinatorialMapsRefIO IO Functions for CMap
+/// \ingroup PkgCombinatorialMapsRef
+
 /*!
 \addtogroup PkgCombinatorialMapsRef
 \cgalPkgDescriptionBegin{Combinatorial Maps,PkgCombinatorialMaps}
@@ -36,5 +39,9 @@
 - `CGAL::Cell_attribute_with_id<CMap,Info_,Tag,OnMerge,OnSplit>`
 - `CGAL::Generic_map_min_items`
 
+\cgalCRPSubsection{IO Functions for CMap}
+- \link PkgCombinatorialMapsRefIO `std::ostream& operator<< (std::ostream& os, const GenericMap& amap)` \endlink
+- \link PkgCombinatorialMapsRefIO `std::ifstream& operator>> (std::ifstream& is, GenericMap& amap)` \endlink
+
 */
 

Combinatorial_map/include/CGAL/Combinatorial_map.h

@@ -255,7 +255,7 @@ namespace CGAL {
         }
       }
 
-      // Create an mapping between darts of the two maps (originals->copies).
+      // Creates a mapping between darts of the two maps (originals->copies).
       // (here we cannot use CGAL::Unique_hash_map because it does not provide
       // iterators...
       std::unordered_map<Dart_descriptor_2, Dart_descriptor> local_dartmap;
@@ -585,7 +585,7 @@ namespace CGAL {
                                     bool copy_perforated_darts=false,
                                     size_type mark_perforated=INVALID_MARK)
     {
-      // Create an mapping between darts of the two maps (originals->copies).
+      // Creates a mapping between darts of the two maps (originals->copies).
       // (here we cannot use CGAL::Unique_hash_map because it does not provide
       // iterators...
       std::unordered_map
@@ -661,7 +661,7 @@ namespace CGAL {
       return is;
     }
 
-    /** Create a new dart and add it to the map.
+    /** Creates a new dart and add it to the map.
      * The marks of the darts are initialized with mmask_marks, i.e. the dart
      * is unmarked for all the marks.
      * @return a Dart_descriptor on the new dart.
@@ -968,7 +968,7 @@ namespace CGAL {
     size_type number_of_used_marks() const
     { return mnb_used_marks; }
 
-    /** Test if a given mark is reserved.
+    /** Tests if a given mark is reserved.
      *  @return true iff the mark is reserved (i.e. in used).
      */
     bool is_reserved(size_type amark) const
@@ -997,14 +997,14 @@ namespace CGAL {
       return number_of_darts() - number_of_marked_darts(amark);
     }
 
-    /** Test if all the darts are unmarked for a given mark.
+    /** Tests if all the darts are unmarked for a given mark.
      * @param amark the mark index.
      * @return true iff all the darts are unmarked for amark.
      */
     bool is_whole_map_unmarked(size_type amark) const
     { return number_of_marked_darts(amark) == 0; }
 
-    /** Test if all the darts are marked for a given mark.
+    /** Tests if all the darts are marked for a given mark.
      * @param amark the mark index.
      * @return true iff all the darts are marked for amark.
      */
@@ -1071,7 +1071,7 @@ namespace CGAL {
       mmask_marks.flip(amark);
     }
 
-    /** Test if a given dart is marked for a given mark.
+    /** Tests if a given dart is marked for a given mark.
      * @param adart the dart to test.
      * @param amark the given mark.
      * @return true iff adart is marked for the mark amark.
@@ -1239,7 +1239,7 @@ namespace CGAL {
     std::size_t orient(size_type amark) const
     { negate_mark(amark); return number_of_darts(); }
 
-    /** Test if this map is without boundary for a given dimension.
+    /** Tests if this map is without boundary for a given dimension.
      * @param i the dimension.
      * @return true iff all the darts are not i-free.
      * @pre 1<=i<=n
@@ -1253,7 +1253,7 @@ namespace CGAL {
       return true;
     }
 
-    /** Test if this map is without boundary for all the dimensions.
+    /** Tests if this map is without boundary for all the dimensions.
      * @return true iff all the darts are non free.
      */
     bool is_without_boundary() const
@@ -1334,7 +1334,7 @@ namespace CGAL {
       return res;
     }
 
-    /** Test if the map is valid.
+    /** Tests if the map is valid.
      * @return true iff the map is valid.
      */
     bool is_valid(bool show_errors=true) const
@@ -1579,7 +1579,7 @@ namespace CGAL {
       return os;
     }
 
-    /// Create a new attribute.
+    /// Creates a new attribute.
     /// @return a descriptor on the new attribute.
     template<unsigned int i, typename ...Args>
     typename Attribute_descriptor<i>::type create_attribute(const Args&... args)
@@ -1988,7 +1988,7 @@ namespace CGAL {
       else unlink_beta_for_involution(adart, i);
     }
 
-    /** Test if it is possible to sew by betai the two given darts
+    /** Tests if it is possible to sew by betai the two given darts
      * @param adart1 the first dart.
      * @param adart2 the second dart.
      * @return true iff \em adart1 can be i-sewn with \em adart2.
@@ -3439,7 +3439,7 @@ namespace CGAL {
     }
 
 
-    /** Test if the connected component of cmap containing dart dh1 is
+    /** Tests if the connected component of cmap containing dart dh1 is
      *  isomorphic to the connected component of map2 containing dart dh2,
      *  starting from dh1 and dh2.
      * @param dh1  initial dart for this map
@@ -3648,7 +3648,7 @@ namespace CGAL {
       return match;
     }
 
-    /** Test if this cmap is isomorphic to map2.
+    /** Tests if this cmap is isomorphic to map2.
      * @pre cmap is connected.
      * @param map2 the second combinatorial map
      * @param testDartInfo Boolean to test the equality of dart info (true)
@@ -3687,7 +3687,7 @@ namespace CGAL {
       return false;
     }
 
-    /** Test if the attributes of this map are automatically updated.
+    /** Tests if the attributes of this map are automatically updated.
      * @return true iff the boolean automatic_attributes_management is set to true.
      */
     bool are_attributes_automatically_managed() const
@@ -3710,13 +3710,13 @@ namespace CGAL {
     void set_automatic_attributes_management_without_correction(bool newval)
     { this->automatic_attributes_management = newval; }
 
-    /** Create a halfedge.
-     * @return a dart of the new halfedge.
+    /** Creates a halfedge.
+     * @return a dart of the new half-edge.
      */
     Dart_descriptor make_half_edge()
     { return create_dart(); }
 
-    /** Create an edge.
+    /** Creates an edge.
      * if closed==true, the edge has no 2-free dart.
      * (note that for CMap there is no difference between true and false, but
      *  this is not the case for GMap)
@@ -3730,7 +3730,7 @@ namespace CGAL {
       return d1;
     }
 
-    /** Create an edge given 2 Attribute_descriptor<0>.
+    /** Creates an edge given 2 Attribute_descriptor<0>.
      * Note that this function can be used only if 0-attributes are non void
      * @param h0 the first vertex descriptor.
      * @param h1 the second vertex descriptor.
@@ -3751,7 +3751,7 @@ namespace CGAL {
       return d1;
     }
 
-    /** Create a combinatorial polygon of length alg
+    /** Creates a combinatorial polygon of length alg
      * (a cycle of alg darts beta1 links together).
      * @return a new dart.
      */
@@ -3772,7 +3772,7 @@ namespace CGAL {
       return start;
     }
 
-    /** Test if a face is a combinatorial polygon of length alg
+    /** Tests if a face is a combinatorial polygon of length alg
      *  (a cycle of alg darts beta1 links together).
      * @param adart an initial dart
      * @return true iff the face containing adart is a polygon of length alg.
@@ -3794,7 +3794,7 @@ namespace CGAL {
       return (nb==alg);
     }
 
-    /** Create a triangle given 3 Attribute_descriptor<0>.
+    /** Creates a triangle given 3 Attribute_descriptor<0>.
      * @param h0 the first descriptor.
      * @param h1 the second descriptor.
      * @param h2 the third descriptor.
@@ -3814,7 +3814,7 @@ namespace CGAL {
       return d1;
     }
 
-    /** Create a quadrangle given 4 Vertex_attribute_descriptor.
+    /** Creates a quadrangle given 4 Vertex_attribute_descriptor.
      * @param h0 the first vertex descriptor.
      * @param h1 the second vertex descriptor.
      * @param h2 the third vertex descriptor.
@@ -3837,7 +3837,7 @@ namespace CGAL {
       return d1;
     }
 
-    /** Create a combinatorial tetrahedron from 4 triangles.
+    /** Creates a combinatorial tetrahedron from 4 triangles.
      * @param d1 a dart onto a first triangle.
      * @param d2 a dart onto a second triangle.
      * @param d3 a dart onto a third triangle.
@@ -3859,9 +3859,9 @@ namespace CGAL {
       return d1;
     }
 
-    /** Test if a volume is a combinatorial tetrahedron.
-     * @param adart an initial dart
-     * @return true iff the volume containing adart is a combinatorial tetrahedron.
+    /** Tests if a volume is a combinatorial tetrahedron.
+     * @param d1 an initial dart
+     * @return true iff the volume containing d1 is a combinatorial tetrahedron.
      */
     bool is_volume_combinatorial_tetrahedron(Dart_const_descriptor d1) const
     {
@@ -3892,7 +3892,7 @@ namespace CGAL {
       return true;
     }
 
-    /** Create a new combinatorial tetrahedron.
+    /** Creates a new combinatorial tetrahedron.
      * @return a new dart.
      */
     Dart_descriptor make_combinatorial_tetrahedron()
@@ -3905,7 +3905,7 @@ namespace CGAL {
       return make_combinatorial_tetrahedron(d1, d2, d3, d4);
     }
 
-    /** Create a combinatorial hexahedron from 6 quadrilaterals.
+    /** Creates a combinatorial hexahedron from 6 quadrilaterals.
      * @param d1 a dart onto a first quadrilateral.
      * @param d2 a dart onto a second quadrilateral.
      * @param d3 a dart onto a third quadrilateral.
@@ -3952,9 +3952,9 @@ namespace CGAL {
       return d1;
     }
 
-    /** Test if a volume is a combinatorial hexahedron.
-     * @param adart an initial dart
-     * @return true iff the volume containing adart is a combinatorial hexahedron.
+    /** Tests if a volume is a combinatorial hexahedron.
+     * @param d1 an initial dart
+     * @return true iff the volume containing d1 is a combinatorial hexahedron.
      */
     bool is_volume_combinatorial_hexahedron(Dart_const_descriptor d1) const
     {
@@ -4004,7 +4004,7 @@ namespace CGAL {
       return true;
     }
 
-    /** Create a new combinatorial hexahedron.
+    /** Creates a new combinatorial hexahedron.
      * @return a new dart.
      */
     Dart_descriptor make_combinatorial_hexahedron()
@@ -4019,7 +4019,362 @@ namespace CGAL {
       return make_combinatorial_hexahedron(d1, d2, d3, d4, d5, d6);
     }
 
-    /** Test if an i-cell can be removed.
+    /** Tests if a volume is a combinatorial prism.
+     * @param d1 an initial dart
+     * @return true iff the volume containing d1 is a combinatorial prism.
+     */
+    bool is_volume_combinatorial_prism(Dart_const_descriptor d1) const
+    {
+      Dart_const_descriptor d2=beta(d1, 2);
+      Dart_const_descriptor d3=beta(d1, 1, 2);
+      Dart_const_descriptor d4=beta(d1, 0, 2);
+      Dart_const_descriptor d5=beta(d2, 1, 1, 2);
+
+      if ( d1==null_dart_descriptor || d2==null_dart_descriptor ||
+           d3==null_dart_descriptor || d4==null_dart_descriptor ||
+           d5==null_dart_descriptor ) { return false; }
+
+      if (!is_face_combinatorial_polygon(d1, 3) ||
+          !is_face_combinatorial_polygon(d2, 4) ||
+          !is_face_combinatorial_polygon(d3, 4) ||
+          !is_face_combinatorial_polygon(d4, 4) ||
+          !is_face_combinatorial_polygon(d5, 3)) { return false; }
+
+      // TODO do better with marks.
+      if (belong_to_same_cell<2,1>(d1, d2) ||
+          belong_to_same_cell<2,1>(d1, d3) ||
+          belong_to_same_cell<2,1>(d1, d4) ||
+          belong_to_same_cell<2,1>(d1, d5) ||
+          belong_to_same_cell<2,1>(d2, d3) ||
+          belong_to_same_cell<2,1>(d2, d4) ||
+          belong_to_same_cell<2,1>(d2, d5) ||
+          belong_to_same_cell<2,1>(d3, d4) ||
+          belong_to_same_cell<2,1>(d3, d5) ||
+          belong_to_same_cell<2,1>(d4, d5))
+      { return false; }
+
+      if (beta(d2,0,2)  !=beta(d3,1) ||
+          beta(d2,1,2)  !=beta(d4,0) ||
+          beta(d3,0,2)  !=beta(d4,1) ||
+          beta(d3,1,1,2)!=beta(d5,0) ||
+          beta(d4,1,1,2)!=beta(d5,1)) { return false; }
+
+      return true;
+    }
+
+    /** Creates a combinatorial prism from 2 triangles and 3 squares.
+     * @param d1 a dart onto a first triangle.
+     * @param d2 a dart onto a first square.
+     * @param d3 a dart onto a second square.
+     * @param d4 a dart onto a thirth square.
+     * @param d5 a dart onto a second triangle.
+     * @return a new dart.
+     */
+    Dart_descriptor make_combinatorial_prism(Dart_descriptor d1,
+                                             Dart_descriptor d2,
+                                             Dart_descriptor d3,
+                                             Dart_descriptor d4,
+                                             Dart_descriptor d5)
+    {
+      // 2-link for first triangle
+      basic_link_beta_for_involution(d1, d2, 2);
+      basic_link_beta_for_involution(beta(d1, 1), d3, 2);
+      basic_link_beta_for_involution(beta(d1, 0), d4, 2);
+
+      // 2-link for quandrangles between them
+      basic_link_beta_for_involution(beta(d2, 0), beta(d3, 1), 2);
+      basic_link_beta_for_involution(beta(d2, 1), beta(d4, 0), 2);
+      basic_link_beta_for_involution(beta(d3, 0), beta(d4, 1), 2);
+
+      // 2-link for second triangle
+      basic_link_beta_for_involution(beta(d2, 1, 1), d5, 2);
+      basic_link_beta_for_involution(beta(d3, 1, 1), beta(d5, 0), 2);
+      basic_link_beta_for_involution(beta(d4, 1, 1), beta(d5, 1), 2);
+
+      return d1;
+    }
+
+    /** Creates a new combinatorial prism.
+     * @return a new dart.
+     */
+    Dart_descriptor make_combinatorial_prism()
+    {
+      Dart_descriptor d1 = make_combinatorial_polygon(3);
+      Dart_descriptor d2 = make_combinatorial_polygon(4);
+      Dart_descriptor d3 = make_combinatorial_polygon(4);
+      Dart_descriptor d4 = make_combinatorial_polygon(4);
+      Dart_descriptor d5 = make_combinatorial_polygon(3);
+
+      return make_combinatorial_prism( d1, d2, d3, d4, d5);
+    }
+
+    /** Tests if a volume is a combinatorial pyramid.
+     * @param d1 an intial dart
+     * @return true iff the volume containing d1 is a combinatorial pyramid.
+     */
+    bool is_volume_combinatorial_pyramid(Dart_const_descriptor d1) const
+    {
+      Dart_const_descriptor d2=beta(d1, 2);
+      Dart_const_descriptor d3=beta(d1, 0, 2);
+      Dart_const_descriptor d4=beta(d1, 1, 1, 2);
+      Dart_const_descriptor d5=beta(d1, 1, 2);
+
+      if (d1==null_dart_descriptor || d2==null_dart_descriptor ||
+          d3==null_dart_descriptor || d4==null_dart_descriptor ||
+          d5==null_dart_descriptor) { return false; }
+
+      if (!is_face_combinatorial_polygon(d1, 4) ||
+          !is_face_combinatorial_polygon(d2, 3) ||
+          !is_face_combinatorial_polygon(d3, 3) ||
+          !is_face_combinatorial_polygon(d4, 3) ||
+          !is_face_combinatorial_polygon(d5, 3)) { return false; }
+
+      // TODO do better with marks.
+      if (belong_to_same_cell<2,1>(d1, d2) ||
+          belong_to_same_cell<2,1>(d1, d3) ||
+          belong_to_same_cell<2,1>(d1, d4) ||
+          belong_to_same_cell<2,1>(d1, d5) ||
+          belong_to_same_cell<2,1>(d2, d3) ||
+          belong_to_same_cell<2,1>(d2, d4) ||
+          belong_to_same_cell<2,1>(d2, d5) ||
+          belong_to_same_cell<2,1>(d3, d4) ||
+          belong_to_same_cell<2,1>(d3, d5) ||
+          belong_to_same_cell<2,1>(d4, d5))
+      { return false; }
+
+      if (beta(d2,1,2)!=beta(d3,0) ||
+          beta(d2,0,2)!=beta(d5,1) ||
+          beta(d5,0,2)!=beta(d4,1) ||
+          beta(d4,0,2)!=beta(d3,1)) { return false; }
+
+      return true;
+    }
+
+    /** Creates a combinatorial pyramid from 1 square and 4 triangles.
+     * @param d1 a dart onto the square.
+     * @param d2 a dart onto a first triangle.
+     * @param d3 a dart onto a second triangle.
+     * @param d4 a dart onto a thirth triangle.
+     * @param d5 a dart onto a fourth triangle.
+     * @return a new dart.
+     */
+    Dart_descriptor make_combinatorial_pyramid(Dart_descriptor d1,
+                                               Dart_descriptor d2,
+                                               Dart_descriptor d3,
+                                               Dart_descriptor d4,
+                                               Dart_descriptor d5)
+    {
+      // 2-link for the square
+      basic_link_beta_for_involution(d1, d2, 2);
+      basic_link_beta_for_involution(beta(d1, 1), d5, 2);
+      basic_link_beta_for_involution(beta(d1, 1, 1), d4, 2);
+      basic_link_beta_for_involution(beta(d1, 0), d3, 2);
+
+      // 2-link for first triangle
+      basic_link_beta_for_involution(beta(d2, 1), beta(d3, 0), 2);
+      basic_link_beta_for_involution(beta(d2, 0), beta(d5, 1), 2);
+
+      // 2-link for triangles between them
+      basic_link_beta_for_involution(beta(d5, 0), beta(d4, 1), 2);
+      basic_link_beta_for_involution(beta(d4, 0), beta(d3, 1), 2);
+
+      return d1;
+    }
+
+    /** Creates a new combinatorial pyramid.
+     * @return a new dart.
+     */
+    Dart_descriptor make_combinatorial_pyramid()
+    {
+      Dart_descriptor d1=make_combinatorial_polygon(4);
+      Dart_descriptor d2=make_combinatorial_polygon(3);
+      Dart_descriptor d3=make_combinatorial_polygon(3);
+      Dart_descriptor d4=make_combinatorial_polygon(3);
+      Dart_descriptor d5=make_combinatorial_polygon(3);
+
+      return make_combinatorial_pyramid(d1, d2, d3, d4, d5);
+    }
+
+    /** Tests if a volume is a combinatorial pentagonal prism.
+     * @param d1 an initial dart
+     * @return true iff the volume containing d1 is a combinatorial pentagonal prism.
+     */
+    bool is_volume_combinatorial_pentagonal_prism(Dart_const_descriptor d1) const
+    {
+      Dart_const_descriptor d2=beta(d1, 2);
+      Dart_const_descriptor d3=beta(d1, 1, 2);
+      Dart_const_descriptor d4=beta(d1, 1, 1, 2);
+      Dart_const_descriptor d5=beta(d1, 0, 0, 2);
+      Dart_const_descriptor d6=beta(d1, 0, 2);
+      Dart_const_descriptor d7=beta(d2, 1, 1, 2);
+
+      if (d1==null_dart_descriptor || d2==null_dart_descriptor ||
+          d3==null_dart_descriptor || d4==null_dart_descriptor ||
+          d5==null_dart_descriptor || d6==null_dart_descriptor ||
+          d7==null_dart_descriptor)
+      { return false; }
+
+      if (!is_face_combinatorial_polygon(d1, 5) ||
+          !is_face_combinatorial_polygon(d2, 4) ||
+          !is_face_combinatorial_polygon(d3, 4) ||
+          !is_face_combinatorial_polygon(d4, 4) ||
+          !is_face_combinatorial_polygon(d5, 4) ||
+          !is_face_combinatorial_polygon(d6, 4) ||
+          !is_face_combinatorial_polygon(d7, 5)) { return false; }
+
+      // TODO do better with marks.
+      if (belong_to_same_cell<2,1>(d1, d2) ||
+          belong_to_same_cell<2,1>(d1, d3) ||
+          belong_to_same_cell<2,1>(d1, d4) ||
+          belong_to_same_cell<2,1>(d1, d5) ||
+          belong_to_same_cell<2,1>(d1, d6) ||
+          belong_to_same_cell<2,1>(d1, d7) ||
+          belong_to_same_cell<2,1>(d2, d3) ||
+          belong_to_same_cell<2,1>(d2, d4) ||
+          belong_to_same_cell<2,1>(d2, d5) ||
+          belong_to_same_cell<2,1>(d2, d6) ||
+          belong_to_same_cell<2,1>(d2, d7) ||
+          belong_to_same_cell<2,1>(d3, d4) ||
+          belong_to_same_cell<2,1>(d3, d5) ||
+          belong_to_same_cell<2,1>(d3, d6) ||
+          belong_to_same_cell<2,1>(d3, d7) ||
+          belong_to_same_cell<2,1>(d4, d5) ||
+          belong_to_same_cell<2,1>(d4, d6) ||
+          belong_to_same_cell<2,1>(d4, d7) ||
+          belong_to_same_cell<2,1>(d5, d6) ||
+          belong_to_same_cell<2,1>(d5, d7) ||
+          belong_to_same_cell<2,1>(d6, d7))
+      { return false; }
+
+      if (beta(d2,0,2)  !=beta(d3,1) ||
+          beta(d3,0,2)  !=beta(d4,1) ||
+          beta(d4,0,2)  !=beta(d5,1) ||
+          beta(d5,0,2)  !=beta(d6,1) ||
+          beta(d6,0,2)  !=beta(d2,1) ||
+          beta(d3,1,1,2)!=beta(d7,0) ||
+          beta(d4,1,1,2)!=beta(d7,0,0) ||
+          beta(d5,1,1,2)!=beta(d7,1,1) ||
+          beta(d6,1,1,2)!=beta(d7,1)) { return false; }
+
+      return true;
+
+    }
+
+    /** Tests if a volume is a combinatorial hexagonal prism.
+     * @param d1 an initial dart
+     * @return true iff the volume containing d1 is a combinatorial hexagonal prism.
+     */
+    bool is_volume_combinatorial_hexagonal_prism(Dart_const_descriptor d1) const
+    {
+      Dart_const_descriptor d2=beta(d1, 2);
+      Dart_const_descriptor d3=beta(d1, 1, 2);
+      Dart_const_descriptor d4=beta(d1, 1, 1, 2);
+      Dart_const_descriptor d5=beta(d1, 1, 1, 1, 2);
+      Dart_const_descriptor d6=beta(d1, 0, 0, 2);
+      Dart_const_descriptor d7=beta(d1, 0, 2);
+      Dart_const_descriptor d8=beta(d2, 1, 1, 2);
+
+      if (d1==null_dart_descriptor || d2==null_dart_descriptor ||
+          d3==null_dart_descriptor || d4==null_dart_descriptor ||
+          d5==null_dart_descriptor || d6==null_dart_descriptor ||
+          d7==null_dart_descriptor || d8==null_dart_descriptor)
+      { return false; }
+
+      if (!is_face_combinatorial_polygon(d1, 6) ||
+          !is_face_combinatorial_polygon(d2, 4) ||
+          !is_face_combinatorial_polygon(d3, 4) ||
+          !is_face_combinatorial_polygon(d4, 4) ||
+          !is_face_combinatorial_polygon(d5, 4) ||
+          !is_face_combinatorial_polygon(d6, 4) ||
+          !is_face_combinatorial_polygon(d7, 4) ||
+          !is_face_combinatorial_polygon(d8, 6)) { return false; }
+
+      // TODO do better with marks.
+      if (belong_to_same_cell<2,1>(d1, d2) ||
+          belong_to_same_cell<2,1>(d1, d3) ||
+          belong_to_same_cell<2,1>(d1, d4) ||
+          belong_to_same_cell<2,1>(d1, d5) ||
+          belong_to_same_cell<2,1>(d1, d6) ||
+          belong_to_same_cell<2,1>(d1, d7) ||
+          belong_to_same_cell<2,1>(d1, d8) ||
+          belong_to_same_cell<2,1>(d2, d3) ||
+          belong_to_same_cell<2,1>(d2, d4) ||
+          belong_to_same_cell<2,1>(d2, d5) ||
+          belong_to_same_cell<2,1>(d2, d6) ||
+          belong_to_same_cell<2,1>(d2, d7) ||
+          belong_to_same_cell<2,1>(d2, d8) ||
+          belong_to_same_cell<2,1>(d3, d4) ||
+          belong_to_same_cell<2,1>(d3, d5) ||
+          belong_to_same_cell<2,1>(d3, d6) ||
+          belong_to_same_cell<2,1>(d3, d7) ||
+          belong_to_same_cell<2,1>(d3, d8) ||
+          belong_to_same_cell<2,1>(d4, d5) ||
+          belong_to_same_cell<2,1>(d4, d6) ||
+          belong_to_same_cell<2,1>(d4, d7) ||
+          belong_to_same_cell<2,1>(d4, d8) ||
+          belong_to_same_cell<2,1>(d5, d6) ||
+          belong_to_same_cell<2,1>(d5, d7) ||
+          belong_to_same_cell<2,1>(d5, d8) ||
+          belong_to_same_cell<2,1>(d6, d7) ||
+          belong_to_same_cell<2,1>(d6, d8) ||
+          belong_to_same_cell<2,1>(d7, d8))
+      { return false; }
+
+      if (beta(d2,0,2)  !=beta(d3,1) ||
+          beta(d3,0,2)  !=beta(d4,1) ||
+          beta(d4,0,2)  !=beta(d5,1) ||
+          beta(d5,0,2)  !=beta(d6,1) ||
+          beta(d6,0,2)  !=beta(d7,1) ||
+          beta(d7,0,2)  !=beta(d2,1) ||
+          beta(d3,1,1,2)!=beta(d8,0) ||
+          beta(d4,1,1,2)!=beta(d8,0,0) ||
+          beta(d5,1,1,2)!=beta(d8,0,0,0) ||
+          beta(d6,1,1,2)!=beta(d8,1,1) ||
+          beta(d7,1,1,2)!=beta(d8,1)) { return false; }
+
+      return true;
+    }
+
+    /** Tests if a volume is a combinatorial tetrahedron10.
+     * @param d1 an initial dart
+     * @return true iff the volume containing d1 is a combinatorial tetrahedron10.
+     */
+    bool is_volume_combinatorial_tetrahedron10(Dart_const_descriptor d1) const
+    {
+      Dart_const_descriptor d2=beta(d1, 2,0);
+      Dart_const_descriptor d3=beta(d2, 0,2);
+      Dart_const_descriptor d4=beta(d2, 1,1,1,2);
+
+      if(d1==null_dart_descriptor || d2==null_dart_descriptor ||
+         d3==null_dart_descriptor || d4==null_dart_descriptor)
+      { return false; }
+
+      if(!is_face_combinatorial_polygon(d1, 6) ||
+         !is_face_combinatorial_polygon(d2, 6) ||
+         !is_face_combinatorial_polygon(d3, 6) ||
+         !is_face_combinatorial_polygon(d4, 6)) { return false; }
+
+      if(beta(d1, 1,2)!=beta(d1, 2,0) ||
+         beta(d2, 1,2)!=beta(d2, 2,0) ||
+         beta(d3, 1,2)!=beta(d3, 2,0) ||
+         beta(d4, 1,2)!=beta(d4, 2,0)) { return false; }
+
+      // TODO do better with marks (?).
+      if(belong_to_same_cell<2,1>(d1, d2) ||
+         belong_to_same_cell<2,1>(d1, d3) ||
+         belong_to_same_cell<2,1>(d1, d4) ||
+         belong_to_same_cell<2,1>(d2, d3) ||
+         belong_to_same_cell<2,1>(d2, d4) ||
+         belong_to_same_cell<2,1>(d3, d4)) { return false; }
+
+      if(beta(d1,1,1,2)!=beta(d3,0) ||
+         beta(d1,0,2)!=beta(d4,1,1) ||
+         beta(d4,0,2)!=beta(d3,1,1)) { return false; }
+
+      return true;
+    }
+
+    /** Tests if an i-cell can be removed.
      *  An i-cell can be removed if i==dimension or i==dimension-1,
      *     or if there are at most two (i+1)-cell incident to it.
      * @param adart a dart of the i-cell.
@@ -4041,7 +4396,7 @@ namespace CGAL {
         run(*this,adart,update_attributes);
     }
 
-    /** Test if an i-cell can be contracted.
+    /** Tests if an i-cell can be contracted.
      *  An i-cell can be contracted if i==1
      *     or if there are at most two (i-1)-cell incident to it.
      * @param adart a dart of the i-cell.
@@ -4407,7 +4762,7 @@ namespace CGAL {
       return this->template beta<0>(adart1);
     }
 
-    /** Test if an edge can be inserted onto a 2-cell between two given darts.
+    /** Tests if an edge can be inserted onto a 2-cell between two given darts.
      * @param adart1 a first dart.
      * @param adart2 a second dart.
      * @return true iff an edge can be inserted between adart1 and adart2.
@@ -4443,7 +4798,7 @@ namespace CGAL {
       return generic_insert_cell_1(adart1, adart2, false, update_attributes);
     }
 
-    /** Test if an edge can be inserted between two different 2-cells
+    /** Tests if an edge can be inserted between two different 2-cells
      *   between two given darts.
      * @param adart1 a first dart.
      * @param adart2 a second dart.
@@ -4627,7 +4982,7 @@ namespace CGAL {
       return this->template beta<0>(adart1);
     }
 
-    /** Test if a 2-cell can be inserted onto a given 3-cell along
+    /** Tests if a 2-cell can be inserted onto a given 3-cell along
      * a path of edges.
      * @param afirst iterator on the beginning of the path.
      * @param alast  iterator on the end of the path.

Combinatorial_map/include/CGAL/Element_topo.h

@@ -0,0 +1,208 @@
+// Copyright (c) 2025 CNRS and LIRIS' Establishments (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org)
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
+//
+// Author(s)     : Guillaume Damiand <guillaume.damiand@liris.cnrs.fr>
+//
+////////////////////////////////////////////////////////////////////////////////
+#ifndef CMAP_ELEMENT_TOPO_H
+#define CMAP_ELEMENT_TOPO_H
+
+#include <string>
+
+namespace CGAL {
+  namespace CMap {
+    namespace Element_topo {
+
+enum cell_topo
+  {
+    SQUARE=0,
+    TRIANGLE=1,
+    HEXAHEDRON=2,
+    TETRAHEDRON=3,
+    PRISM=4,
+    PYRAMID=5,
+    GENERIC_2D=6,
+    GENERIC_3D=7,
+    EDGE=8,
+    TETRAHEDRON10=9,
+    PENTAGONAL_PRISM=10,
+    HEXAGONAL_PRISM=11,
+    NO_TYPE=-1
+  };
+
+inline
+std::string topo_name(cell_topo t)
+{
+  switch(t)
+  {
+    case SQUARE: return "SQUARE";
+    case TRIANGLE: return "TRIANGLE";
+    case HEXAHEDRON: return "HEXAHEDRON";
+    case TETRAHEDRON: return "TETRAHEDRON";
+    case PRISM: return "PRISM";
+    case PYRAMID: return "PYRAMID";
+    case GENERIC_2D: return "GENERIC_2D";
+    case GENERIC_3D: return "GENERIC_3D";
+    case EDGE: return "EDGE";
+    case TETRAHEDRON10: return "TETRAHEDRON10";
+    case PENTAGONAL_PRISM: return "PENTAGONAL_PRISM";
+    case HEXAGONAL_PRISM: return "HEXAGONAL_PRISM";
+    case NO_TYPE: return "NO_TYPE";
+  }
+  return "UNKNOWN";
+}
+
+inline
+cell_topo topo_from_name(const std::string& t)
+{
+  if (t=="SQUARE") return SQUARE;
+  if (t=="TRIANGLE") return TRIANGLE;
+  if (t=="HEXAHEDRON") return HEXAHEDRON;
+  if (t=="TETRAHEDRON") return TETRAHEDRON;
+  if (t=="PRISM") return PRISM;
+  if (t=="PYRAMID") return PYRAMID;
+  if (t=="GENERIC_2D") return GENERIC_2D;
+  if (t=="GENERIC_3D") return GENERIC_3D;
+  if (t=="EDGE") return EDGE;
+  if (t=="TETRAHEDRON10") return TETRAHEDRON10;
+  if (t=="PENTAGONAL_PRISM") return PENTAGONAL_PRISM;
+  if (t=="HEXAGONAL_PRISM") return HEXAGONAL_PRISM;
+  if (t=="NO_TYPE") return NO_TYPE;
+  return NO_TYPE;
+}
+
+/**
+ * @brief To get the type of `dimD` cell of the `CMap` of `cmapdim` dimension.
+ */
+template<typename CMap, unsigned int dimcell,
+         unsigned int cmapdim=CMap::dimension>
+struct Get_cell_topo
+{
+  static cell_topo run(CMap&, typename CMap::Dart_descriptor dh,
+                       typename CMap::Dart_descriptor& starting_dart)
+  {
+    starting_dart=dh;
+    return NO_TYPE;
+  }
+};
+
+/**
+ * @brief To get the type associated of an edge. For now only one type.
+ */
+template<typename CMap, unsigned int cmapdim>
+struct Get_cell_topo<CMap, 1, cmapdim>
+{
+  static cell_topo run(CMap&, typename CMap::Dart_descriptor it,
+                       typename CMap::Dart_descriptor& starting_dart)
+  {
+    starting_dart=it;
+    return EDGE;
+  }
+};
+
+/**
+ * @brief To get the type of 2D cell of the CMap of cmapdim dimension.
+ */
+template<typename CMap, unsigned int cmapdim>
+struct Get_cell_topo<CMap, 2, cmapdim>
+{
+  static cell_topo run(CMap& cmap, typename CMap::Dart_descriptor it,
+                       typename CMap::Dart_descriptor& starting_dart)
+  {
+    starting_dart=it;
+
+    if (cmap.is_face_combinatorial_polygon(it, 3))
+    { return TRIANGLE; }
+
+    else if (cmap.is_face_combinatorial_polygon(it, 4))
+    { return SQUARE; }
+
+    return GENERIC_2D;
+  }
+};
+
+/**
+ * @brief To get the type of 3D cell of the CMap of dimension 3.
+ */
+template<typename CMap>
+struct Get_cell_topo<CMap, 3, 3>
+{
+  static cell_topo run(CMap& cmap, typename CMap::Dart_descriptor it,
+                       typename CMap::Dart_descriptor& starting_dart)
+  {
+    starting_dart=it;
+
+    if (cmap.is_volume_combinatorial_tetrahedron(it))
+    { return TETRAHEDRON; }
+
+    else if (cmap.is_volume_combinatorial_hexahedron(it))
+    { return HEXAHEDRON; }
+
+    else if(cmap.is_volume_combinatorial_tetrahedron10(it))
+    { return TETRAHEDRON10; }
+
+    // For non symetric object, we need to test all darts
+    for (auto itv=cmap.template darts_of_cell<3>(it).begin(),
+         itvend=cmap.template darts_of_cell<3>(it).end(); itv!=itvend; ++itv)
+    {
+      starting_dart=itv;
+
+      if (cmap.is_volume_combinatorial_prism(itv))
+      { return PRISM; }
+
+      else if (cmap.is_volume_combinatorial_pentagonal_prism(itv))
+      { return PENTAGONAL_PRISM; }
+
+      else if (cmap.is_volume_combinatorial_pyramid(itv))
+      { return PYRAMID; }
+
+      else if (cmap.is_volume_combinatorial_hexagonal_prism(itv))
+      { return HEXAGONAL_PRISM; }
+
+    }
+
+    return GENERIC_3D;
+  }
+};
+
+template<unsigned int dimcell, typename CMap>
+cell_topo get_cell_topo(CMap& cmap, typename CMap::Dart_descriptor it,
+                        typename CMap::Dart_descriptor& starting_dart)
+{ return Get_cell_topo<CMap, dimcell>::run(cmap, it, starting_dart); }
+
+template<unsigned int dimcell, typename CMap>
+cell_topo get_cell_topo(CMap& cmap, typename CMap::Dart_descriptor it)
+{
+  typename CMap::Dart_descriptor dummy;
+  return get_cell_topo<dimcell, CMap>(cmap, it, dummy);
+}
+
+template<unsigned int dimcell, typename CMap>
+cell_topo get_cell_topo(const CMap& cmap, typename CMap::Dart_const_descriptor it,
+    typename CMap::Dart_const_descriptor& starting_dart)
+{
+  typename CMap::Dart_descriptor it2=const_cast<CMap&>(cmap).dart_descriptor
+                                       (cmap.darts().index(it));
+  typename CMap::Dart_descriptor sd2;
+  cell_topo res=Get_cell_topo<CMap, dimcell>::run(const_cast<CMap&>(cmap),
+                                                    it2, sd2);
+  starting_dart=sd2;
+  return res;
+}
+
+template<unsigned int dimcell, typename CMap>
+cell_topo get_cell_topo(const CMap& cmap, typename CMap::Dart_const_descriptor it)
+{
+  typename CMap::Dart_descriptor it2=it;
+  return Get_cell_topo<CMap, dimcell>::run(const_cast<CMap&>(cmap), it2);
+}
+
+} } } // namespace CGAL::CMap::Element_topo
+
+#endif // CMAP_ELEMENT_TOPO_H

Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConformingConstrainedDelaunayTriangulationCellBase_3.h

@@ -3,7 +3,7 @@
 \cgalConcept
 
 The concept `ConformingConstrainedDelaunayTriangulationCellBase_3` refines the concept
-`TriangulationCellBase_3` and and describes the requirements for a base cell class of
+`TriangulationCellBase_3` and describes the requirements for a base cell class of
 the `CGAL::Conforming_constrained_Delaunay_triangulation_3` class.
 
 \cgalRefines{TriangulationCellBase_3, BaseWithTimeStamp}

Constrained_triangulation_3/examples/Constrained_triangulation_3/ccdt_3_from_soup.cpp

@@ -5,6 +5,7 @@
 #include <CGAL/make_conforming_constrained_Delaunay_triangulation_3.h>
 
 #include <vector>
+#include <algorithm>
 
 using K = CGAL::Exact_predicates_inexact_constructions_kernel;
 
@@ -29,6 +30,18 @@ int main(int argc, char* argv[])
             << "Number of constrained facets in the CDT: "
             << ccdt.number_of_constrained_facets() << '\n';
 
+  // Collect constrained facets per polygon
+  std::vector<std::size_t> constrained_facets(polygons.size());
+  for(auto facet : ccdt.constrained_facets())
+  {
+    int i = ccdt.face_constraint_index(facet);
+    ++constrained_facets[i];
+  }
+  auto it = std::max_element(constrained_facets.begin(), constrained_facets.end());
+
+  std::cout << "The polygon with the most constrained facets has index "
+            << (it - constrained_facets.begin()) << " and " << *it << " facets.\n";
+
   std::ofstream ofs(argc > 2 ? argv[2] : "out.mesh");
   ofs.precision(17);
   CGAL::IO::write_MEDIT(ofs, ccdt);

Constrained_triangulation_3/include/CGAL/Conforming_Delaunay_triangulation_3.h

@@ -17,6 +17,7 @@
 #include <CGAL/Constrained_triangulation_3/internal/config.h>
 
 #include <CGAL/Conforming_constrained_Delaunay_triangulation_vertex_data_3.h>
+#include <CGAL/Real_timer.h>
 #include <CGAL/Triangulation_2/internal/Polyline_constraint_hierarchy_2.h>
 #include <CGAL/Triangulation_segment_traverser_3.h>
 #include <CGAL/unordered_flat_set.h>
@@ -34,8 +35,209 @@
 
 #ifndef DOXYGEN_RUNNING
 
+#if CGAL_USE_ITT
+#  include <ittnotify.h>
+#endif
+
 namespace CGAL {
 
+namespace CDT_3 {
+
+struct Debug_options {
+  enum class Flags {
+    Steiner_points = 0,
+    conforming,
+    input_faces,
+    missing_region,
+    regions,
+    copy_triangulation_into_hole,
+    validity,
+    use_older_cavity_algorithm,
+    debug_finite_edges_map,
+    use_finite_edges_map,
+    debug_subconstraints_to_conform,
+    verbose_special_cases,
+    debug_encroaching_vertices,
+    debug_conforming_validation,
+    debug_constraint_hierarchy,
+    debug_geometric_errors,
+    debug_polygon_insertion,
+    display_statistics,
+    nb_of_flags
+  };
+
+  bool Steiner_points() const { return flags[static_cast<int>(Flags::Steiner_points)]; }
+  void Steiner_points(bool b) { flags.set(static_cast<int>(Flags::Steiner_points), b); }
+
+  bool input_faces() const { return flags[static_cast<int>(Flags::input_faces)]; }
+  void input_faces(bool b) { flags.set(static_cast<int>(Flags::input_faces), b); }
+
+  bool missing_region() const { return flags[static_cast<int>(Flags::missing_region)]; }
+  void missing_region(bool b) { flags.set(static_cast<int>(Flags::missing_region), b); }
+
+  bool regions() const { return flags[static_cast<int>(Flags::regions)]; }
+  void regions(bool b) { flags.set(static_cast<int>(Flags::regions), b); }
+
+  bool copy_triangulation_into_hole() const { return flags[static_cast<int>(Flags::copy_triangulation_into_hole)]; }
+  void copy_triangulation_into_hole(bool b) { flags.set(static_cast<int>(Flags::copy_triangulation_into_hole), b); }
+
+  bool validity() const { return flags[static_cast<int>(Flags::validity)]; }
+  void validity(bool b) { flags.set(static_cast<int>(Flags::validity), b); }
+
+  bool use_older_cavity_algorithm() const { return flags[static_cast<int>(Flags::use_older_cavity_algorithm)]; }
+  bool use_newer_cavity_algorithm() const { return !flags[static_cast<int>(Flags::use_older_cavity_algorithm)]; }
+  void use_older_cavity_algorithm(bool b) { flags.set(static_cast<int>(Flags::use_older_cavity_algorithm), b); }
+
+  bool finite_edges_map() const { return flags[static_cast<int>(Flags::debug_finite_edges_map)]; }
+  void finite_edges_map(bool b) { flags.set(static_cast<int>(Flags::debug_finite_edges_map), b); }
+
+  bool subconstraints_to_conform() const { return flags[static_cast<int>(Flags::debug_subconstraints_to_conform)]; }
+  void subconstraints_to_conform(bool b) { flags.set(static_cast<int>(Flags::debug_subconstraints_to_conform), b); }
+
+  bool use_finite_edges_map_flag() const { return flags[static_cast<int>(Flags::use_finite_edges_map)]; }
+  void use_finite_edges_map(bool b) { flags.set(static_cast<int>(Flags::use_finite_edges_map), b); }
+
+  bool verbose_special_cases() const { return flags[static_cast<int>(Flags::verbose_special_cases)]; }
+  void verbose_special_cases(bool b) { flags.set(static_cast<int>(Flags::verbose_special_cases), b); }
+
+  bool encroaching_vertices() const { return flags[static_cast<int>(Flags::debug_encroaching_vertices)]; }
+  void encroaching_vertices(bool b) { flags.set(static_cast<int>(Flags::debug_encroaching_vertices), b); }
+
+  bool conforming_validation() const { return flags[static_cast<int>(Flags::debug_conforming_validation)]; }
+  void conforming_validation(bool b) { flags.set(static_cast<int>(Flags::debug_conforming_validation), b); }
+
+  bool constraint_hierarchy() const { return flags[static_cast<int>(Flags::debug_constraint_hierarchy)]; }
+  void constraint_hierarchy(bool b) { flags.set(static_cast<int>(Flags::debug_constraint_hierarchy), b); }
+
+  bool geometric_errors() const { return flags[static_cast<int>(Flags::debug_geometric_errors)]; }
+  void geometric_errors(bool b) { flags.set(static_cast<int>(Flags::debug_geometric_errors), b); }
+
+  bool polygon_insertion() const { return flags[static_cast<int>(Flags::debug_polygon_insertion)]; }
+  void polygon_insertion(bool b) { flags.set(static_cast<int>(Flags::debug_polygon_insertion), b); }
+
+  bool display_statistics() const { return flags[static_cast<int>(Flags::display_statistics)]; }
+  void display_statistics(bool b) { flags.set(static_cast<int>(Flags::display_statistics), b); }
+
+  double segment_vertex_epsilon() const { return segment_vertex_epsilon_; }
+  void set_segment_vertex_epsilon(double eps) { segment_vertex_epsilon_ = eps; }
+
+  double vertex_vertex_epsilon() const { return vertex_vertex_epsilon_; }
+  void set_vertex_vertex_epsilon(double eps) { vertex_vertex_epsilon_ = eps; }
+
+private:
+  std::bitset<static_cast<int>(Flags::nb_of_flags)> flags{};
+  double segment_vertex_epsilon_ = 0.0;
+  double vertex_vertex_epsilon_  = 0.0;
+}; // end struct Debug_options
+
+namespace internal {
+
+auto& tasks_manager() {
+  struct Tasks_manager {
+    enum {
+      READ_INPUT = 0,
+      MERGE_FACETS,
+      INSERT_VERTICES,
+      COMPUTE_DISTANCES,
+      CONFORMING,
+      CDT,
+      OUTPUT,
+      VALIDATION,
+      NB_TASKS
+    };
+
+  #if CGAL_USE_ITT
+    __itt_domain* cdt_3_domain = __itt_domain_create("org.cgal.CDT_3");
+    const std::array<__itt_string_handle*, NB_TASKS> task_handles = {
+      __itt_string_handle_create("CDT_3: read input file"),
+      __itt_string_handle_create("CDT_3: merge facets"),
+      __itt_string_handle_create("CDT_3: insert vertices"),
+      __itt_string_handle_create("CDT_3: compute distances"),
+      __itt_string_handle_create("CDT_3: conforming"),
+      __itt_string_handle_create("CDT_3: cdt"),
+      __itt_string_handle_create("CDT_3: outputs"),
+      __itt_string_handle_create("CDT_3: validation")
+    };
+  #endif
+    std::array<CGAL::Real_timer, NB_TASKS> timers{};
+    struct Scope_guard {
+      Tasks_manager *instance = nullptr;
+      int task_id;
+      Scope_guard(Tasks_manager *instance, int task_id) : instance(instance), task_id(task_id) {
+        instance->timers[task_id].start();
+#if CGAL_USE_ITT
+        __itt_task_begin(instance->cdt_3_domain, __itt_null, __itt_null, instance->task_handles[task_id]);
+#endif
+      }
+      auto time() const {
+        return instance->timers[task_id].time();
+      }
+      auto time_ms() const {
+        return instance->timers[task_id].time() / 1000.;
+      }
+      ~Scope_guard() {
+        instance->timers[task_id].stop();
+#if CGAL_USE_ITT
+        __itt_task_end(instance->cdt_3_domain);
+#endif
+      }
+    };
+
+    Scope_guard make_task_scope_guard(int task_id) {
+      return Scope_guard(this, task_id);
+    }
+
+    Scope_guard READ_INPUT_TASK_guard() { return make_task_scope_guard(READ_INPUT); }
+    Scope_guard MERGE_FACETS_TASK_guard() { return make_task_scope_guard(MERGE_FACETS); }
+    Scope_guard INSERT_VERTICES_TASK_guard() { return make_task_scope_guard(INSERT_VERTICES); }
+    Scope_guard COMPUTE_DISTANCES_TASK_guard() { return make_task_scope_guard(COMPUTE_DISTANCES); }
+    Scope_guard CONFORMING_TASK_guard() { return make_task_scope_guard(CONFORMING); }
+    Scope_guard CDT_TASK_guard() { return make_task_scope_guard(CDT); }
+    Scope_guard OUTPUT_TASK_guard() { return make_task_scope_guard(OUTPUT); }
+    Scope_guard VALIDATION_TASK_guard() { return make_task_scope_guard(VALIDATION); }
+
+  }; // end struct Intel_OneAPI_ITT_API
+
+  static Tasks_manager instance;
+  return instance;
+} // end auto& tasks_manager()
+
+} // end namespace internal
+
+} // end namespace CDT_3
+
+inline auto CDT_3_READ_INPUT_TASK_guard() {
+  return CDT_3::internal::tasks_manager().READ_INPUT_TASK_guard();
+}
+
+inline auto CDT_3_MERGE_FACETS_TASK_guard() {
+  return CDT_3::internal::tasks_manager().MERGE_FACETS_TASK_guard();
+}
+
+inline auto CDT_3_INSERT_VERTICES_TASK_guard() {
+  return CDT_3::internal::tasks_manager().INSERT_VERTICES_TASK_guard();
+}
+
+inline auto CDT_3_COMPUTE_DISTANCES_TASK_guard() {
+  return CDT_3::internal::tasks_manager().COMPUTE_DISTANCES_TASK_guard();
+}
+
+inline auto CDT_3_CONFORMING_TASK_guard() {
+  return CDT_3::internal::tasks_manager().CONFORMING_TASK_guard();
+}
+
+inline auto CDT_3_CDT_TASK_guard() {
+  return CDT_3::internal::tasks_manager().CDT_TASK_guard();
+}
+
+inline auto CDT_3_OUTPUT_TASK_guard() {
+  return CDT_3::internal::tasks_manager().OUTPUT_TASK_guard();
+}
+
+inline auto CDT_3_VALIDATION_TASK_guard() {
+  return CDT_3::internal::tasks_manager().VALIDATION_TASK_guard();
+}
+
 template <typename T_3>
 class Conforming_Delaunay_triangulation_3 : public T_3 {
 public:
@@ -50,9 +252,9 @@ public:
   using Line = typename T_3::Geom_traits::Line_3;
   using Locate_type = typename T_3::Locate_type;
 
-  inline static With_offset_tag with_offset{};
-  inline static With_point_tag with_point{};
-  inline static With_point_and_info_tag with_point_and_info{};
+  inline static With_offset_tag with_offset{ -1 };
+  inline static With_point_tag with_point{ {-1} };
+  inline static With_point_and_info_tag with_point_and_info{ { {-1} } };
 
   Conforming_Delaunay_triangulation_3(const Geom_traits& gt = Geom_traits())
     : T_3(gt)
@@ -110,7 +312,7 @@ protected:
               if(v1 > v2) std::swap(v1, v2);
               auto v1_index = v1->time_stamp();
               [[maybe_unused]] auto nb_erased = self->all_finite_edges[v1_index].erase(v2);
-              if constexpr (cdt_3_can_use_cxx20_format()) if(self->debug_finite_edges_map() && nb_erased > 0) {
+              if constexpr (cdt_3_can_use_cxx20_format()) if(self->debug().finite_edges_map() && nb_erased > 0) {
                 std::cerr << cdt_3_format("erasing edge {} {}\n", self->display_vert((std::min)(v1, v2)),
                                         self->display_vert((std::max)(v1, v2)));
               }
@@ -169,18 +371,17 @@ protected:
   void add_to_subconstraints_to_conform(Vertex_handle va, Vertex_handle vb,
                                         Constrained_polyline_id id) {
     const auto pair = make_subconstraint(va, vb);
-#if CGAL_DEBUG_CDT_3 & 32
-    std::cerr << "tr().subconstraints_to_conform.push("
-              << display_subcstr(pair) << ")\n";
-#endif // CGAL_DEBUG_CDT_3
+    if(debug().subconstraints_to_conform()) {
+      std::cerr << "tr().subconstraints_to_conform.push("
+                << display_subcstr(pair) << ")\n";
+    }
     subconstraints_to_conform.push({pair, id});
   }
 
   template <typename Visitor>
-  Constrained_polyline_id insert_constrained_edge_impl(Vertex_handle va, Vertex_handle vb,
-                                             Visitor&) {
+  Constrained_polyline_id insert_constrained_edge_impl(Vertex_handle va, Vertex_handle vb, Visitor&) {
     if(va != vb) {
-      if(segment_vertex_epsilon != 0.) {
+      if(debug().segment_vertex_epsilon() != 0.) {
         auto [min_dist, min_vertex] = min_distance_and_vertex_between_constraint_and_encroaching_vertex(va, vb);
         check_segment_vertex_distance_or_throw(va, vb, min_vertex, CGAL::to_double(min_dist),
                                                Check_distance::NON_SQUARED_DISTANCE);
@@ -217,7 +418,7 @@ protected:
     if(tr().is_infinite(v1) || tr().is_infinite(v2))
       return;
     [[maybe_unused]] auto [_, inserted] = all_finite_edges[v1->time_stamp()].insert(v2);
-    if constexpr (cdt_3_can_use_cxx20_format()) if (debug_finite_edges_map() && inserted) {
+    if constexpr (cdt_3_can_use_cxx20_format()) if (debug().finite_edges_map() && inserted) {
       if(v2 < v1) std::swap(v1, v2);
       std::cerr << cdt_3_format("new_edge({}, {})\n", display_vert(v1), display_vert(v2));
     }
@@ -268,7 +469,7 @@ protected:
       if(use_finite_edges_map()) {
         new_vertex(v);
         all_finite_edges.clear();
-        if (debug_finite_edges_map()) std::cerr << "all_finite_edges.clear()\n";
+        if (debug().finite_edges_map()) std::cerr << "all_finite_edges.clear()\n";
         for(auto e: tr().all_edges()) {
           new_edge(e);
         }
@@ -304,7 +505,7 @@ protected:
     }
   }
 
-  void update_max_bbox_edge_length() {
+  void update_max_bbox_edge_length() const {
     double d_x = bbox.xmax() - bbox.xmin();
     double d_y = bbox.ymax() - bbox.ymin();
     double d_z = bbox.zmax() - bbox.zmin();
@@ -313,85 +514,15 @@ protected:
   }
 
 public:
-  void set_segment_vertex_epsilon(double epsilon) {
-    segment_vertex_epsilon = epsilon;
-  }
+  CDT_3::Debug_options& debug() { return debug_options_; }
+  const CDT_3::Debug_options& debug() const { return debug_options_; }
 
-  bool debug_Steiner_points() const {
-    return debug_flags[static_cast<int>(Debug_flags::Steiner_points)];
-  }
-
-  void debug_Steiner_points(bool b) {
-    debug_flags.set(static_cast<int>(Debug_flags::Steiner_points), b);
-  }
-
-  bool debug_input_faces() const {
-    return debug_flags[static_cast<int>(Debug_flags::input_faces)];
-  }
-
-  void debug_input_faces(bool b) {
-    debug_flags.set(static_cast<int>(Debug_flags::input_faces), b);
-  }
-
-  bool debug_missing_region() const {
-    return debug_flags[static_cast<int>(Debug_flags::missing_region)];
-  }
-
-  void debug_missing_region(bool b) {
-    debug_flags.set(static_cast<int>(Debug_flags::missing_region), b);
-  }
-
-  bool debug_regions() const {
-    return debug_flags[static_cast<int>(Debug_flags::regions)];
-  }
-
-  void debug_regions(bool b) {
-    debug_flags.set(static_cast<int>(Debug_flags::regions), b);
-  }
-
-  bool debug_copy_triangulation_into_hole() const {
-    return debug_flags[static_cast<int>(Debug_flags::copy_triangulation_into_hole)];
-  }
-
-  void debug_copy_triangulation_into_hole(bool b) {
-    debug_flags.set(static_cast<int>(Debug_flags::copy_triangulation_into_hole), b);
-  }
-
-  bool debug_validity() const {
-    return debug_flags[static_cast<int>(Debug_flags::validity)];
-  }
-
-  void debug_validity(bool b) {
-    debug_flags.set(static_cast<int>(Debug_flags::validity), b);
-  }
-
-  bool use_older_cavity_algorithm() const {
-    return debug_flags[static_cast<int>(Debug_flags::use_older_cavity_algorithm)];
-  }
-
-  bool use_newer_cavity_algorithm() const {
-    return !debug_flags[static_cast<int>(Debug_flags::use_older_cavity_algorithm)];
-  }
-
-  void use_older_cavity_algorithm(bool b) {
-    debug_flags.set(static_cast<int>(Debug_flags::use_older_cavity_algorithm), b);
-  }
-
-  bool debug_finite_edges_map() const {
-    return debug_flags[static_cast<int>(Debug_flags::debug_finite_edges_map)];
-  }
-
-  void debug_finite_edges_map(bool b) {
-    debug_flags.set(static_cast<int>(Debug_flags::debug_finite_edges_map), b);
-  }
-
-  bool use_finite_edges_map() const {
-    return update_all_finite_edges_ && debug_flags[static_cast<int>(Debug_flags::use_finite_edges_map)];
-  }
-
-  void use_finite_edges_map(bool b) {
-    debug_flags.set(static_cast<int>(Debug_flags::use_finite_edges_map), b);
-  }
+  // Backward compatibility wrappers (deprecated, use debug().method() instead)
+  bool use_older_cavity_algorithm() const { return debug_options_.use_older_cavity_algorithm(); }
+  bool use_newer_cavity_algorithm() const { return debug_options_.use_newer_cavity_algorithm(); }
+  void use_older_cavity_algorithm(bool b) { debug_options_.use_older_cavity_algorithm(b); }
+  bool use_finite_edges_map() const { return update_all_finite_edges_ && debug_options_.use_finite_edges_map_flag(); }
+  void use_finite_edges_map(bool b) { debug_options_.use_finite_edges_map(b); }
 
   Vertex_handle insert(const Point &p, Locate_type lt, Cell_handle c,
                        int li, int lj)
@@ -419,14 +550,14 @@ public:
 
   bool is_edge(Vertex_handle va, Vertex_handle vb) const {
     const bool is_edge_v1 =
-        ((debug_finite_edges_map() && use_finite_edges_map()) || !use_finite_edges_map()) && tr().tds().is_edge(va, vb);
+        ((debug().finite_edges_map() && use_finite_edges_map()) || !use_finite_edges_map()) && tr().tds().is_edge(va, vb);
 
     if(use_finite_edges_map() && va > vb) std::swap(va, vb);
     const auto va_index = va->time_stamp();
     const bool is_edge_v2 =
         use_finite_edges_map() && all_finite_edges[va_index].find(vb) != all_finite_edges[va_index].end();
 
-    if(debug_finite_edges_map() && use_finite_edges_map() && is_edge_v1 != is_edge_v2) {
+    if(debug().finite_edges_map() && use_finite_edges_map() && is_edge_v1 != is_edge_v2) {
       std::cerr << "!! Inconsistent edge status\n";
       std::cerr << "  -> constraint " << display_vert(va) << "     " << display_vert(vb) << '\n';
       std::cerr << "  ->     edge " << (is_edge_v1 ? "is" : "is not") << " in the triangulation\n";
@@ -446,12 +577,12 @@ public:
                        [this](const auto &sc) {
                          const auto [va, vb] = sc;
                          const auto is_edge = this->is_edge(va, vb);
-#if CGAL_DEBUG_CDT_3 & 128 && CGAL_CAN_USE_CXX20_FORMAT
-                         std::cerr << cdt_3_format("is_conforming>> Edge is 3D: {}  ({} , {})\n",
-                                                  is_edge,
-                                                  CGAL::IO::oformat(va, with_point_and_info),
-                                                  CGAL::IO::oformat(vb, with_point_and_info));
-#endif // CGAL_DEBUG_CDT_3
+                         if constexpr (cdt_3_can_use_cxx20_format()) if(debug().conforming_validation()) {
+                           std::cerr << cdt_3_format("is_conforming>> Edge is 3D: {}  ({} , {})\n",
+                                                    is_edge,
+                                                    CGAL::IO::oformat(va, with_point_and_info),
+                                                    CGAL::IO::oformat(vb, with_point_and_info));
+                         }
                          return is_edge;
                        });
   }
@@ -462,14 +593,15 @@ public:
                                               Vertex_handle vb,
                                               Vertex_handle min_vertex,
                                               double min_dist,
-                                              Check_distance option)
+                                              Check_distance distance_type = Check_distance::NON_SQUARED_DISTANCE) const
   {
     if(!max_bbox_edge_length) {
       update_max_bbox_edge_length();
     }
-    if((option == Check_distance::NON_SQUARED_DISTANCE && min_dist < segment_vertex_epsilon * *max_bbox_edge_length) ||
-       (option == Check_distance::SQUARED_DISTANCE &&
-        min_dist < CGAL::square(segment_vertex_epsilon * *max_bbox_edge_length)))
+    if((distance_type == Check_distance::NON_SQUARED_DISTANCE &&
+        min_dist < debug().segment_vertex_epsilon() * *max_bbox_edge_length) ||
+       (distance_type == Check_distance::SQUARED_DISTANCE &&
+        min_dist < CGAL::square(debug().segment_vertex_epsilon() * *max_bbox_edge_length)))
     {
       std::stringstream ss;
       ss.precision(std::cerr.precision());
@@ -482,6 +614,26 @@ public:
     }
   }
 
+  void check_vertex_vertex_distance_or_throw(Vertex_handle va,
+                                             Vertex_handle vb,
+                                             double min_dist) const
+  {
+    if(!max_bbox_edge_length) {
+      update_max_bbox_edge_length();
+    }
+    if(min_dist < debug_options_.vertex_vertex_epsilon() * *max_bbox_edge_length)
+    {
+      std::stringstream ss;
+      ss.precision(std::cerr.precision());
+      ss << "Two vertices are too close to each other.\n";
+      ss << "  -> vertex " << display_vert(va) << '\n';
+      ss << "  -> vertex " << display_vert(vb) << '\n';
+      ss << "  -> distance = " << min_dist << '\n';
+      ss << "  -> max_bbox_edge_length = " << *max_bbox_edge_length << '\n';
+      CGAL_error_msg(ss.str().c_str());
+    }
+  }
+
   auto ancestors_of_Steiner_vertex_on_edge(Vertex_handle v) const {
     std::pair<Vertex_handle, Vertex_handle> result;
     CGAL_precondition(v->ccdt_3_data().is_Steiner_vertex_on_edge());
@@ -587,10 +739,10 @@ protected:
       if(!constraint_hierarchy.is_subconstraint(va, vb)) {
         continue;
       }
-#if CGAL_DEBUG_CDT_3 & 32
-      std::cerr << "tr().subconstraints_to_conform.pop()="
-                << display_subcstr(subconstraint) << "\n";
-#endif // CGAL_DEBUG_CDT_3
+      if(debug().subconstraints_to_conform()) {
+        std::cerr << "tr().subconstraints_to_conform.pop()="
+                  << display_subcstr(subconstraint) << "\n";
+      }
       conform_subconstraint(subconstraint, constrained_polyline_id, visitor);
     }
   }
@@ -633,7 +785,7 @@ protected:
       const auto& [steiner_pt, hint, ref_vertex] = construct_Steiner_point(constraint, subconstraint);
       [[maybe_unused]] const auto v =
           insert_Steiner_point_on_subconstraint(steiner_pt, hint, subconstraint, constraint, visitor);
-      if(debug_Steiner_points()) {
+      if(debug().Steiner_points()) {
         const auto [c_start, c_end] = constraint_extremities(constraint);
         std::cerr << "(" << IO::oformat(va, with_offset) << ", " << IO::oformat(vb, with_offset) << ")";
         std::cerr << ": [ " << display_vert(c_start) << " - " << display_vert(c_end) << " ] ";
@@ -669,10 +821,10 @@ protected:
                                this->constraint_hierarchy.constraints_end(), c_id) != this->constraint_hierarchy.constraints_end());
       CGAL_assertion(this->constraint_hierarchy.vertices_in_constraint_begin(c_id) !=
                      this->constraint_hierarchy.vertices_in_constraint_end(c_id));
-#if CGAL_DEBUG_CDT_3 & 8
-      std::cerr << "constraint " << (void*) c_id.vl_ptr() << " has "
-                << c_id.vl_ptr()->skip_size() << " vertices\n";
-#endif // CGAL_DEBUG_CDT_3
+      if(debug().constraint_hierarchy()) {
+        std::cerr << "constraint " << static_cast<void*>(c_id.vl_ptr()) << " has "
+                  << c_id.vl_ptr()->skip_size() << " vertices\n";
+      }
       const auto begin = this->constraint_hierarchy.vertices_in_constraint_begin(c_id);
       const auto end = this->constraint_hierarchy.vertices_in_constraint_end(c_id);
       const auto c_va = *begin;
@@ -730,9 +882,9 @@ protected:
       encroaching_vertices.insert(v);
     };
     auto fill_encroaching_vertices = [&](const auto simplex) {
-#if CGAL_DEBUG_CDT_3 & 0x10
-      std::cerr << " - " << IO::oformat(simplex, With_point_tag{}) << '\n';
-#endif // CGAL_DEBUG_CDT_3
+      if(debug().encroaching_vertices()) {
+        std::cerr << " - " << IO::oformat(simplex, With_point_tag{}) << '\n';
+      }
       auto visit_cell = [&](Cell_handle cell) {
         for(int i = 0, end = this->tr().dimension() + 1; i < end; ++i) {
           const auto v = cell->vertex(i);
@@ -776,9 +928,9 @@ protected:
           std::cerr << "!! The constraint passes through a vertex!\n";
           std::cerr << "  -> constraint " << display_vert(va) << "     " << display_vert(vb) << '\n';
           std::cerr << "  ->     vertex " << display_vert(v) << '\n';
-#if CGAL_DEBUG_CDT_3
-          debug_dump("bug-through-vertex");
-#endif
+          if(debug().geometric_errors()) {
+            debug_dump("bug-through-vertex");
+          }
           CGAL_error();
         }
       } break;
@@ -788,14 +940,14 @@ protected:
     std::for_each(tr().segment_traverser_simplices_begin(va, vb), tr().segment_traverser_simplices_end(),
                   fill_encroaching_vertices);
     auto vector_of_encroaching_vertices = encroaching_vertices.extract_sequence();
-#if CGAL_DEBUG_CDT_3 & 0x10
-    std::cerr << "  -> vector_of_encroaching_vertices (before filter):\n";
-    std::for_each(vector_of_encroaching_vertices.begin(),
-                  vector_of_encroaching_vertices.end(),
-                  [this](Vertex_handle v){
-                    std::cerr << "    " << this->display_vert(v) << '\n';
-                  });
-#endif // CGAL_DEBUG_CDT_3
+    if(debug().encroaching_vertices()) {
+      std::cerr << "  -> vector_of_encroaching_vertices (before filter):\n";
+      std::for_each(vector_of_encroaching_vertices.begin(),
+                    vector_of_encroaching_vertices.end(),
+                    [this](Vertex_handle v){
+                      std::cerr << "    " << this->display_vert(v) << '\n';
+                    });
+    }
     auto end = std::remove_if(vector_of_encroaching_vertices.begin(),
                               vector_of_encroaching_vertices.end(),
                               [va, vb, pa, pb, &angle_functor, this](Vertex_handle v) {
@@ -804,13 +956,13 @@ protected:
                                                     this->tr().point(v),
                                                     pb) == ACUTE;
                               });
-#if CGAL_DEBUG_CDT_3 & 0x10
-    std::cerr << "  -> vector_of_encroaching_vertices (after filter):\n";
-    std::for_each(vector_of_encroaching_vertices.begin(), end, [&](Vertex_handle v) {
-      std::cerr << "    " << this->display_vert(v) << "  angle " << approximate_angle(pa, this->tr().point(v), pb)
-                << '\n';
-    });
-#endif // CGAL_DEBUG_CDT_3
+    if(debug().encroaching_vertices()) {
+      std::cerr << "  -> vector_of_encroaching_vertices (after filter):\n";
+      std::for_each(vector_of_encroaching_vertices.begin(), end, [&](Vertex_handle v) {
+        std::cerr << "    " << this->display_vert(v) << "  angle " << approximate_angle(pa, this->tr().point(v), pb)
+                  << '\n';
+      });
+    }
     vector_of_encroaching_vertices.erase(end, vector_of_encroaching_vertices.end());
     return vector_of_encroaching_vertices;
   }
@@ -840,10 +992,10 @@ protected:
       return {midpoint_functor(pa, pb), va->cell(), va};
     }
 
-#if CGAL_DEBUG_CDT_3 & 0x10
-    std::cerr << "construct_Steiner_point( " << display_vert(va) << " , "
-              << display_vert(vb) << " )\n";
-#endif // CGAL_DEBUG_CDT_3
+    if(debug().encroaching_vertices()) {
+      std::cerr << "construct_Steiner_point( " << display_vert(va) << " , "
+                << display_vert(vb) << " )\n";
+    }
 
     const auto vector_of_encroaching_vertices = encroaching_vertices(va, vb);
     CGAL_assertion(vector_of_encroaching_vertices.size() > 0);
@@ -909,7 +1061,7 @@ protected:
         return return_orig_result_point(lambda, orig_pb, orig_pa);
       }
     } else {
-      if(segment_vertex_epsilon > 0) {
+      if(debug().segment_vertex_epsilon() > 0) {
         if(!max_bbox_edge_length) {
           update_max_bbox_edge_length();
         }
@@ -940,8 +1092,7 @@ protected:
   Constraint_hierarchy constraint_hierarchy = {comp};
   static_assert(CGAL::cdt_3_msvc_2019_or_older() || CGAL::is_nothrow_movable_v<Constraint_hierarchy>);
   Bbox_3 bbox{};
-  double segment_vertex_epsilon = 1e-8;
-  std::optional<double> max_bbox_edge_length;
+  mutable std::optional<double> max_bbox_edge_length;
   using Pair_of_vertex_handles = std::pair<Vertex_handle, Vertex_handle>;
   boost::container::map<Pair_of_vertex_handles, Constrained_polyline_id> pair_of_vertices_to_cid;
   Insert_in_conflict_visitor insert_in_conflict_visitor = {this};
@@ -973,20 +1124,7 @@ protected:
     }
   }
 
-  enum class Debug_flags {
-    Steiner_points = 0,
-    conforming,
-    input_faces,
-    missing_region,
-    regions,
-    copy_triangulation_into_hole,
-    validity,
-    use_older_cavity_algorithm,
-    debug_finite_edges_map,
-    use_finite_edges_map,
-    nb_of_flags
-  };
-  std::bitset<static_cast<int>(Debug_flags::nb_of_flags)> debug_flags{};
+  CDT_3::Debug_options debug_options_{};
   bool is_Delaunay = true;
 };
 
@@ -994,6 +1132,5 @@ protected:
 
 #endif // not DOXYGEN_RUNNING
 
-#
 
 #endif // CGAL_CONFORMING_DELAUNAY_TRIANGULATION_3_H

Constrained_triangulation_3/include/CGAL/Conforming_constrained_Delaunay_triangulation_cell_base_3.h

@@ -98,7 +98,7 @@ public:
         CGAL::read(is, i);
       }
       if(!is) return is;
-      c.face_id[li] = i;
+      c->ccdt_3_data().set_face_constraint_index(li, i);
     }
     return is;
   }

Constrained_triangulation_3/include/CGAL/Conforming_constrained_Delaunay_triangulation_cell_data_3.h

@@ -52,31 +52,33 @@ class Conforming_constrained_Delaunay_triangulation_cell_data_3 {
   void clear_mark(CDT_3_cell_marker m) { markers.reset(static_cast<unsigned>(m)); }
   void clear_marks() { markers.reset(); }
 
+  static unsigned int uint(int i) { return static_cast<unsigned int>(i); }
+
   template <typename Facet_handle>
   void set_facet_constraint(int i, CDT_3_signed_index face_id,
                             Facet_handle facet_2d)
   {
-    this->face_id[unsigned(i)] = face_id;
-    this->facet_2d[unsigned(i)] = static_cast<void*>(facet_2d == Facet_handle{} ?  nullptr : std::addressof(*facet_2d));
+    this->face_id[uint(i)] = face_id;
+    this->facet_2d[uint(i)] = static_cast<void*>(facet_2d == Facet_handle{} ?  nullptr : std::addressof(*facet_2d));
   }
 
   template <typename CDT_2>
   auto face_2 (const CDT_2& cdt, int i) const {
     using Face = typename CDT_2::Face;
-    auto ptr = static_cast<Face*>(facet_2d[unsigned(i)]);
+    auto ptr = static_cast<Face*>(facet_2d[uint(i)]);
     return cdt.tds().faces().iterator_to(*ptr);
   }
 public:
   /// @{
   // @cond SKIP_IN_MANUAL
-  bool is_facet_constrained(int i) const { return face_id[unsigned(i)] >= 0; }
+  bool is_facet_constrained(int i) const { return face_id[uint(i)] >= 0; }
 
   CDT_3_signed_index face_constraint_index(int i) const {
-    return face_id[unsigned(i)];
+    return face_id[uint(i)];
   }
 
   void set_face_constraint_index(int i, CDT_3_signed_index index) {
-    face_id[unsigned(i)] = index;
+    face_id[uint(i)] = index;
   }
   /// @endcond
 };

Constrained_triangulation_3/include/CGAL/Conforming_constrained_Delaunay_triangulation_vertex_data_3.h

@@ -16,6 +16,7 @@
 
 #include <CGAL/assertions.h>
 #include <CGAL/Constrained_triangulation_3/internal/config.h>
+#include <CGAL/Constrained_triangulation_3_types.h>
 
 #include <bitset>
 
@@ -34,7 +35,7 @@ namespace CGAL {
 struct Conforming_constrained_Delaunay_triangulation_vertex_data_3 {};
 #else // DOXYGEN_RUNNING
 
-enum class CDT_3_vertex_type { FREE, CORNER, STEINER_ON_EDGE, STEINER_IN_FACE };
+enum class CDT_3_vertex_type { FREE, CORNER, INPUT_VERTEX = CORNER, STEINER_ON_EDGE, STEINER_IN_FACE };
 
 enum class CDT_3_vertex_marker {
   CLEAR = 0,
@@ -91,6 +92,8 @@ public:
   }
 
   int number_of_incident_constraints() const {
+    if(vertex_type() == CDT_3_vertex_type::STEINER_IN_FACE)
+      return 0;
     CGAL_assertion(u.on_edge.nb_of_incident_constraints >= 0);
     return u.on_edge.nb_of_incident_constraints;
   }

Constrained_triangulation_3/test/Constrained_triangulation_3/CMakeLists.txt

@@ -26,13 +26,6 @@ create_single_source_cgal_program( "cdt_3_from_off_with_Epeck.cpp")
 target_link_libraries(cdt_3_from_off_with_Epeck PRIVATE CDT_3_dependencies)
 create_single_source_cgal_program( "snap_and_cdt3.cpp")
 
-if(cxx_std_20 IN_LIST CMAKE_CXX_COMPILE_FEATURES)
-  add_executable(cdt_3_from_off_CGAL_DEBUG_CDT_3 cdt_3_from_off)
-  target_compile_definitions(cdt_3_from_off_CGAL_DEBUG_CDT_3 PRIVATE CGAL_DEBUG_CDT_3=255)
-  target_link_libraries(cdt_3_from_off_CGAL_DEBUG_CDT_3 PRIVATE CDT_3_dependencies)
-  cgal_add_test(cdt_3_from_off_CGAL_DEBUG_CDT_3)
-endif()
-
 add_executable(test_CDT_3_insert_constrained_edge_from_EDG_file cdt_test_insert_constrained_edge_from_EDG_file.cpp)
 target_link_libraries(test_CDT_3_insert_constrained_edge_from_EDG_file PRIVATE CDT_3_dependencies)
 target_compile_definitions(test_CDT_3_insert_constrained_edge_from_EDG_file PUBLIC CGAL_TEST_CDT_3_USE_CDT)
@@ -85,7 +78,7 @@ function(CGAL_add_cdt3_from_off_test_aux data_name data_dir)
 endfunction()
 
 function(CGAL_add_cdt3_from_off_test data_name)
-  CGAL_add_cdt3_from_off_test_aux(${data_name} ${CGAL_DATA_DIR}/meshes)
+  CGAL_add_cdt3_from_off_test_aux(${data_name} ${CGAL_DATA_DIR}/meshes ${ARGN})
 endfunction()
 
 CGAL_add_cdt3_from_off_test("cube")
@@ -95,9 +88,10 @@ CGAL_add_cdt3_from_off_test("mpi")
 CGAL_add_cdt3_from_off_test("3torus")
 CGAL_add_cdt3_from_off_test("cheese-selection")
 CGAL_add_cdt3_from_off_test("cheese-selection-2")
+CGAL_add_cdt3_from_off_test("non_manifold_face_graph")
 
 function(CGAL_add_cdt3_from_local_off_test data_name)
-  CGAL_add_cdt3_from_off_test_aux(${data_name} ${CMAKE_CURRENT_SOURCE_DIR}/data)
+  CGAL_add_cdt3_from_off_test_aux(${data_name} ${CMAKE_CURRENT_SOURCE_DIR}/data ${ARGN})
 endfunction()
 
 CGAL_add_cdt3_from_local_off_test(cheese18)
@@ -130,17 +124,15 @@ if (CGAL_CDT_TEST_USE_THINGI)
   CGAL_add_cdt3_from_local_off_test(1514904-min8)
   CGAL_add_cdt3_from_local_off_test(1147177-min1)
   CGAL_add_cdt3_from_local_off_test(1452672-min1)
+  CGAL_add_cdt3_from_local_off_test(135777-min3)
+  CGAL_add_cdt3_from_local_off_test(196123-min3)
+  CGAL_add_cdt3_from_local_off_test(200695-min3)
+  CGAL_add_cdt3_from_local_off_test(285604-min8)
   CGAL_add_cdt3_from_local_off_test(error_mesh-p_not_equal_0-min2)
 
   include(./Thingi10k-CDT.cmake)
 endif()
 
-if(cxx_std_20 IN_LIST CMAKE_CXX_COMPILE_FEATURES)
-  add_test(NAME "execution   of  cdt_3_from_off_CGAL_DEBUG_CDT_3 3torus" COMMAND cdt_3_from_off_CGAL_DEBUG_CDT_3 ${CGAL_DATA_DIR}/meshes/3torus.off)
-  cgal_add_compilation_test(cdt_3_from_off_CGAL_DEBUG_CDT_3)
-  cgal_setup_test_properties("execution   of  cdt_3_from_off_CGAL_DEBUG_CDT_3 3torus" cdt_3_from_off_CGAL_DEBUG_CDT_3)
-endif()
-
 get_directory_property(all_tests TESTS)
 foreach(test ${all_tests})
   if(test MATCHES cdt|CDT)

Constrained_triangulation_3/test/Constrained_triangulation_3/Thingi10k-CDT.cmake

@@ -109,6 +109,152 @@ set(thingi10k_FAILED_WITH_MERGE_FACETS_CTest_20240222_2201
 1514904.stl
 )
 
+set(thingi10k_FAILED_WITH_SEGFAULT_CTest_20251002
+1439534.stl
+196123.stl
+200695.stl
+135777.stl
+285604.stl
+822697.stl
+)
+
+set(thingi10k_FAILED_CTest_20251002
+100606.stl
+100644.stl
+101955.stl
+109130.stl
+116873.stl
+116876.stl
+135777.stl
+139737.stl
+1439534.stl
+145329.stl
+145330.stl
+1505036.stl
+1514900.stl
+196121.stl
+196122.stl
+196123.stl
+196126.stl
+196127.stl
+199814.stl
+199818.stl
+200695.stl
+215991.stl
+230152.stl
+230153.stl
+239188.stl
+276937.stl
+285604.stl
+285605.stl
+288352.stl
+288353.stl
+288354.stl
+288355.stl
+39182.stl
+39245.stl
+472050.stl
+55278.stl
+61418.stl
+622000.stl
+669962.stl
+67817.stl
+702204.stl
+723893.stl
+822697.stl
+904476.stl
+91474.stl
+95796.stl
+95797.stl
+97515.stl
+)
+
+set(thingi10k_FAILED_WITH_MERGE_FACETS_CTest_20251028
+139765.stl
+1452677.stl
+1452678.stl
+1452679.stl
+145329.stl
+145330.stl
+145331.stl
+1505036.stl
+1514900.stl
+153100.stl
+1652975.stl
+1652976.stl
+1706457.stl
+186546.stl
+196121.stl
+196122.stl
+196123.stl
+196126.stl
+196127.stl
+196194.stl
+199814.stl
+199818.stl
+206318.stl
+215991.stl
+230152.stl
+230153.stl
+237632.stl
+239188.stl
+255657.stl
+255658.stl
+276937.stl
+285603.stl
+286161.stl
+288352.stl
+288446.stl
+360073.stl
+362398.stl
+37743.stl
+383022.stl
+39182.stl
+39245.stl
+39495.stl
+39499.stl
+40841.stl
+41521.stl
+42040.stl
+44025.stl
+44064.stl
+44901.stl
+472050.stl
+50659.stl
+51797.stl
+57811.stl
+61418.stl
+61431.stl
+622000.stl
+62592.stl
+62593.stl
+65144.stl
+65395.stl
+65402.stl
+669962.stl
+68255.stl
+702204.stl
+70381.stl
+71461.stl
+723893.stl
+72419.stl
+726665.stl
+77343.stl
+84624.stl
+90225.stl
+906183.stl
+91147.stl
+91474.stl
+93702.stl
+93703.stl
+95796.stl
+95797.stl
+97515.stl
+97590.stl
+97593.stl
+99895.stl
+)
+
 function(CGAL_add_cdt3_test_from_Thingi10k data_name data_filename)
   set(options "ONLY_MERGE_FACETS")
   set(oneValueArgs TIMEOUT)
@@ -145,6 +291,15 @@ foreach(thingi_file_name ${thingi10k_max_10k_solid})
   if(thingi_file_name IN_LIST thingi10k_FAILED_WITH_MERGE_FACETS_CTest_20240222_2201)
     list(APPEND LABELS "CTest_20240222_2201_failed_merge_facets")
   endif()
+  if(thingi_file_name IN_LIST thingi10k_FAILED_CTest_20251002)
+    list(APPEND LABELS "CTest_20251002_failed")
+  endif()
+  if(thingi_file_name IN_LIST thingi10k_FAILED_WITH_SEGFAULT_CTest_20251002)
+    list(APPEND LABELS "CTest_20251002_failed_segfault")
+  endif()
+  if(thingi_file_name IN_LIST thingi10k_FAILED_WITH_MERGE_FACETS_CTest_20251028)
+    list(APPEND LABELS "CTest_20251028_failed_merge_facets")
+  endif()
   get_filename_component(thingi_ID "${thingi_file_name}" NAME_WE)
   CGAL_add_cdt3_test_from_Thingi10k(Thingi10K_${thingi_ID} ${thingi_file_name}
       TIMEOUT 600 LABELS ${LABELS} ${MY_ONLY_MERGE_FACETS})

Constrained_triangulation_3/test/Constrained_triangulation_3/cdt_test_insert_constrained_edge_from_EDG_file.cpp

@@ -1,6 +1,3 @@
-#if __has_include(<format>)
-#define CGAL_DEBUG_CDT_3 1
-#endif
 #define CGAL_TRIANGULATION_CHECK_EXPENSIVE 1
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Delaunay_triangulation_3.h>

Constrained_triangulation_3/test/Constrained_triangulation_3/cdt_test_insert_constrained_edge_from_OFF_file.cpp

@@ -1,6 +1,3 @@
-#if __has_include(<format>)
-#define CGAL_DEBUG_CDT_3 1
-#endif
 #define CGAL_TRIANGULATION_CHECK_EXPENSIVE 1
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Delaunay_triangulation_3.h>

Constrained_triangulation_3/test/Constrained_triangulation_3/data/135777-min3.off

@@ -0,0 +1,69 @@
+OFF
+42 23 0
+
+9.4220000000000006 6.265949 1.2926169999999999
+9.4220000000000006 6.4378760000000002 0.4304
+9.4299999999999997 6.3669419999999999 1.3120000000000001
+9.4220000000000006 6.522742 1.2616000000000001
+9.4299999999999997 1.737943 2.867
+9.4299999999999997 1.310943 1.46
+9.4299999999999997 1.167238 0
+9.4299999999999997 5.7969429999999997 6.9269999999999996
+9.4299999999999997 16.167649999999998 0
+9.4299999999999997 4.499943 6.2329999999999997
+9.4299999999999997 3.3639420000000002 5.3010000000000002
+9.4299999999999997 2.4309430000000001 4.1639999999999997
+12.430999999999999 1.167238 0
+12.430999999999999 1.310943 1.46
+-7.2230889999999999 -5.1901419999999998 1.2724260000000001
+-7.2389999999999999 -5.1100570000000003 1.3959999999999999
+3.7330000000000001 -6.7590570000000003 0.79200000000000004
+-7.255185 -4.6623049999999999 0.88247529999999996
+-7.2552779999999997 -4.6682399999999999 0.88692839999999995
+3.7330000000000001 -6.2710569999999999 0.42699999999999999
+-7.262251 -4.5335140000000003 0.78721229999999998
+-7.7199999999999998 -4.2110570000000003 1.929
+-7.6440000000000001 -4.1590579999999999 1.6100000000000001
+-7.5739999999999998 -4.3940570000000001 1.726
+-7.5469999999999997 -3.6850580000000002 1.224
+-7.5369999999999999 -3.8630580000000001 1.3169999999999999
+-7.4050000000000002 -4.4780569999999997 1.4410000000000001
+-7.3220000000000001 -4.3380580000000002 1.022
+-7.4009999999999998 -4.689057 1.677
+-7.2534720000000004 -4.6835990000000001 0.89814380000000005
+9.4299999999999997 10.06494 1.929
+-7.2789999999999999 -4.0440569999999996 0.34699999999999998
+9.4299999999999997 6.3669419999999999 1.3120000000000001
+-7.2230889999999999 -5.1901419999999998 1.2724260000000001
+3.68716 -6.0934090000000003 0
+3.7330000000000001 -6.2710569999999999 0.42699999999999999
+3.7330000000000001 -6.2710569999999999 0.42699999999999999
+-7.262251 -4.5335140000000003 0.78721229999999998
+-7.6029999999999998 -4.5610569999999999 2.0139999999999998
+-7.4050000000000002 -4.4780569999999997 1.4410000000000001
+-7.3220000000000001 -4.3380580000000002 1.022
+-7.2599 -4.5207920000000001 0.75421059999999995
+3  0 1 2
+3  1 3 2
+3  4 32 5
+3  6 5 32
+3  8 32 30
+3  9 7 32
+3  32 7 30
+3  10 32 11
+3  4 11 32
+3  10 9 32
+3  6 32 8
+3  13 5 12
+3  38 23 21
+3  26 25 22
+3  24 25 26
+3  27 39 28
+3  16 19 14
+3  35 34 20
+3  18 29 36
+3  18 28 29
+3  15 33 29
+3  31 40 41
+3  40 17 37
+

Constrained_triangulation_3/test/Constrained_triangulation_3/data/196123-min3.off

@@ -0,0 +1,75 @@
+OFF
+37 34 0
+
+172.45960998535156 327.00732421875 10.000033378601074
+173.35765075683594 327.18472290039062 10.000033378601074
+172.45960998535156 327.00732421875 10
+174.25531005859375 327.36398315429688 10.000033378601074
+175.282470703125 327.571533203125 10
+170.58482360839844 325.87066650390625 10
+170.58482360839844 325.87066650390625 10.000033378601074
+170.58476257324219 326.1373291015625 10
+170.58476257324219 326.1373291015625 10.000033378601074
+170.58488464355469 326.67068481445312 10.000033378601074
+170.58488464355469 326.67068481445312 10
+170.58477783203125 326.40402221679688 10.000033378601074
+170.58477783203125 326.40402221679688 10
+171.21096801757812 326.77630615234375 10
+171.21096801757812 326.77630615234375 10.000033378601074
+171.83589172363281 326.88851928710938 10.000033378601074
+171.83589172363281 326.88851928710938 10
+198.59626770019531 331.45306396484375 10
+171.3594970703125 325.91452026367188 10
+171.3594970703125 325.91452026367188 10.000033378601074
+171.10134887695312 325.89859008789062 10
+171.10134887695312 325.89859008789062 10.000033378601074
+170.84312438964844 325.88397216796875 10.000033378601074
+170.84312438964844 325.88397216796875 10
+173.88740539550781 326.08248901367188 10.000033378601074
+174.88548278808594 326.13330078125 10
+173.12164306640625 326.03756713867188 10
+172.62298583984375 326.00552368164062 10.000033378601074
+176.65058898925781 326.20169067382812 10
+179.54045104980469 326.31793212890625 10
+182.43142700195312 326.40179443359375 10
+192.267333984375 331.10971069335938 10
+197.96424865722656 332.17782592773438 10
+175.15260314941406 328.56558227539062 10.000033378601074
+175.15260314941406 325.1444091796875 10.000033378601074
+161.37049865722656 320.09548950195312 10.000033378601074
+161.37049865722656 332.70773315429688 10.000033378601074
+3  1 3 2
+3  2 3 4
+3  18 26 27
+3  27 26 24
+3  4 30 2
+3  31 32 17
+3  30 29 2
+3  2 29 16
+3  25 10 28
+3  10 25 12
+3  18 7 26
+3  18 20 7
+3  20 23 7
+3  23 5 7
+3  7 12 26
+3  26 12 25
+3  10 13 28
+3  13 16 28
+3  21 19 34
+3  21 34 22
+3  19 27 34
+3  36 11 35
+3  3 1 33
+3  1 0 33
+3  0 15 33
+3  15 14 33
+3  14 9 33
+3  33 9 36
+3  11 8 35
+3  8 6 35
+3  35 6 34
+3  6 22 34
+3  34 27 24
+3  11 36 9
+

Constrained_triangulation_3/test/Constrained_triangulation_3/data/200695-min3.off

@@ -0,0 +1,46 @@
+OFF
+25 17 0
+
+137.05000305175781 47.498001098632812 132.02400207519531
+137.05000305175781 42.498001098632812 132.65000915527344
+137.05000305175781 20 131.40000915527344
+137.05000305175781 14.998001098632812 90.316001892089844
+137.05000305175781 0 133.90000915527344
+137.05000305175781 5 131.40000915527344
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Constrained_triangulation_3/test/Constrained_triangulation_3/data/285604-min8.off

@@ -0,0 +1,119 @@
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Constrained_triangulation_3/test/Constrained_triangulation_3/test_ccdt_remeshing.cpp

@@ -40,7 +40,7 @@ int main(int argc, char* argv[])
   auto cdt = CGAL::make_conforming_constrained_Delaunay_triangulation_3<CDT>(mesh);
   static_assert(std::is_same_v<decltype(cdt), CDT>);
   CDT cdt2(mesh);
-  const auto nb_cstr_facets = cdt2.number_of_constrained_facets();
+  [[maybe_unused]] const auto nb_cstr_facets = cdt2.number_of_constrained_facets();
 
   assert(cdt.triangulation().number_of_vertices() == cdt2.triangulation().number_of_vertices());
   assert(cdt.number_of_constrained_facets() == cdt2.number_of_constrained_facets());

Data/data/meshes/non_manifold_face_graph.off

@@ -0,0 +1,39 @@
+OFF
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+4  21 18 22 17
+4  18 15 23 22
+

Documentation/doc/biblio/geom.bib

@@ -118600,7 +118600,7 @@ both for rendering and for modeling. Contains C code."
 
 @article{ph-ddocs-92
 , author =      "J. P. Pratt and V. P. Heuring"
-, title =       "Designing digital optical computing systems: power and and crosstalk"
+, title =       "Designing digital optical computing systems: power and crosstalk"
 , journal =     "Appl. Optics"
 , volume =      31
 , number =      23

Frechet_distance/doc/Frechet_distance/Frechet_distance.txt

@@ -123,11 +123,11 @@ In the example below, we can see a query where:
 </center>
 
 
-\subsection subsecFrechetDistanceImageCredits  Image Credits
+\section subsecFrechetDistanceImageCredits  Image Credits
 
 The character image is a visualization of two data points from the <a href="https://archive.ics.uci.edu/dataset/175/character+trajectories">Character Trajectories</a> data set.
 
-\subsection subsecFrechetDistanceImplementation  Implementation History
+\section subsecFrechetDistanceImplementation  Implementation History
 
 An initial version using floating point arithmetic was developed by the authors
 while working at the Max-Planck Institute for Informatics in Saarbrücken, Germany.

GraphicsView/doc/GraphicsView/PackageDescription.txt

@@ -13,12 +13,12 @@
 \cgalPkgPicture{detail.png}
 \cgalPkgSummaryBegin
 \cgalPkgAuthors{Andreas Fabri and Laurent Rineau}
-\cgalPkgDesc{This package provides classes for displaying \cgal objects  and data structures in the <A HREF="https://doc.qt.io/qt-6/graphicsview.html">Qt 5 Graphics View Framework</A>.}
+\cgalPkgDesc{This package provides classes for displaying \cgal objects  and data structures in the <A HREF="https://doc.qt.io/qt-6/graphicsview.html">Qt 6 Graphics View Framework</A>.}
 \cgalPkgManuals{Chapter_CGAL_and_the_Qt_Graphics_View_Framework,PkgGraphicsViewRef}
 \cgalPkgSummaryEnd
 \cgalPkgShortInfoBegin
 \cgalPkgSince{3.4}
-\cgalPkgDependsOn{\qt 5}
+\cgalPkgDependsOn{\qt 6}
 \cgalPkgBib{cgal:fr-cqgvf}
 \cgalPkgLicense{\ref licensesGPL  "GPL"}
 \cgalPkgShortInfoEnd

Installation/include/CGAL/config.h

@@ -462,10 +462,6 @@ namespace CGAL {
 } // end of the temporary compatibility with CGAL-4.14
 #endif // CGAL_NO_DEPRECATED_CODE
 
-#if __has_include(<version>)
-#  include <version>
-#endif
-
 namespace CGAL {
 
 // Typedef for the type of nullptr.

Installation/include/CGAL/use.h

@@ -14,15 +14,15 @@
 
 namespace CGAL { namespace internal {
 
-template < typename T > inline
-void use(const T&) {}
+template <typename ...T> inline
+void use(T&&...) {}
 
 template<typename> void use_type() {}
 
 } }
 
 /// CGAL_USE() is a macro which aims at removing "variable is unused" warnings.
-#define CGAL_USE(x) ::CGAL::internal::use(x)
+#define CGAL_USE(...) ::CGAL::internal::use(__VA_ARGS__)
 
 /// CGAL_USE_TYPE() is a macro which aims at removing "typedef locally
 /// defined but not used" warnings.

Interval_skip_list/include/CGAL/Interval_skip_list.h

@@ -177,7 +177,7 @@ class Interval_for_container : public Interval_
 
 
     // remove markers for Interval I starting at left, the left endpoint
-    // of I, and and stopping at the right endpoint of I.
+    // of I, and stopping at the right endpoint of I.
     Interval_handle removeMarkers(IntervalSLnode<Interval>* left,
                                   const Interval& I);
 

Kernel_23/include/CGAL/Kernel/hash_functions.h

@@ -1,4 +1,4 @@
-// Copyright (c) 2019
+// Copyright (c) 2019,2025
 // GeometryFactory (France)
 //
 // This file is part of CGAL (www.cgal.org)
@@ -9,6 +9,8 @@
 //
 //
 // Author(s)     : Simon Giraudot
+//
+// Test file: test/Kernel_23/test_hash_functions.cpp
 
 #ifndef CGAL_KERNEL_HASH_FUNCTIONS_H
 #define CGAL_KERNEL_HASH_FUNCTIONS_H
@@ -16,18 +18,73 @@
 #include <boost/functional/hash.hpp>
 #include <type_traits>
 
+#include <CGAL/representation_tags.h>
+#include <CGAL/Aff_transformation_2.h>
+#include <CGAL/Aff_transformation_3.h>
+#include <CGAL/Bbox_2.h>
+#include <CGAL/Bbox_3.h>
+#include <CGAL/Circle_2.h>
+#include <CGAL/Iso_rectangle_2.h>
+#include <CGAL/Iso_cuboid_3.h>
+#include <CGAL/Point_2.h>
+#include <CGAL/Point_3.h>
+#include <CGAL/Segment_2.h>
+#include <CGAL/Segment_3.h>
+#include <CGAL/Sphere_3.h>
+#include <CGAL/Vector_2.h>
+#include <CGAL/Vector_3.h>
+#include <CGAL/Weighted_point_2.h>
+#include <CGAL/Weighted_point_3.h>
+
+
 namespace CGAL
 {
 
 using boost::hash_value;
 
+template <typename K, typename = void>
+inline constexpr bool has_rep_tag_v = false;
+
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline constexpr bool has_rep_tag_v<K, std::void_t<typename K::Rep_tag>> = true;
+
+template <typename K, typename = void>
+struct Rep_tag {
+  using type = void;
+};
+
+template <typename K>
+struct Rep_tag<K, std::enable_if_t<has_rep_tag_v<K>>> {
+  using type = typename K::Rep_tag;
+};
+
+template <typename K>
+using Rep_tag_t = typename Rep_tag<K>::type;
+
+template <typename K>
+inline constexpr bool is_Cartesian_v = std::is_same<Rep_tag_t<K>, Cartesian_tag>::value;
+
+template <typename K, typename = void>
+struct Is_kernel_hashable : public std::false_type {};
+
+template <typename K>
+struct Is_kernel_hashable<K, std::void_t<decltype(hash_value(std::declval<typename K::FT>()))>> : public std::true_type {};
+
+template <typename K>
+inline constexpr bool is_kernel_hashable_v = Is_kernel_hashable<K>::value;
+
+template <typename K, typename T>
+using enable_if_Cartesian_and_hashable_t =
+    std::enable_if_t<is_Cartesian_v<K> && is_kernel_hashable_v<K>, T>;
+
+template <typename K>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Aff_transformation_2<K>& transform)
 {
   std::size_t result = hash_value(transform.cartesian(0,0));
   for(int i=0; i < 3; ++i)
-    for(int j = 0; j < 3; ++j)
+    for(int j=0; j < 3; ++j)
+      // Skip (0,0) as it was already used to initialize the hash
       if (!(i == 0 && j == 0))
         boost::hash_combine(result, hash_value(transform.cartesian(i,j)));
   return result;
@@ -44,7 +101,7 @@ hash_value (const Bbox_2& bbox)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Circle_2<K>& circle)
 {
   std::size_t result = hash_value(circle.center());
@@ -54,7 +111,7 @@ hash_value (const Circle_2<K>& circle)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Iso_rectangle_2<K>& iso_rectangle)
 {
   std::size_t result = hash_value((iso_rectangle.min)());
@@ -63,7 +120,7 @@ hash_value (const Iso_rectangle_2<K>& iso_rectangle)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Point_2<K>& point)
 {
   std::size_t result = hash_value(point.x());
@@ -72,7 +129,7 @@ hash_value (const Point_2<K>& point)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Segment_2<K>& segment)
 {
   std::size_t result = hash_value(segment.source());
@@ -81,7 +138,7 @@ hash_value (const Segment_2<K>& segment)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Vector_2<K>& vector)
 {
   std::size_t result = hash_value(vector.x());
@@ -90,7 +147,7 @@ hash_value (const Vector_2<K>& vector)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Weighted_point_2<K>& weighed_point)
 {
   std::size_t result = hash_value(weighed_point.point());
@@ -99,14 +156,13 @@ hash_value (const Weighted_point_2<K>& weighed_point)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Aff_transformation_3<K>& transform)
 {
   std::size_t result = hash_value(transform.cartesian(0,0));
   for(int i = 0; i < 3; ++i)
-    for(int j = 0; j < 4; ++j)
-      if (!(i == 0 && j == 0))
-        boost::hash_combine(result, hash_value(transform.cartesian(i,j)));
+    for(int j = (i == 0 ? 1 : 0); j < 4; ++j)
+      boost::hash_combine(result, hash_value(transform.cartesian(i,j)));
   return result;
 }
 
@@ -123,7 +179,7 @@ hash_value (const Bbox_3& bbox)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Iso_cuboid_3<K>& iso_cuboid)
 {
   std::size_t result = hash_value((iso_cuboid.min)());
@@ -132,7 +188,7 @@ hash_value (const Iso_cuboid_3<K>& iso_cuboid)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Point_3<K>& point)
 {
   std::size_t result = hash_value(point.x());
@@ -142,7 +198,7 @@ hash_value (const Point_3<K>& point)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Segment_3<K>& segment)
 {
   std::size_t result = hash_value(segment.source());
@@ -151,7 +207,7 @@ hash_value (const Segment_3<K>& segment)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Sphere_3<K>& sphere)
 {
   std::size_t result = hash_value(sphere.center());
@@ -161,7 +217,7 @@ hash_value (const Sphere_3<K>& sphere)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Vector_3<K>& vector)
 {
   std::size_t result = hash_value(vector.x());
@@ -171,7 +227,7 @@ hash_value (const Vector_3<K>& vector)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
+inline enable_if_Cartesian_and_hashable_t<K, std::size_t>
 hash_value (const Weighted_point_3<K>& weighed_point)
 {
   std::size_t result = hash_value(weighed_point.point());
@@ -179,93 +235,46 @@ hash_value (const Weighted_point_3<K>& weighed_point)
   return result;
 }
 
+struct Forward_to_hash_value {
+  template <typename T>
+  std::size_t operator()(T&& t) const {
+    using boost::hash_value;
+    return hash_value(std::forward<T>(t));
+  }
+};
+
+template <typename K, typename = void>
+struct Maybe_forward_to_hash_value {
+  Maybe_forward_to_hash_value() = delete;
+  Maybe_forward_to_hash_value(const Maybe_forward_to_hash_value&) = delete;
+};
+
+template <typename K>
+struct Maybe_forward_to_hash_value<K, std::enable_if_t<is_kernel_hashable_v<K>>>
+    : public Forward_to_hash_value {};
+
+
 } //namespace CGAL
 
 // overloads of std::hash used for using std::unordered_[set/map] on CGAL Kernel objects
-namespace std
-{
+namespace std {
+template <typename K> struct hash<CGAL::Aff_transformation_2<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Circle_2<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Iso_rectangle_2<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Point_2<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Segment_2<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Vector_2<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Weighted_point_2<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <> struct hash<CGAL::Bbox_2> : CGAL::Forward_to_hash_value {};
+template <typename K> struct hash<CGAL::Aff_transformation_3<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Iso_cuboid_3<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Point_3<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Segment_3<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Sphere_3<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Vector_3<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <typename K> struct hash<CGAL::Weighted_point_3<K>> : CGAL::Maybe_forward_to_hash_value<K> {};
+template <> struct hash<CGAL::Bbox_3> : CGAL::Forward_to_hash_value {};
+} // namespace std
 
-template <typename K> struct hash<CGAL::Aff_transformation_2<K> > {
-  std::size_t operator() (const CGAL::Aff_transformation_2<K>& transform) const   {
-    return CGAL::hash_value<K> (transform);
-  }
-};
-template <> struct hash<CGAL::Bbox_2> {
-  std::size_t operator() (const CGAL::Bbox_2& bbox) const   {
-    return CGAL::hash_value (bbox);
-  }
-};
-template <typename K> struct hash<CGAL::Circle_2<K> > {
-  std::size_t operator() (const CGAL::Circle_2<K>& circle) const   {
-    return CGAL::hash_value<K> (circle);
-  }
-};
-template <typename K> struct hash<CGAL::Iso_rectangle_2<K> > {
-  std::size_t operator() (const CGAL::Iso_rectangle_2<K>& iso_rectangle) const   {
-    return CGAL::hash_value<K> (iso_rectangle);
-  }
-};
-template <typename K> struct hash<CGAL::Point_2<K> > {
-  std::size_t operator() (const CGAL::Point_2<K>& point) const   {
-    return CGAL::hash_value<K> (point);
-  }
-};
-template <typename K> struct hash<CGAL::Segment_2<K> > {
-  std::size_t operator() (const CGAL::Segment_2<K>& segment) const   {
-    return CGAL::hash_value<K> (segment);
-  }
-};
-template <typename K> struct hash<CGAL::Vector_2<K> > {
-  std::size_t operator() (const CGAL::Vector_2<K>& vector) const   {
-    return CGAL::hash_value<K> (vector);
-  }
-};
-template <typename K> struct hash<CGAL::Weighted_point_2<K> > {
-  std::size_t operator() (const CGAL::Weighted_point_2<K>& weighted_point) const   {
-    return CGAL::hash_value<K> (weighted_point);
-  }
-};
-template <typename K> struct hash<CGAL::Aff_transformation_3<K> > {
-  std::size_t operator() (const CGAL::Aff_transformation_3<K>& transform) const   {
-    return CGAL::hash_value<K> (transform);
-  }
-};
-template <> struct hash<CGAL::Bbox_3> {
-  std::size_t operator() (const CGAL::Bbox_3& bbox) const   {
-    return CGAL::hash_value (bbox);
-  }
-};
-template <typename K> struct hash<CGAL::Iso_cuboid_3<K> > {
-  std::size_t operator() (const CGAL::Iso_cuboid_3<K>& iso_cuboid) const   {
-    return CGAL::hash_value<K> (iso_cuboid);
-  }
-};
-template <typename K> struct hash<CGAL::Point_3<K> > {
-  std::size_t operator() (const CGAL::Point_3<K>& point) const   {
-    return CGAL::hash_value<K> (point);
-  }
-};
-template <typename K> struct hash<CGAL::Segment_3<K> > {
-  std::size_t operator() (const CGAL::Segment_3<K>& segment) const   {
-    return CGAL::hash_value<K> (segment);
-  }
-};
-template <typename K> struct hash<CGAL::Sphere_3<K> > {
-  std::size_t operator() (const CGAL::Sphere_3<K>& sphere) const   {
-    return CGAL::hash_value<K> (sphere);
-  }
-};
-template <typename K> struct hash<CGAL::Vector_3<K> > {
-  std::size_t operator() (const CGAL::Vector_3<K>& vector) const   {
-    return CGAL::hash_value<K> (vector);
-  }
-};
-template <typename K> struct hash<CGAL::Weighted_point_3<K> > {
-  std::size_t operator() (const CGAL::Weighted_point_3<K>& weighted_point) const   {
-    return CGAL::hash_value<K> (weighted_point);
-  }
-};
-
-}
 
 #endif  // CGAL_KERNEL_HASH_FUNCTIONS_H

Kernel_23/test/Kernel_23/test_hash_functions.cpp

@@ -1,13 +1,18 @@
+// test partially generated by Github Copilot
+
 #include <unordered_set>
 
 #include <CGAL/Simple_cartesian.h>
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
-
 #include <CGAL/Bbox_2.h>
+#include <CGAL/Bbox_3.h>
 
 typedef CGAL::Simple_cartesian<double> SC;
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Epick;
 
+static_assert(CGAL::is_kernel_hashable_v<SC>);
+static_assert(CGAL::is_kernel_hashable_v<Epick>);
+
 template <typename Object>
 void test (const Object& obj)
 {
@@ -67,5 +72,3 @@ int main()
 
   return 0;
 }
-
-

Kinetic_space_partition/package_info/Kinetic_space_partition/dependencies

@@ -25,7 +25,6 @@ Modular_arithmetic
 Number_types
 Orthtree
 Point_set_3
-Point_set_processing_3
 Polygon
 Polygon_mesh_processing
 Principal_component_analysis

Kinetic_surface_reconstruction/package_info/Kinetic_surface_reconstruction/dependencies

@@ -26,7 +26,6 @@ Modular_arithmetic
 Number_types
 Orthtree
 Point_set_3
-Point_set_processing_3
 Polygon
 Polygon_mesh_processing
 Principal_component_analysis

Lab/demo/Lab/MainWindow.cpp

@@ -1795,8 +1795,8 @@ bool MainWindow::loadScript(QFileInfo info)
   QString program;
   QString filename = info.absoluteFilePath();
   QFile script_file(filename);
-  script_file.open(QIODevice::ReadOnly);
-  if(!script_file.isReadable()) {
+  bool success = script_file.open(QIODevice::ReadOnly);
+  if((! success) || (!script_file.isReadable())) {
     throw std::ios_base::failure(script_file.errorString().toStdString());
   }
   program = script_file.readAll();
@@ -2747,9 +2747,9 @@ void MainWindow::exportStatistics()
   if(filename.isEmpty())
     return;
   QFile output(filename);
-  output.open(QIODevice::WriteOnly | QIODevice::Text);
+  bool success = output.open(QIODevice::WriteOnly | QIODevice::Text);
 
-  if(!output.isOpen()){
+  if((! success) || (!output.isOpen())){
     qDebug() << "- Error, unable to open" << "outputFilename" << "for output";
   }
   QTextStream outStream(&output);

Lab/demo/Lab/Plugins/Camera_position/Camera_positions_list.cpp

@@ -93,18 +93,20 @@ bool Camera_positions_list::save(QString filename) {
   if(m_model->rowCount() <1)
     return false;
   QFile file(filename);
-  file.open(QIODevice::WriteOnly);
-  QTextStream out(&file);
-  for(int i = 0; i < m_model->rowCount(); ++i)
-  {
-    QStandardItem* item = m_model->item(i);
-    out << item->data(Qt::DisplayRole).toString()
-        << "\n"
-        << item->data(Qt::UserRole).toString()
-        << "\n";
+  if(file.open(QIODevice::WriteOnly)){
+    QTextStream out(&file);
+    for(int i = 0; i < m_model->rowCount(); ++i)
+    {
+      QStandardItem* item = m_model->item(i);
+      out << item->data(Qt::DisplayRole).toString()
+          << "\n"
+          << item->data(Qt::UserRole).toString()
+          << "\n";
+    }
+    file.close();
+    return true;
   }
-  file.close();
-  return true;
+  return false;
 }
 
 void Camera_positions_list::on_saveButton_pressed()
@@ -129,19 +131,24 @@ void Camera_positions_list::on_openButton_pressed()
 
 void Camera_positions_list::load(QString filename) {
   QFile file(filename);
-  std::clog << "Loading camera positions " << qPrintable(filename) << std::endl;
-  file.open(QIODevice::ReadOnly);
-  QTextStream input(&file);
-  while(!input.atEnd()) {
-    QString text = input.readLine(1000);
-    QString coord = input.readLine(1000);
-    if(text.isNull() || coord.isNull()) return;
-    CGAL::qglviewer::Frame frame;
-    if(Three::activeViewer()->readFrame(coord, frame))
-    {
-      addItem(text,
-              Three::activeViewer()->dumpFrame(frame));
+
+  if(file.open(QIODevice::ReadOnly)){
+    std::clog << "Loading camera positions " << qPrintable(filename) << std::endl;
+
+    QTextStream input(&file);
+    while(!input.atEnd()) {
+      QString text = input.readLine(1000);
+      QString coord = input.readLine(1000);
+      if(text.isNull() || coord.isNull()) return;
+      CGAL::qglviewer::Frame frame;
+      if(Three::activeViewer()->readFrame(coord, frame))
+      {
+        addItem(text,
+                Three::activeViewer()->dumpFrame(frame));
+      }
     }
+  }else {
+    std::clog << "Loading camera positions " << qPrintable(filename) << " failed" << std::endl;
   }
 }
 

Linear_cell_complex/doc/Linear_cell_complex/CGAL/Linear_cell_complex/IO/VTK.h

@@ -0,0 +1,68 @@
+namespace CGAL {
+namespace IO {
+
+/** \file VTK.h
+ * Functions to import/export 3D Linear_cell_complex from/to VTK legacy ASCII
+ * format.
+ *
+ * Only supports:
+ * - `CGAL::Linear_cell_complex_for_combinatorial_map<3,3>`
+ * - VTK legacy ASCII format (.vtk files)
+ * - Optional scalar fields for vertices and volumes
+ *
+ * Supported VTK cell types:
+ * - VTK_TETRA (10): Tetrahedron
+ * - VTK_VOXEL (11): Voxel (special hexahedron ordering)
+ * - VTK_HEXAHEDRON (12): Hexahedron
+ * - VTK_WEDGE (13): Prism/Wedge
+ * - VTK_PYRAMID (14): Pyramid
+ * - VTK_PENTAGONAL_PRISM (15): Pentagonal prism
+ * - VTK_HEXAGONAL_PRISM (16): Hexagonal prism
+ * - VTK_POLYHEDRON (42): Generic polyhedron
+ */
+
+/**
+ * \brief Reads a VTK legacy ASCII file and load it into a 3D
+ *        linear cell complex.
+ * \ingroup PkgLinearCellComplexRefIOVTK
+ *
+ * \tparam LCC must be a `CGAL::Linear_cell_complex_for_combinatorial_map<3,3>`
+ * \tparam VertexScalarType Type for vertex scalar data (default: float)
+ * \tparam VolumeScalarType Type for volume scalar data (default: float)
+ * \param filename Path to the VTK file
+ * \param alcc The linear cell complex to populate (will be cleared first)
+ * \param vertex_scalars Optional output vector to store per-vertex scalar values.
+ *                      If provided, will be resized to match number of vertices.
+ * \param volume_scalars Optional output vector to store per-volume scalar values.
+ *                      If provided, will be resized to match number of volumes.
+ * \return `true` if loading was successful, `false` otherwise
+ */
+template <typename LCC, typename VertexScalarType, typename VolumeScalarType>
+bool read_VTK(const char* filename,
+              LCC& alcc,
+              std::vector<VertexScalarType>* vertex_scalars=nullptr,
+              std::vector<VolumeScalarType>* volume_scalars=nullptr);
+
+/**
+ * \brief Writes a 3D Linear_cell_complex to a VTK legacy ASCII file.
+ * \ingroup PkgLinearCellComplexRefIOVTK
+ *
+ * \tparam LCC must be a `CGAL::Linear_cell_complex_for_combinatorial_map<3,3>`
+ * \tparam VertexScalarType Type for vertex scalar data (default: float)
+ * \tparam VolumeScalarType Type for volume scalar data (default: float)
+ * \param filename Path to the output VTK file
+ * \param alcc The linear cell complex to export
+ * \param vertex_scalars Optional per-vertex scalar data. If provided, must have
+ *                      same size as number of vertex attributes in the LCC.
+ * \param volume_scalars Optional per-volume scalar data. If provided, must have
+ *                      same size as number of 3-cells in the LCC.
+ * \return `true` if writing was successful, `false` otherwise
+ */
+template <typename LCC, typename VertexScalarType, typename VolumeScalarType>
+bool write_VTK(const char* filename,
+               const LCC& alcc,
+               const std::vector<VertexScalarType>* vertex_scalars=nullptr,
+               const std::vector<VolumeScalarType>* volume_scalars=nullptr);
+
+} // namespace IO
+} // namespace CGAL

Linear_cell_complex/doc/Linear_cell_complex/Linear_cell_complex.txt

@@ -289,6 +289,18 @@ The following example shows the use of \link GenericMap::insert_cell_1_between_t
 Result of the run of the linear_cell_complex_3_insert program. A window shows the 3D cube where one face has a hole.
 \cgalFigureEnd
 
+\subsection Linear_cell_complexWriteVTK Writing a Linear Cell Complex to a VTK File
+\anchor ssecLCCWriteVtK
+
+This example loads a 3D linear cell complex from a `.3map` file (using the `operator>>`). It computes for each 3-cell (volume) the number of incident vertices (0-cells), stores these values in a `std::vector<std::size_t>`, and writes the result to a `.vtk` file using `CGAL::IO::write_VTK()`, with the computed values as scalars for each volume.
+
+\cgalExample{Linear_cell_complex/linear_cell_complex_3_vtk_io.cpp}
+
+\cgalFigureBegin{fig_lcc_export_vtk,lcc-export-vtk.png}
+Visualization of the VTK file generated by the `linear_cell_complex_3_vtk_io` program, using Paraview. Each volume is colored depending on its number of vertices.
+\cgalFigureEnd
+
+
 \section Linear_cell_complexDesign Design and Implementation History
 
 This package was developed by Guillaume Damiand, with the help of Andreas Fabri, S&eacute;bastien Loriot and Laurent Rineau. Monique Teillaud and Bernd G&auml;rtner contributed to the manual.

Linear_cell_complex/doc/Linear_cell_complex/PackageDescription.txt

@@ -23,6 +23,14 @@
 /// \defgroup PkgDrawLinearCellComplex Draw a Linear Cell Complex
 /// \ingroup PkgLinearCellComplexRef
 
+/// \defgroup PkgLinearCellComplexRefIO IO Functions for LCC
+/// \ingroup PkgLinearCellComplexRef
+
+/*! High-level operations.
+\cgalInclude{CGAL/Linear_cell_complex/IO/VTK.h}
+*/
+/// \defgroup PkgLinearCellComplexRefIOVTK VTK IO Functions for LCC
+/// \ingroup PkgLinearCellComplexRefIO
 
 /*!
 \addtogroup PkgLinearCellComplexRef
@@ -74,4 +82,10 @@
 - \link PkgDrawLinearCellComplex CGAL::draw<LCC>() \endlink
 - \link PkgDrawLinearCellComplex CGAL::add_in_graphics_scene<LCC, BufferType, DrawingFunctor>() \endlink
 
+\cgalCRPSubsection{IO Functions for LCC}
+- \link PkgCombinatorialMapsRefIO `std::ostream& operator<< (std::ostream& os, const GenericMap& amap)` \endlink
+- \link PkgCombinatorialMapsRefIO `std::ifstream& operator>> (std::ifstream& is, GenericMap& amap)` \endlink
+- \link PkgLinearCellComplexRefIOVTK `CGAL::IO::Read_VTK<LCC>()` \endlink
+- \link PkgLinearCellComplexRefIOVTK `CGAL::IO::Write_VTK<LCC>()` \endlink
+
 */

Linear_cell_complex/doc/Linear_cell_complex/examples.txt

@@ -6,4 +6,5 @@
 \example Linear_cell_complex/linear_cell_complex_3_incremental_builder.cpp
 \example Linear_cell_complex/draw_linear_cell_complex.cpp
 \example Linear_cell_complex/linear_cell_complex_3_insert.cpp
+\example Linear_cell_complex/linear_cell_complex_3_vtk_io.cpp
 */

Linear_cell_complex/examples/Linear_cell_complex/CMakeLists.txt

@@ -27,6 +27,7 @@ create_single_source_cgal_program("linear_cell_complex_4.cpp")
 create_single_source_cgal_program("read_plane_graph_in_lcc_2.cpp")
 create_single_source_cgal_program("voronoi_2.cpp")
 create_single_source_cgal_program("voronoi_3.cpp")
+create_single_source_cgal_program("linear_cell_complex_3_vtk_io.cpp")
 
 create_single_source_cgal_program("draw_linear_cell_complex.cpp")
 if(CGAL_Qt6_FOUND)

Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3_vtk_io.cpp

@@ -0,0 +1,34 @@
+#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
+#include <CGAL/Linear_cell_complex/IO/VTK.h>
+#include <vector>
+#include <cstdlib>
+
+int main()
+{
+  CGAL::Linear_cell_complex_for_combinatorial_map<3> lcc;
+  std::ifstream is("data/beam-with-mixed-cells.3map");
+  if(!is)
+  {
+    std::cout<<"Error opening data/beam-with-mixed-cells.3map."<<std::endl;
+    return EXIT_FAILURE;
+  }
+
+  is>>lcc;
+  // Compute per-volume vertex count
+  std::vector<std::size_t> volume_scalars;
+  for(auto it=lcc.template one_dart_per_cell<3>().begin(),
+        itend=lcc.template one_dart_per_cell<3>().end(); it!=itend; ++it)
+  {
+    std::size_t nbv=lcc.template one_dart_per_incident_cell<0,3>(it).size();
+    volume_scalars.push_back(nbv);
+  }
+
+  if(!CGAL::IO::write_VTK("beam-with-mixed-cells.vtk", lcc, nullptr,
+                          &volume_scalars))
+  {
+    std::cout<<"Error for write_VTK."<<std::endl;
+    return EXIT_FAILURE;
+  }
+
+  return EXIT_SUCCESS;
+}

Linear_cell_complex/include/CGAL/Linear_cell_complex/IO/VTK.h

@@ -0,0 +1,719 @@
+// Copyright (c) 2025 CNRS and LIRIS' Establishments (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org)
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
+//
+// Author(s)     : Guillaume Damiand <guillaume.damiand@liris.cnrs.fr>
+
+#ifndef CGAL_LCC_IO_VTK_H
+#define CGAL_LCC_IO_VTK_H
+
+#include <CGAL/Linear_cell_complex_incremental_builder_3.h>
+#include <CGAL/assertions.h>
+#include <CGAL/Element_topo.h>
+
+#include <fstream>
+#include <iostream>
+#include <sstream>
+#include <string>
+#include <unordered_map>
+#include <vector>
+#include <set>
+
+namespace CGAL {
+namespace IO {
+
+/*
+ * Functions to import/export 3D Linear_cell_complex from/to VTK legacy ASCII
+ * format.
+ *
+ * Only supports:
+ * - Linear_cell_complex_for_combinatorial_map<3,3>
+ * - VTK legacy ASCII format (.vtk files)
+ * - Optional scalar fields for vertices and volumes
+ *
+ * Supported VTK cell types:
+ * - VTK_TETRA (10): Tetrahedron
+ * - VTK_VOXEL (11): Voxel (special hexahedron ordering)
+ * - VTK_HEXAHEDRON (12): Hexahedron
+ * - VTK_WEDGE (13): Prism/Wedge
+ * - VTK_PYRAMID (14): Pyramid
+ * - VTK_PENTAGONAL_PRISM (15): Pentagonal prism
+ * - VTK_HEXAGONAL_PRISM (16): Hexagonal prism
+ * - VTK_POLYHEDRON (42): Generic polyhedron
+ */
+
+// ============================================================================
+//                              Declarations
+// ============================================================================
+
+/*
+ * Read a VTK legacy ASCII file and load it into a 3D Linear_cell_complex.
+ *
+ * \tparam LCC must be a Linear_cell_complex_for_combinatorial_map<3,3>
+ * \tparam VertexScalarType Type for vertex scalar data (default: float)
+ * \tparam VolumeScalarType Type for volume scalar data (default: float)
+ * \param alcc The Linear_cell_complex to populate (will be cleared first)
+ * \param filename Path to the VTK file
+ * \param vertex_scalars Optional output vector to store per-vertex scalar values.
+ *                      If provided, will be resized to match number of vertices.
+ * \param volume_scalars Optional output vector to store per-volume scalar values.
+ *                      If provided, will be resized to match number of volumes.
+ * \return `true` if loading was successful, `false` otherwise
+ */
+template <typename LCC, typename VertexScalarType,
+          typename VolumeScalarType>
+bool read_VTK(const char* filename,
+              LCC& alcc,
+              std::vector<VertexScalarType>* vertex_scalars,
+              std::vector<VolumeScalarType>* volume_scalars);
+
+/*
+ * Write a 3D Linear_cell_complex to a VTK legacy ASCII file.
+ *
+ * \tparam LCC must be a Linear_cell_complex_for_combinatorial_map<3,3>
+ * \tparam VertexScalarType Type for vertex scalar data (default: float)
+ * \tparam VolumeScalarType Type for volume scalar data (default: float)
+ * \param alcc The Linear_cell_complex to export
+ * \param filename Path to the output VTK file
+ * \param vertex_scalars Optional per-vertex scalar data. If provided, must have
+ *                      same size as number of vertex attributes in the LCC.
+ * \param volume_scalars Optional per-volume scalar data. If provided, must have
+ *                      same size as number of 3-cells in the LCC.
+ * \return `true` if writing was successful, `false` otherwise
+ */
+template <typename LCC, typename VertexScalarType,
+          typename VolumeScalarType>
+bool write_VTK(const char* filename,
+               const LCC& alcc,
+               const std::vector<VertexScalarType>* vertex_scalars,
+               const std::vector<VolumeScalarType>* volume_scalars);
+
+// "Advanced" versions with functors
+template <typename LCC, typename PointFunctor, typename CellFunctor>
+bool write_VTK_with_fct(const char* filename, const LCC& alcc,
+                        PointFunctor ptval, CellFunctor cellval);
+
+// ============================================================================
+//                          Implementation details
+// ============================================================================
+
+namespace internal
+{
+  /////////////////////////////////////////////////////////////////////////////
+  // VTK type name mapping
+  // bit, unsigned_char, char, unsigned_short, short, unsigned_int, int,
+  // unsigned_long, long, float, double.
+  template<typename T>
+  struct gettype
+  { static std::string name() { return "unknown"; }};
+  template<>
+  struct gettype<bool>
+  { static std::string name() { return "bit"; }};
+  template<>
+  struct gettype<unsigned char>
+  { static std::string name() { return "unsigned_char"; }};
+  template<>
+  struct gettype<char>
+  { static std::string name() { return "char"; }};
+  template<>
+  struct gettype<unsigned short int>
+  { static std::string name() { return "unsigned_short"; }};
+  template<>
+  struct gettype<short int>
+  { static std::string name() { return "short"; }};
+  template<>
+  struct gettype<unsigned int>
+  { static std::string name() { return "unsigned_int"; }};
+  template<>
+  struct gettype<int>
+  { static std::string name() { return "int"; }};
+  template<>
+  struct gettype<unsigned long int>
+  { static std::string name() { return "unsigned_long"; }};
+  template<>
+  struct gettype<long int>
+  { static std::string name() { return "long"; }};
+  template<>
+  struct gettype<float>
+  { static std::string name() { return "float"; }};
+  template<>
+  struct gettype<double>
+  { static std::string name() { return "double"; }};
+  /////////////////////////////////////////////////////////////////////////////
+  // VTK cell type constants
+  enum VTK_Cell_Type
+  {
+    VTK_TETRA = 10,
+    VTK_VOXEL = 11,
+    VTK_HEXAHEDRON = 12,
+    VTK_WEDGE = 13, // Prism
+    VTK_PYRAMID = 14,
+    VTK_PENTAGONAL_PRISM = 15,
+    VTK_HEXAGONAL_PRISM = 16,
+    VTK_POLYHEDRON = 42 // Generic cell
+  };
+  /////////////////////////////////////////////////////////////////////////////
+  /// Write cell_data.
+  template<typename FCT>
+  struct Write_cell_data
+  {
+    /// nb is the number of cells,
+    /// fct is a function having 3 parameters: a lcc,  a dart_descriptor,
+    ///    an the index of the cell.
+    template<typename LCC>
+    static void run(std::ofstream& fo, LCC& lcc, std::size_t nb, FCT fct)
+    {
+      fo<<"CELL_DATA "<<nb<<std::endl;
+      fo<<"SCALARS cell_scalars "
+         <<gettype<decltype(fct(lcc, lcc.null_dart_descriptor, 0))>::name()
+         <<" 1"<<std::endl;
+      fo<<"LOOKUP_TABLE default"<<std::endl;
+      std::size_t i=0;
+      for(auto itvol=lcc.template one_dart_per_cell<3>().begin(),
+           itvolend=lcc.template one_dart_per_cell<3>().end();
+           itvol!=itvolend; ++itvol, ++i)
+      { fo<<fct(lcc, itvol, i)<<std::endl; }
+      fo<<std::endl;
+    }
+  };
+  template<>
+  struct Write_cell_data<std::nullptr_t>
+  {
+    template<typename LCC>
+    static void run(std::ofstream&, LCC&, std::size_t, std::nullptr_t)
+    {}
+  };
+  /////////////////////////////////////////////////////////////////////////////
+  /// Write point_data.
+  template<typename FCT>
+  struct Write_point_data
+  {
+    /// nb is the number of cells,
+    /// fct is a function having 3 parameters: a lcc,  a dart_descriptor,
+    ///    an the index of the cell.
+    template<typename LCC>
+    static void run(std::ofstream& fo, LCC& lcc, std::size_t nb, FCT fct)
+    {
+      fo<<"POINT_DATA "<<nb<<std::endl;
+      fo<<"SCALARS point_scalars "
+         <<gettype<decltype(fct(lcc, lcc.null_dart_descriptor, 0))>::name()
+         <<" 1"<<std::endl;
+      fo<<"LOOKUP_TABLE default"<<std::endl;
+      std::size_t i=0;
+      for(auto itv=lcc.vertex_attributes().begin(),
+           itvend=lcc.vertex_attributes().end(); itv!=itvend; ++itv, ++i)
+      { fo<<fct(lcc, lcc.template dart_of_attribute<0>(itv), i)<<std::endl; }
+      fo<<std::endl;
+    }
+  };
+  /////////////////////////////////////////////////////////////////////////////
+  template<>
+  struct Write_point_data<std::nullptr_t>
+  {
+    template<typename LCC>
+    static void run(std::ofstream&, LCC&, std::size_t, std::nullptr_t)
+    {}
+  };
+  /////////////////////////////////////////////////////////////////////////////
+  // Read data, stored values as T.
+  template<typename T>
+  bool read_data(std::istream& fi, std::string& line, std::vector<T>& data)
+  {
+    std::string txt, data_type;
+    std::size_t nb;
+    std::istringstream inputline(line);
+    inputline>>txt>>nb;  // "CELL_DATA xxx"
+    fi>>txt>>txt; // "SCALARS cell_scalars "
+    fi>>data_type>>txt; // type for data
+    fi>>txt>>txt; // "LOOKUP_TABLE default"
+    if(!fi.good())
+    { return false; }
+    data.clear();
+    data.reserve(nb);
+    for(std::size_t i=0; i<nb; ++i)
+    {
+      if(!(fi>>txt))
+      { return false; }
+
+      std::stringstream ss{txt};
+      T t;
+      ss>>t;
+
+      data.push_back(t);
+    }
+    return true;
+  }
+  /////////////////////////////////////////////////////////////////////////////
+  // Helper: detect VTK cell type from a 3-cell
+  template<typename LCC>
+  VTK_Cell_Type get_vtk_cell_type(const LCC& lcc,
+                                  typename LCC::Dart_const_descriptor itvol,
+                                  typename LCC::Dart_const_descriptor& sd)
+  {
+    using namespace CGAL::CMap::Element_topo;
+    cell_topo vol_type=get_cell_topo<3>(lcc, itvol, sd);
+    switch(vol_type)
+    {
+      case TETRAHEDRON: return VTK_TETRA;
+      case PYRAMID: return VTK_PYRAMID;
+      case PRISM: return VTK_WEDGE;
+      case HEXAHEDRON: return VTK_HEXAHEDRON;
+      // case PENTAGONAL_PRISM: return VTK_PENTAGONAL_PRISM;
+      // case HEXAGONAL_PRISM: return VTK_HEXAGONAL_PRISM;
+        //       24 QUADRATIC_TETRA
+        //       25 QUADRATIC_HEXAHEDRON
+        //       26 QUADRATIC_WEDGE
+        //       27 QUADRATIC_PYRAMID
+      default: break;
+    }
+    return VTK_POLYHEDRON;
+  }
+  /////////////////////////////////////////////////////////////////////////////
+template <typename LCC, typename VertexScalarType=float,
+          typename CellScalarType=float>
+bool read_lcc_from_vtk_ascii(std::istream& is, LCC& alcc,
+                             std::vector<VertexScalarType>* vertex_scalars=nullptr,
+                             std::vector<CellScalarType>* cell_scalars=nullptr)
+{
+  static_assert(LCC::dimension==3 && LCC::ambient_dimension==3,
+                "read_VTK() only supports 3D Linear_cell_complexes (3,3)");
+
+  using Point=typename LCC::Point;
+  using FT=typename LCC::FT;
+
+  Linear_cell_complex_incremental_builder_3<LCC> ib(alcc);
+
+  std::string line, tmp;
+  std::size_t npoints, ncells;
+
+  // Skip to POINTS section
+  while(std::getline(is, line) && line.find("POINTS")==std::string::npos)
+  {}
+  if(is.eof())
+  {
+    std::cerr<<"[ERROR] read_VTK: POINTS section not found"<<std::endl;
+    return false;
+  }
+
+  std::stringstream ss(line);
+  std::getline(ss, tmp, ' '); // skip "POINTS"
+  ss>>npoints;
+
+  // Read points
+  std::vector<typename LCC::Vertex_attribute_descriptor> points(npoints);
+  for(std::size_t i=0; i<npoints; ++i)
+  {
+    FT x, y, z;
+    if(!(is>>x>>y>>z))
+    {
+      std::cerr<<"[ERROR] read_VTK: failed to read point "<<i<<std::endl;
+      return false;
+    }
+    points[i]=ib.add_vertex(Point(x, y, z));
+  }
+
+  // Skip to CELLS section
+  while(std::getline(is, line) && line.find("CELLS")==std::string::npos)
+  {}
+  if(is.eof())
+  {
+    std::cerr<<"[ERROR] read_VTK: CELLS section not found"<<std::endl;
+    return false;
+  }
+
+  ss=std::stringstream(line);
+  std::getline(ss, tmp, ' '); // skip "CELLS"
+  ss>>ncells;
+
+  // Read connectivity
+  std::vector<std::vector<std::size_t>> faces(ncells);
+  std::size_t points_per_cell;
+  for(std::size_t i=0; i<ncells; ++i)
+  {
+    if(!(is>>points_per_cell))
+    {
+      std::cerr<<"[ERROR] read_VTK: failed to read cell "<<i<<std::endl;
+      return false;
+    }
+    faces[i].resize(points_per_cell);
+    for(std::size_t j=0; j<points_per_cell; ++j)
+    {
+      if(!(is>>faces[i][j]))
+      {
+        std::cerr<<"[ERROR] read_VTK: failed to read cell "<<i<<" vertex "<<j<< std::endl;
+        return false;
+      }
+    }
+  }
+
+  // Skip to CELL_TYPES section
+  while(std::getline(is, line) && line.find("CELL_TYPES")==std::string::npos)
+  {}
+  if(is.eof())
+  {
+    std::cerr<<"[ERROR] read_VTK: CELL_TYPES section not found"<<std::endl;
+    return false;
+  }
+
+  // Create cells based on types
+  std::size_t cell_type;
+  std::set<std::size_t> error_types;
+  for(std::size_t i = 0; i<ncells; ++i)
+  {
+    if(!(is>>cell_type))
+    {
+      std::cerr<<"[ERROR] read_VTK: failed to read cell type "<<i<< std::endl;
+      return false;
+    }
+    const auto& v=faces[i];
+    switch(cell_type)
+    {
+    case VTK_TETRA:
+      if(v.size()==4)
+      { make_tetrahedron_with_builder(ib, v[0], v[1], v[2], v[3]); }
+      break;
+    case VTK_VOXEL:
+      if(v.size()==8)
+      { make_hexahedron_with_builder(ib, v[0], v[1], v[3], v[2], v[4], v[5],
+                                     v[7], v[6]); }
+      break;
+    case VTK_HEXAHEDRON:
+      if(v.size()==8)
+      { make_hexahedron_with_builder(ib, v[0], v[1], v[2], v[3], v[4], v[5],
+                                     v[6], v[7]); }
+      break;
+    case VTK_WEDGE: // PRISM
+      if(v.size()==6)
+      { make_prism_with_builder(ib, v[0], v[1], v[2], v[3], v[4], v[5]); }
+      break;
+    case VTK_PYRAMID:
+      if(v.size()==5)
+      { make_pyramid_with_builder(ib, v[0], v[1], v[2], v[3], v[4]); }
+      break;
+    case VTK_PENTAGONAL_PRISM:
+      if(v.size()==10)
+      { make_pentagonal_prism_with_builder(ib, v[0], v[1], v[2], v[3], v[4],
+                                           v[5], v[6], v[7], v[8], v[9]); }
+      break;
+    case VTK_HEXAGONAL_PRISM:
+      if(v.size()==12)
+      { make_hexagonal_prism_with_builder(ib, v[0], v[1], v[2], v[3], v[4],
+                                          v[5], v[6], v[7], v[8], v[9],
+                                          v[10], v[11]); }
+      break;
+    case VTK_POLYHEDRON: // GENERIC CELL
+      make_generic_cell_with_builder(ib, v);
+      break;
+    default:
+      if(error_types.count(cell_type)==0)
+      {
+        std::cerr<<"[ERROR] read_VTK: type "<<cell_type<<" unknown."<<std::endl;
+        error_types.insert(cell_type);
+      }
+    }
+  }
+
+  // Clean up unused vertex attributes
+  for(auto itv=alcc.vertex_attributes().begin();
+       itv!=alcc.vertex_attributes().end(); ++itv)
+  {
+    if(alcc.template dart_of_attribute<0>(itv)==alcc.null_descriptor)
+    { alcc.erase_vertex_attribute(itv); }
+  }
+
+  if(vertex_scalars!=nullptr)
+  { vertex_scalars->clear(); }
+  if(cell_scalars!=nullptr)
+  { cell_scalars->clear(); }
+
+  while(std::getline(is, line))
+  {
+    // Read POINT_DATA scalars if present
+    if(vertex_scalars!=nullptr && line.find("POINT_DATA")!=std::string::npos)
+    {
+      if(!read_data(is, line, *vertex_scalars))
+      {
+        std::cerr<<"[ERROR] read_VTK: error when reading POINT_DATA."
+                 <<std::endl;
+      }
+    }
+    // Read CELL_DATA scalars if present
+    else if(cell_scalars!=nullptr && line.find("CELL_DATA")!=std::string::npos)
+    {
+      if(!read_data(is, line, *cell_scalars))
+      {
+        std::cerr<<"[ERROR] read_VTK: error when reading CELL_DATA."
+                  <<std::endl;
+      }
+    }
+  }
+  return true;
+}
+/////////////////////////////////////////////////////////////////////////////
+template<class LCC>
+bool write_lcc_topo_to_vtk_ascii(std::ostream& os, const LCC& alcc,
+                                 std::size_t& nbpts, std::size_t& nbcells)
+{
+  static_assert(LCC::dimension==3 && LCC::ambient_dimension==3,
+                "write_VTK() only supports 3D Linear_cell_complexes (3,3)");
+
+  // Write VTK header
+  os<<"# vtk DataFile Version 2.0\n";
+  os<<"CGAL Linear_cell_complex\n";
+  os<<"ASCII\n";
+  os<<"DATASET UNSTRUCTURED_GRID\n\n";
+
+  // Build vertex index map and write points
+  std::unordered_map<typename LCC::Vertex_attribute_const_descriptor, std::size_t>
+      index;
+  nbpts=0;
+  os<<"POINTS "<<alcc.vertex_attributes().size()<<" double"<<std::endl;
+  for(auto itv=alcc.vertex_attributes().begin(),
+       itvend=alcc.vertex_attributes().end(); itv!=itvend; ++itv)
+  {
+    os<<" "<<itv->point()<<std::endl;
+    index[itv]=nbpts++;
+  }
+  os<<std::endl;
+
+  // Count cells and build connectivity
+  nbcells=0;
+  std::size_t total_size=0;
+  std::ostringstream cell_stream, type_stream;
+  typename LCC::Dart_const_descriptor sd;
+
+  // Write cells section
+  for(typename LCC::template One_dart_per_cell_range<3>::const_iterator
+           itvol=alcc.template one_dart_per_cell<3>().begin(),
+       itvolend=alcc.template one_dart_per_cell<3>().end();
+      itvol!=itvolend; ++itvol)
+  {
+    ++nbcells;
+    ++total_size; // for the number of vertices
+    VTK_Cell_Type cell_type=get_vtk_cell_type(alcc, itvol, sd);
+    type_stream<<static_cast<int>(cell_type)<<std::endl;
+
+    if(cell_type==VTK_TETRA)
+    {
+      cell_stream<<" 4 "
+         <<index[alcc.vertex_attribute(sd)]<<" "
+         <<index[alcc.vertex_attribute(alcc.template beta<1>(sd))]<<" "
+         <<index[alcc.vertex_attribute(alcc.template beta<0>(sd))]<<" "
+         <<index[alcc.vertex_attribute(alcc.template beta<2, 0>(sd))]<<std::endl;
+      total_size+=4;
+    }
+    else if(cell_type==VTK_PYRAMID)
+    {
+      cell_stream<<" 5 "
+         <<index[alcc.vertex_attribute(sd)]<<" "
+         <<index[alcc.vertex_attribute(alcc.template beta<1>(sd))]<<" "
+         <<index[alcc.vertex_attribute(alcc.template beta<1,1>(sd))]<<" "
+         <<index[alcc.vertex_attribute(alcc.template beta<0>(sd))]<<" "
+         <<index[alcc.vertex_attribute(alcc.template beta<2,0>(sd))]<<std::endl;
+      total_size+=5;
+    }
+    else if(cell_type==VTK_WEDGE)
+    {
+      cell_stream<<" 6 "
+         <<index[alcc.vertex_attribute(sd)]<<" "
+         <<index[alcc.vertex_attribute(alcc.template beta<1>(sd))]<<" "
+         <<index[alcc.vertex_attribute(alcc.template beta<0>(sd))]<<" ";
+      // Move to the up face
+      typename LCC::Dart_const_descriptor d2=alcc.template beta<2, 1, 1, 2>(sd);
+      cell_stream<<index[alcc.vertex_attribute(alcc.template beta<1>(d2))]<<" "
+         <<index[alcc.vertex_attribute(d2)]<<" "
+         <<index[alcc.vertex_attribute(alcc.template beta<0>(d2))]<<std::endl;
+      total_size+=6;
+    }
+    else if(cell_type==VTK_HEXAHEDRON)
+    {
+      cell_stream<<" 8 ";
+      for(unsigned int i=0; i<4; ++i)
+      {
+        cell_stream<<index[alcc.vertex_attribute(sd)]<<" ";
+        sd=alcc.template beta<1>(sd);
+      }
+      typename LCC::Dart_const_descriptor d2=alcc.template beta<2, 1, 1, 2, 1>(sd);
+      // Darts associated with particles 4, 5, 6, 7
+      for(unsigned int i = 0; i < 4; i++)
+      {
+        cell_stream<<index[alcc.vertex_attribute(d2)]<<" ";
+        d2 = alcc.template beta<0>(d2);
+      }
+      cell_stream<<std::endl;
+      total_size+=8;
+    }
+    // TODO: 15 PENTAGONAL_PRISM
+    //       16 HEXAGONAL_PRISM
+    //       24 QUADRATIC_TETRA
+    //       25 QUADRATIC_HEXAHEDRON
+    //       26 QUADRATIC_WEDGE
+    //       27 QUADRATIC_PYRAMID
+    else
+    {
+      // Generic polyhedron format write as face-vertex connectivity
+      std::vector<std::vector<std::size_t>> faces;
+      std::size_t cell_size=1; // Start with 1 for number of faces
+      ++total_size; // for the same reason
+      for(auto itface=alcc.template one_dart_per_incident_cell<2, 3, 2>(itvol).begin(),
+               itfaceend=alcc.template one_dart_per_incident_cell<2, 3, 2>(itvol).end();
+          itface!=itfaceend; ++itface)
+      {
+        faces.push_back(std::vector<std::size_t>());
+        typename LCC::Dart_const_descriptor curdh=itface;
+        do
+        {
+          faces.back().push_back(index[alcc.vertex_attribute(curdh)]);
+          curdh=alcc.template beta<1>(curdh);
+        }
+        while(curdh!=itface);
+        cell_size+=faces.back().size()+1; // +1 for the number of vertices in the face
+      }
+      cell_stream<<cell_size<<" "<<faces.size();
+      for(const auto& face : faces)
+      {
+        cell_stream<<" "<<face.size();
+        for(auto v : face)
+        { cell_stream<<" "<<v; }
+        total_size+=face.size()+1; // +1 for the number of vertices in the face
+      }
+      cell_stream<<std::endl;
+    }
+  }
+  os<<"CELLS "<<nbcells<<" "<<total_size<<std::endl;
+  os<<cell_stream.str()<<std::endl;
+
+  // Write cell types
+  os<<"CELL_TYPES "<<nbcells<<std::endl;
+  os<<type_stream.str()<<std::endl;
+
+  return true;
+}
+
+} // namespace internal
+
+// ============================================================================
+//                        Public interface implementation
+// ============================================================================
+
+////////////////////////////////////////////////////////////////////////////////////
+template <typename LCC, typename VertexScalarType, typename VolumeScalarType>
+bool read_VTK(const char* filename, LCC& alcc,
+              std::vector<VertexScalarType>* vertex_scalars,
+              std::vector<VolumeScalarType>* volume_scalars)
+{
+  CGAL_assertion(filename!=nullptr);
+  std::ifstream file(filename);
+  if(!file.is_open())
+  {
+    std::cerr<<"[ERROR] read_VTK: cannot open file "<<filename<<std::endl;
+    return false;
+  }
+  return internal::read_lcc_from_vtk_ascii(file, alcc,
+                                           vertex_scalars, volume_scalars);
+}
+
+template <typename LCC>
+bool read_VTK(const char* filename, LCC& alcc)
+{ return read_VTK<LCC, float, float>(filename, alcc, nullptr, nullptr); }
+
+template <typename LCC, typename VertexScalarType>
+bool read_VTK(const char* filename, LCC& alcc,
+              std::vector<VertexScalarType>* vertex_scalars)
+{ return read_VTK<LCC, VertexScalarType, float>
+      (filename, alcc, vertex_scalars, nullptr); }
+
+template <typename LCC, typename VolumeScalarType>
+bool read_VTK(const char* filename, LCC& alcc,
+              std::nullptr_t,
+              std::vector<VolumeScalarType>* volume_scalars)
+{ return read_VTK<LCC, float, VolumeScalarType>
+      (filename, alcc, nullptr, volume_scalars); }
+////////////////////////////////////////////////////////////////////////////////////
+template <typename LCC, typename PointFunctor, typename CellFunctor>
+inline bool write_VTK_with_fct(const char* filename, const LCC& alcc,
+                               PointFunctor pointfct, CellFunctor cellfct)
+{
+  CGAL_assertion(filename!=nullptr);
+  std::ofstream file(filename);
+  if(!file.good())
+  {
+    std::cerr<<"[ERROR] write_VTK: cannot open file "<<filename<<std::endl;
+    return false;
+  }
+  std::size_t nbpts=0, nbcells=0;
+  bool res=internal::write_lcc_topo_to_vtk_ascii(file, alcc, nbpts, nbcells);
+  if(res)
+  {
+    if(pointfct)
+    { internal::Write_point_data<PointFunctor>::
+          run(file, alcc, nbpts, pointfct); }
+    if(cellfct)
+    { internal::Write_cell_data<CellFunctor>::
+          run(file, alcc, nbcells, cellfct); }
+  }
+  file.close();
+  return true;
+}
+////////////////////////////////////////////////////////////////////////////////////
+template <typename LCC, typename VertexScalarType, typename VolumeScalarType>
+bool write_VTK(const char* filename, const LCC& alcc,
+               const std::vector<VertexScalarType>* vertex_scalars,
+               const std::vector<VolumeScalarType>* volume_scalars)
+{
+  std::function<VertexScalarType(const LCC&,
+                                 typename LCC::Dart_const_descriptor,
+                                 std::size_t i)> vertexfct;
+  std::function<VolumeScalarType(const LCC&,
+                                 typename LCC::Dart_const_descriptor,
+                                 std::size_t i)> cellfct;
+  if(vertex_scalars!=nullptr)
+  {
+    vertexfct=[&vertex_scalars](const LCC&, typename LCC::Dart_const_descriptor,
+                               std::size_t i) -> VertexScalarType
+    { return (*vertex_scalars)[i]; };
+  }
+
+  if(volume_scalars!=nullptr)
+  {
+    cellfct=[&volume_scalars](const LCC&, typename LCC::Dart_const_descriptor,
+                             std::size_t i) -> VolumeScalarType
+    { return (*volume_scalars)[i]; };
+  }
+
+  return write_VTK_with_fct(filename, alcc, vertexfct, cellfct);
+}
+
+template <typename LCC>
+bool write_VTK(const char* filename, const LCC& alcc)
+{
+  return write_VTK<LCC, float, float>(filename, alcc, nullptr, nullptr);
+}
+
+template <typename LCC, typename VertexScalarType>
+bool write_VTK(const char* filename, const LCC& alcc,
+               const std::vector<VertexScalarType>* vertex_scalars)
+{
+  return write_VTK<LCC, VertexScalarType, float>(filename, alcc, vertex_scalars,
+                                                 nullptr);
+}
+
+template <typename LCC, typename VolumeScalarType>
+bool write_VTK(const char* filename, const LCC& alcc,
+               std::nullptr_t,
+               const std::vector<VolumeScalarType>* volume_scalars)
+{
+  return write_VTK<LCC, float, VolumeScalarType>(filename, alcc, nullptr,
+                                                 volume_scalars);
+}
+////////////////////////////////////////////////////////////////////////////////////
+
+} // namespace IO
+} // namespace CGAL
+
+#endif // CGAL_LCC_IO_VTK_H

Linear_cell_complex/include/CGAL/Linear_cell_complex_base.h

@@ -213,7 +213,7 @@ namespace CGAL {
       return *this;
     }
 
-    /** Create a vertex attribute.
+    /** Creates a vertex attribute.
      * @return a handle on the new attribute.
      */
     template<typename ...Args>
@@ -221,7 +221,7 @@ namespace CGAL {
     { return Base::template create_attribute<0>(args...); }
 
     /**
-     * Create a new dart associated with a handle through an attribute.
+     * Creates a new dart associated with a handle through an attribute.
      * @param ahandle the point handle to associated with the dart.
      * @return a Dart_descriptor on the new dart.
      */
@@ -232,7 +232,7 @@ namespace CGAL {
       return res;
     }
 
-    /** Create a new dart associated with a point.
+    /** Creates a new dart associated with a point.
      * @param apoint the point to associated with the dart.
      * @return a Dart_descriptor on the new dart.
      */
@@ -307,7 +307,7 @@ namespace CGAL {
       return point_of_vertex_attribute(this->template attribute<0>(adart));
     }
 
-    /** Test if the lcc is valid.
+    /** Tests if the lcc is valid.
      * A Linear_cell_complex is valid if it is a valid Combinatorial_map with
      * an attribute associated to each dart.
      * @return true iff the map is valid.
@@ -550,7 +550,7 @@ namespace CGAL {
       return res;
     }
 
-    /** Create a segment given 2 points.
+    /** Creates a segment given 2 points.
      * @param p0 the first point.
      * @param p1 the second point.
      * if closed==true, the edge has no 2-free dart.
@@ -564,7 +564,7 @@ namespace CGAL {
                           closed);
     }
 
-    /** Create a triangle given 3 points.
+    /** Creates a triangle given 3 points.
      * @param p0 the first point.
      * @param p1 the second point.
      * @param p2 the third point.
@@ -579,7 +579,7 @@ namespace CGAL {
                            create_vertex_attribute(p2));
     }
 
-    /** Create a quadrangle given 4 points.
+    /** Creates a quadrangle given 4 points.
      * @param p0 the first point.
      * @param p1 the second point.
      * @param p2 the third point.
@@ -598,7 +598,7 @@ namespace CGAL {
     }
 
 
-    /** Create a tetrahedron given 4 Vertex_attribute_descriptor.
+    /** Creates a tetrahedron given 4 Vertex_attribute_descriptor.
      * @param h0 the first vertex handle.
      * @param h1 the second vertex handle.
      * @param h2 the third vertex handle.
@@ -619,7 +619,7 @@ namespace CGAL {
       return this->make_combinatorial_tetrahedron(d1, d2, d3, d4);
     }
 
-    /** Create a tetrahedron given 4 points.
+    /** Creates a tetrahedron given 4 points.
      * @param p0 the first point.
      * @param p1 the second point.
      * @param p2 the third point.
@@ -638,7 +638,7 @@ namespace CGAL {
                               create_vertex_attribute(p3));
     }
 
-    /** Create an hexahedron given 8 Vertex_attribute_descriptor.
+    /** Creates an hexahedron given 8 Vertex_attribute_descriptor.
      *    (8 vertices, 12 edges and 6 facets)
      * \verbatim
      *       4----7
@@ -660,13 +660,13 @@ namespace CGAL {
      *         h0,h5 and to the facet (h0,h5,h6,h1).
      */
     Dart_descriptor make_hexahedron(Vertex_attribute_descriptor h0,
-                                Vertex_attribute_descriptor h1,
-                                Vertex_attribute_descriptor h2,
-                                Vertex_attribute_descriptor h3,
-                                Vertex_attribute_descriptor h4,
-                                Vertex_attribute_descriptor h5,
-                                Vertex_attribute_descriptor h6,
-                                Vertex_attribute_descriptor h7)
+                                    Vertex_attribute_descriptor h1,
+                                    Vertex_attribute_descriptor h2,
+                                    Vertex_attribute_descriptor h3,
+                                    Vertex_attribute_descriptor h4,
+                                    Vertex_attribute_descriptor h5,
+                                    Vertex_attribute_descriptor h6,
+                                    Vertex_attribute_descriptor h7)
     {
       Dart_descriptor d1 = make_quadrangle(h0, h5, h6, h1);
       Dart_descriptor d2 = make_quadrangle(h1, h6, h7, h2);
@@ -678,7 +678,7 @@ namespace CGAL {
       return this->make_combinatorial_hexahedron(d1, d2, d3, d4, d5, d6);
     }
 
-    /** Create an hexahedron given 8 points.
+    /** Creates an hexahedron given 8 points.
      * \verbatim
      *       4----7
      *      /|   /|
@@ -717,6 +717,133 @@ namespace CGAL {
                              create_vertex_attribute(p7));
     }
 
+    /** Creates a prism given 6 Vertex_attribute_descriptor.
+     *    (6 vertices, 9 edges and 5 facets)
+     * \verbatim
+     *      3---4
+     *      |\ /|
+     *      0-5-1
+     *       \|/
+     *        2
+     * \endverbatim
+     * @param h0 the first vertex handle.
+     * @param h1 the second vertex handle.
+     * @param h2 the third vertex handle.
+     * @param h3 the fourth vertex handle.
+     * @param h4 the fifth vertex handle.
+     * @param h5 the sixth vertex handle.
+     * @return the dart of the new prism incident to h0 and to
+     *         the facet (h0,h1,h2).
+     */
+     Dart_descriptor make_prism(Vertex_attribute_descriptor h0,
+                                Vertex_attribute_descriptor h1,
+                                Vertex_attribute_descriptor h2,
+                                Vertex_attribute_descriptor h3,
+                                Vertex_attribute_descriptor h4,
+                                Vertex_attribute_descriptor h5)
+    {
+      Dart_descriptor d1=make_triangle(h0, h1, h2);
+      Dart_descriptor d2=make_quadrangle(h1, h0, h3, h4);
+      Dart_descriptor d3=make_quadrangle(h2, h1, h4, h5);
+      Dart_descriptor d4=make_quadrangle(h0, h2, h5, h3);
+      Dart_descriptor d5=make_triangle(h4, h3, h5);
+
+      return make_combinatorial_prism(d1, d2, d3, d4, d5);
+    }
+
+    /** Creates a prism given 6 points.
+     * \verbatim
+     *      3---4
+     *      |\ /|
+     *      0-5-1
+     *       \|/
+     *        2
+     * \endverbatim
+     * @param p0 the first point.
+     * @param p1 the second point.
+     * @param p2 the third point.
+     * @param p3 the fourth point.
+     * @param p4 the fifth point.
+     * @param p5 the sixth point.
+     * @return the dart of the new prism incident to p0 and to
+     *         the facet (p0,p1,p2).
+     */
+     Dart_descriptor make_prism(const Point& p0,
+                                const Point& p1,
+                                const Point& p2,
+                                const Point& p3,
+                                const Point& p4,
+                                const Point& p5)
+    {
+      return make_prism(create_vertex_attribute(p0),
+                        create_vertex_attribute(p1),
+                        create_vertex_attribute(p2),
+                        create_vertex_attribute(p3),
+                        create_vertex_attribute(p4),
+                        create_vertex_attribute(p5));
+    }
+
+    /** Creates a pyramid given 5 Vertex_attribute_descriptor.
+     *    (5 vertices, 8 edges and 5 facets)
+     * \verbatim
+     *       4
+     *      /|\
+     *     0-|-1
+     *     | | |
+     *     3---2
+     * \endverbatim
+     * @param h0 the first vertex handle.
+     * @param h1 the second vertex handle.
+     * @param h2 the third vertex handle.
+     * @param h3 the fourth vertex handle.
+     * @param h4 the fifth vertex handle.
+     * @return the dart of the new pyramid incident to h0 and to
+     *         the facet (h0,h1,h2,h3).
+     */
+    Dart_descriptor make_pyramid(Vertex_attribute_descriptor h0,
+                                 Vertex_attribute_descriptor h1,
+                                 Vertex_attribute_descriptor h2,
+                                 Vertex_attribute_descriptor h3,
+                                 Vertex_attribute_descriptor h4)
+    {
+      Dart_descriptor d1=make_quadrangle(h0, h1, h2, h3);
+      Dart_descriptor d2=make_triangle(h1, h0, h4);
+      Dart_descriptor d3=make_triangle(h0, h3, h4);
+      Dart_descriptor d4=make_triangle(h3, h2, h4);
+      Dart_descriptor d5=make_triangle(h2, h1, h4);
+
+      return make_combinatorial_pyramid(d1, d2, d3, d4, d5);
+    }
+
+    /** Creates a pyramid given 5 points.
+     * \verbatim
+     *       4
+     *      /|\
+     *     0-|-1
+     *     | | |
+     *     3---2
+     * \endverbatim
+     * @param p0 the first point.
+     * @param p1 the second point.
+     * @param p2 the third point.
+     * @param p3 the fourth point.
+     * @param p4 the fifth point.
+     * @return the dart of the new pyramid incident to p0 and to
+     *         the facet (p0,p1,p2,p3).
+     */
+    Dart_descriptor make_pyramid(const Point& p0,
+                                 const Point& p1,
+                                 const Point& p2,
+                                 const Point& p3,
+                                 const Point& p4)
+    {
+      return make_pyramid(create_vertex_attribute(p0),
+                          create_vertex_attribute(p1),
+                          create_vertex_attribute(p2),
+                          create_vertex_attribute(p3),
+                          create_vertex_attribute(p4));
+    }
+
     /** Compute the barycenter of a given cell.
      * @param adart a dart incident to the cell.
      * @param adim the dimension of the cell.

Linear_cell_complex/include/CGAL/Linear_cell_complex_incremental_builder_3.h

@@ -261,7 +261,7 @@ public:
     prev_dart =lcc.null_descriptor;
   }
 
-  void add_vertex_to_facet(size_type i)
+  void add_vertex_to_facet(size_type i, std::vector<DH>* tabdarts = nullptr)
   {
     CGAL_assertion(i<vertex_map.size());
     // std::cout<<i<<"  "<<std::flush;
@@ -289,6 +289,7 @@ public:
     { first_dart=cur_dart; min_vertex=max_vertex=i; min_dart=cur_dart; }
 
     prev_dart=cur_dart;
+    if(tabdarts != nullptr) { tabdarts->push_back(cur_dart); }
   }
 
   // End of the facet. Return the first dart of this facet.
@@ -325,11 +326,12 @@ public:
     return first_dart;
   }
 
-  DH add_facet(std::initializer_list<size_type> l)
+  DH add_facet(std::initializer_list<size_type> l, std::vector<DH>* tabdarts = nullptr)
   {
+    if(tabdarts != nullptr) { tabdarts->reserve(tabdarts->size() + l.size()); }
     begin_facet();
     for (size_type i:l)
-    { add_vertex_to_facet(i); }
+    { add_vertex_to_facet(i, tabdarts); }
     return end_facet();
   }
 
@@ -404,5 +406,197 @@ private:
 
 } //namespace CGAL
 
+///////////////////////////////////////////////////////////////////////////////
+/* Create an hexahedron, given the indices of its vertices (in the following
+*  order), the vertex must already have been added in the incremental builder.
+*      3
+*     /|\
+*    0-|-2
+*     \|/
+*      1
+*/
+template<typename IncrementalBuilder>
+typename IncrementalBuilder::LCC::Dart_descriptor
+make_tetrahedron_with_builder(IncrementalBuilder& ib,
+                              std::size_t i0,
+                              std::size_t i1,
+                              std::size_t i2,
+                              std::size_t i3,
+                              std::vector<typename IncrementalBuilder::LCC::Dart_descriptor>*
+                              tabdarts=nullptr)
+{
+  ib.begin_surface();
+  ib.add_facet({i0,i1,i2}, tabdarts);
+  ib.add_facet({i1,i0,i3}, tabdarts);
+  ib.add_facet({i2,i1,i3}, tabdarts);
+  ib.add_facet({i0,i2,i3}, tabdarts);
+  return ib.end_surface();
+}
+///////////////////////////////////////////////////////////////////////////////
+/*      4
+ *     /|\
+ *    0-|-3
+ *    | | |
+ *    1---2
+ */
+template<typename IncrementalBuilder>
+typename IncrementalBuilder::LCC::Dart_descriptor
+ make_pyramid_with_builder(IncrementalBuilder& ib,
+                           std::size_t i0,
+                           std::size_t i1,
+                           std::size_t i2,
+                           std::size_t i3,
+                           std::size_t i4,
+                           std::vector<typename IncrementalBuilder::LCC::Dart_descriptor>*
+                           tabdarts=nullptr)
+{
+  ib.begin_surface();
+  ib.add_facet({i0,i1,i2,i3}, tabdarts);
+  ib.add_facet({i1,i0,i4}, tabdarts);
+  ib.add_facet({i2,i1,i4}, tabdarts);
+  ib.add_facet({i3,i2,i4}, tabdarts);
+  ib.add_facet({i0,i3,i4}, tabdarts);
+  return ib.end_surface();
+}
+///////////////////////////////////////////////////////////////////////////////
+/*      3
+ *     /|\
+ *    4---5
+ *    | | |
+ *    | 0 |
+ *    |/ \|
+ *    1---2
+ */
+template<typename IncrementalBuilder>
+typename IncrementalBuilder::LCC::Dart_descriptor
+ make_prism_with_builder(IncrementalBuilder& ib,
+                         std::size_t i0,
+                         std::size_t i1,
+                         std::size_t i2,
+                         std::size_t i3,
+                         std::size_t i4,
+                         std::size_t i5,
+                         std::vector<typename IncrementalBuilder::LCC::Dart_descriptor>*
+                         tabdarts=nullptr)
+{
+  ib.begin_surface();
+  ib.add_facet({i0,i1,i2}, tabdarts);
+  ib.add_facet({i1,i0,i3,i4}, tabdarts);
+  ib.add_facet({i2,i1,i4,i5}, tabdarts);
+  ib.add_facet({i0,i2,i5,i3}, tabdarts);
+  ib.add_facet({i5,i4,i3}, tabdarts);
+  return ib.end_surface();
+}
+///////////////////////////////////////////////////////////////////////////////
+/*      7----6
+ *     /|   /|
+ *    4----5 |
+ *    | 3--|-2
+ *    |/   |/
+ *    0----1
+ */
+template<typename IncrementalBuilder>
+typename IncrementalBuilder::LCC::Dart_descriptor
+ make_hexahedron_with_builder(IncrementalBuilder& ib,
+                              std::size_t i0,
+                              std::size_t i1,
+                              std::size_t i2,
+                              std::size_t i3,
+                              std::size_t i4,
+                              std::size_t i5,
+                              std::size_t i6,
+                              std::size_t i7,
+                              std::vector<typename IncrementalBuilder::LCC::Dart_descriptor>*
+                              tabdarts=nullptr)
+{
+  ib.begin_surface();
+  ib.add_facet({i0,i1,i2,i3}, tabdarts);
+  ib.add_facet({i1,i0,i4,i5}, tabdarts);
+  ib.add_facet({i2,i1,i5,i6}, tabdarts);
+  ib.add_facet({i3,i2,i6,i7}, tabdarts);
+  ib.add_facet({i0,i3,i7,i4}, tabdarts);
+  ib.add_facet({i7,i6,i5,i4}, tabdarts);
+  return ib.end_surface();
+}
+///////////////////////////////////////////////////////////////////////////////
+template<typename IncrementalBuilder>
+typename IncrementalBuilder::LCC::Dart_descriptor
+ make_pentagonal_prism_with_builder(IncrementalBuilder& ib,
+                                    std::size_t i0,
+                                    std::size_t i1,
+                                    std::size_t i2,
+                                    std::size_t i3,
+                                    std::size_t i4,
+                                    std::size_t i5,
+                                    std::size_t i6,
+                                    std::size_t i7,
+                                    std::size_t i8,
+                                    std::size_t i9,
+                                    std::vector<typename IncrementalBuilder::LCC::Dart_descriptor>*
+                                    tabdarts=nullptr)
+{
+  ib.begin_surface();
+  ib.add_facet({i0,i1,i2,i3,i4}, tabdarts);
+  ib.add_facet({i1,i0,i5,i6}, tabdarts);
+  ib.add_facet({i2,i1,i6,i7}, tabdarts);
+  ib.add_facet({i3,i2,i7,i8}, tabdarts);
+  ib.add_facet({i4,i3,i8,i9}, tabdarts);
+  ib.add_facet({i0,i4,i9,i5}, tabdarts);
+  ib.add_facet({i9,i8,i7,i6,i5}, tabdarts);
+  return ib.end_surface();
+}
+///////////////////////////////////////////////////////////////////////////////
+template<typename IncrementalBuilder>
+typename IncrementalBuilder::LCC::Dart_descriptor
+ make_hexagonal_prism_with_builder(IncrementalBuilder& ib,
+                                   std::size_t i0,
+                                   std::size_t i1,
+                                   std::size_t i2,
+                                   std::size_t i3,
+                                   std::size_t i4,
+                                   std::size_t i5,
+                                   std::size_t i6,
+                                   std::size_t i7,
+                                   std::size_t i8,
+                                   std::size_t i9,
+                                   std::size_t i10,
+                                   std::size_t i11,
+                                   std::vector<typename IncrementalBuilder::LCC::Dart_descriptor>*
+                                   tabdarts=nullptr)
+{
+  ib.begin_surface();
+  ib.add_facet({i0,i1,i2,i3,i4,i5}, tabdarts);
+  ib.add_facet({i1,i0,i6,i7}, tabdarts);
+  ib.add_facet({i2,i1,i7,i8}, tabdarts);
+  ib.add_facet({i3,i2,i8,i9}, tabdarts);
+  ib.add_facet({i4,i3,i9,i10}, tabdarts);
+  ib.add_facet({i5,i4,i10,i11}, tabdarts);
+  ib.add_facet({i0,i5,i11,i6}, tabdarts);
+  ib.add_facet({i11,i10,i9,i8,i7,i6}, tabdarts);
+  return ib.end_surface();
+}
+///////////////////////////////////////////////////////////////////////////////
+template<typename IncrementalBuilder>
+typename IncrementalBuilder::LCC::Dart_descriptor
+ make_generic_cell_with_builder(IncrementalBuilder& ib,
+                                const std::vector<std::size_t>& faces,
+                                std::vector<typename IncrementalBuilder::LCC::Dart_descriptor>*
+                                tabdarts=nullptr)
+{
+  ib.begin_surface();
+  std::size_t i=1, end; // Start to 1 because faces[0] is the number of faces
+  for(; i<faces.size(); )
+  {
+    end=i+1+faces[i]; // faces[i] is the number of vertices of the face; +i is the index of the end
+    ++i; // I prefer to increment i after its use!
+    ib.begin_facet();
+    for(; i<end; ++i)
+    { ib.add_vertex_to_facet(faces[i], tabdarts); }
+    ib.end_facet();
+  }
+  return ib.end_surface();
+}
+///////////////////////////////////////////////////////////////////////////////
+
 #endif // CGAL_LINEAR_CELL_COMPLEX_INCREMENTAL_BUILDER_3_H //
 // EOF //

Linear_cell_complex/test/Linear_cell_complex/CMakeLists.txt

@@ -15,6 +15,7 @@ create_single_source_cgal_program(Linear_cell_complex_3_test.cpp ${hfiles})
 create_single_source_cgal_program(Linear_cell_complex_4_test.cpp ${hfiles})
 create_single_source_cgal_program(Linear_cell_complex_copy_test.cpp ${hfiles})
 create_single_source_cgal_program(LCC_3_incremental_builder_test.cpp ${hfiles})
+create_single_source_cgal_program(Linear_cell_complex_vtk_io_test.cpp ${hfiles})
 
 # Same targets, defining USE_COMPACT_CONTAINER_WITH_INDEX to test index version
 add_executable(Linear_cell_complex_2_test_index Linear_cell_complex_2_test.cpp ${hfiles})

Linear_cell_complex/test/Linear_cell_complex/LCC_3_incremental_builder_test.cpp

@@ -5,104 +5,6 @@
 
 #include "Linear_cell_complex_3_test.h"
 
-///////////////////////////////////////////////////////////////////////////////
-/*     3
- *    /|\
- *   0-|-2
- *    \|/
- *     1
- */
-template<typename IncrementalBuilder>
-void make_tetrahedron_with_builder(IncrementalBuilder& ib,
-                                   std::size_t i0,
-                                   std::size_t i1,
-                                   std::size_t i2,
-                                   std::size_t i3)
-{
-  ib.begin_surface();
-  ib.add_facet({i0,i1,i2});
-  ib.add_facet({i1,i0,i3});
-  ib.add_facet({i2,i1,i3});
-  ib.add_facet({i0,i2,i3});
-  ib.end_surface();
-}
-///////////////////////////////////////////////////////////////////////////////
-/*      4
- *     /|\
- *    0-|-3
- *    | | |
- *    1---2
- */
-template<typename IncrementalBuilder>
-void make_pyramid_with_builder(IncrementalBuilder& ib,
-                               std::size_t i0,
-                               std::size_t i1,
-                               std::size_t i2,
-                               std::size_t i3,
-                               std::size_t i4)
-{
-  ib.begin_surface();
-  ib.add_facet({i0,i1,i2,i3});
-  ib.add_facet({i1,i0,i4});
-  ib.add_facet({i2,i1,i4});
-  ib.add_facet({i3,i2,i4});
-  ib.add_facet({i0,i3,i4});
-  ib.end_surface();
-}
-///////////////////////////////////////////////////////////////////////////////
-/*      3
- *     /|\
- *    4---5
- *    | | |
- *    | 0 |
- *    |/ \|
- *    1---2
- */
-template<typename IncrementalBuilder>
-void make_prism_with_builder(IncrementalBuilder& ib,
-                             std::size_t i0,
-                             std::size_t i1,
-                             std::size_t i2,
-                             std::size_t i3,
-                             std::size_t i4,
-                             std::size_t i5)
-{
-  ib.begin_surface();
-  ib.add_facet({i0,i1,i2});
-  ib.add_facet({i1,i0,i3,i4});
-  ib.add_facet({i2,i1,i4,i5});
-  ib.add_facet({i0,i2,i5,i3});
-  ib.add_facet({i5,i4,i3});
-  ib.end_surface();
-}
-///////////////////////////////////////////////////////////////////////////////
-/*      7----6
- *     /|   /|
- *    4----5 |
- *    | 3--|-2
- *    |/   |/
- *    0----1
- */
-template<typename IncrementalBuilder>
-void make_hexahedron_with_builder(IncrementalBuilder& ib,
-                                  std::size_t i0,
-                                  std::size_t i1,
-                                  std::size_t i2,
-                                  std::size_t i3,
-                                  std::size_t i4,
-                                  std::size_t i5,
-                                  std::size_t i6,
-                                  std::size_t i7)
-{
-  ib.begin_surface();
-  ib.add_facet({i0,i1,i2,i3});
-  ib.add_facet({i1,i0,i4,i5});
-  ib.add_facet({i2,i1,i5,i6});
-  ib.add_facet({i3,i2,i6,i7});
-  ib.add_facet({i0,i3,i7,i4});
-  ib.add_facet({i7,i6,i5,i4});
-  ib.end_surface();
-}
 ///////////////////////////////////////////////////////////////////////////////
 template<typename LCC>
 bool test_ib(const char* filename)

Linear_cell_complex/test/Linear_cell_complex/Linear_cell_complex_vtk_io_test.cpp

@@ -0,0 +1,202 @@
+#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
+#include <CGAL/Linear_cell_complex/IO/VTK.h>
+#include <cassert>
+#include <vector>
+#include <cstdlib>
+
+typedef CGAL::Linear_cell_complex_for_combinatorial_map<3, 3> LCC;
+
+bool test_file(const char* filename)
+{
+  LCC lcc1, lcc2;
+  std::vector<float>        vertex_scalars1, vertex_scalars2;
+  std::vector<std::size_t>  volume_scalars1, volume_scalars2;
+
+  bool res=CGAL::IO::read_VTK(filename, lcc1);
+  if(!res)
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error read_VTK in test_file"<<std::endl;
+    return false;
+  }
+
+  std::size_t nb_vertices=lcc1.number_of_vertex_attributes();
+  vertex_scalars1.resize(nb_vertices);
+  for(std::size_t i=0;i<nb_vertices;++i)
+  { vertex_scalars1[i]=static_cast<float>(i); }
+
+  std::size_t nb_volumes=0;
+  for(auto itvol=lcc1.one_dart_per_cell<3>().begin(),
+       itvolend=lcc1.one_dart_per_cell<3>().end(); itvol!=itvolend; ++itvol)
+  { ++nb_volumes; }
+
+  volume_scalars1.reserve(nb_volumes);
+  for(auto itvol=lcc1.one_dart_per_cell<3>().begin(),
+       itvolend=lcc1.one_dart_per_cell<3>().end(); itvol!=itvolend; ++itvol)
+  {
+    std::size_t nbv=lcc1.template one_dart_per_incident_cell<0,3>(itvol).size();
+    volume_scalars1.push_back(nbv);
+  }
+
+  res=CGAL::IO::write_VTK("output.vtk", lcc1,
+                          &vertex_scalars1, &volume_scalars1);
+  if(!res)
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error write_VTK in test_file"<<std::endl;
+    return false;
+  }
+
+  res=CGAL::IO::read_VTK("output.vtk", lcc2,
+                         &vertex_scalars2, &volume_scalars2);
+  if(!res)
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error read_VTK 2 in test_file"<<std::endl;
+    return false;
+  }
+
+  if(!lcc1.is_isomorphic_to(lcc2, false, true, true))
+  {
+    std::cout<<"LCC1: ";
+    lcc1.display_characteristics(std::cout)<<std::endl;
+    std::cout<<"LCC2: ";
+    lcc2.display_characteristics(std::cout)<<std::endl;
+    std::cerr<<"[ERROR] LCC_vtk_io_test error lcc1 and lcc2 are not isomorphic in test_file"<<std::endl;
+    res=false;
+  }
+  if(vertex_scalars1!=vertex_scalars2)
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error vertex_scalars1 and vertex_scalars2 are different in test_file"<<std::endl;
+    res=false;
+  }
+  if(volume_scalars1!=volume_scalars2)
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error volume_scalars1 and volume_scalars2 are different in test_file"<<std::endl;
+    res=false;
+  }
+  return res;
+}
+
+bool test_different_scalars()
+{
+  bool res=true;
+  LCC lcc;
+  std::vector<float>        vertex_scalars;
+  std::vector<std::size_t>  volume_scalars;
+
+  /// Read the last file generated by test_file("data/beam-with-mixed-cells.vtk")
+  /// i.e. beam-with-mixed-cells.vtk with point and cells scalars.
+  if(!CGAL::IO::read_VTK("output.vtk", lcc,
+                          &vertex_scalars, &volume_scalars) ||
+      vertex_scalars.size()!=719 || volume_scalars.size()!=615)
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error read_VTK in test_different_scalars"<<std::endl;
+    return false;
+  }
+
+  /// Test write with and without scalars
+  if(!CGAL::IO::write_VTK("output_vol.vtk", lcc, nullptr, &volume_scalars))
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error write_VTK 1 in test_different_scalars"<<std::endl;
+    return false;
+  }
+
+  if(!CGAL::IO::write_VTK("output_vertex.vtk", lcc, &vertex_scalars))
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error write_VTK 2 in test_different_scalars"<<std::endl;
+    return false;
+  }
+
+  if(!CGAL::IO::write_VTK("output_none.vtk", lcc))
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error write_VTK 3 in test_different_scalars"<<std::endl;
+    return false;
+  }
+
+  /// test read with only some scalars
+  if(!CGAL::IO::read_VTK("output.vtk", lcc, &vertex_scalars) ||
+      vertex_scalars.size()!=719)
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error read_VTK 2 in test_different_scalars"<<std::endl;
+    return false;
+  }
+
+  if(!CGAL::IO::read_VTK("output.vtk", lcc,
+                          nullptr, &volume_scalars) ||
+      volume_scalars.size()!=615)
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error read_VTK 3 in test_different_scalars"<<std::endl;
+    return false;
+  }
+
+  if(!CGAL::IO::read_VTK("output.vtk", lcc))
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error read_VTK 4 in test_different_scalars"<<std::endl;
+    return false;
+  }
+
+  /// test read all scalars when they are not in the file
+  if(!CGAL::IO::read_VTK("output_vertex.vtk", lcc, &vertex_scalars, &volume_scalars) ||
+      vertex_scalars.size()!=719 || volume_scalars.size()!=0)
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error read_VTK 5 in test_different_scalars"<<std::endl;
+    return false;
+  }
+
+  if(!CGAL::IO::read_VTK("output_vol.vtk", lcc, &vertex_scalars, &volume_scalars) ||
+      vertex_scalars.size()!=0 || volume_scalars.size()!=615)
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error read_VTK 6 in test_different_scalars"<<std::endl;
+    return false;
+  }
+
+  if(!CGAL::IO::read_VTK("output_none.vtk", lcc, &vertex_scalars, &volume_scalars) ||
+      vertex_scalars.size()!=0 || volume_scalars.size()!=0)
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error read_VTK 7 in test_different_scalars"<<std::endl;
+    return false;
+  }
+
+  return res;
+}
+
+int main()
+{
+  bool res=true;
+  if(!test_file("data/2tetra.vtk"))
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error for file data/2tetra.vtk"<<std::endl;
+    res=false;
+  }
+  if(!test_file("data/2hexa.vtk"))
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error for file data/2hexa.vtk"<<std::endl;
+    res=false;
+  }
+  if(!test_file("data/2prism.vtk"))
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error for file data/2prism.vtk"<<std::endl;
+    res=false;
+  }
+  if(!test_file("data/2pyramid.vtk"))
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error for file data/2pyramid.vtk"<<std::endl;
+    res=false;
+  }
+  if(!test_file("data/2generic_cell.vtk"))
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error for file data/2generic_cell.vtk"<<std::endl;
+    res=false;
+  }
+  if(!test_file("data/beam-with-mixed-cells.vtk"))
+  {
+    std::cerr<<"[ERROR] LCC_vtk_io_test error for file data/beam-with-mixed-cells.vtk"<<std::endl;
+    res=false;
+  }
+
+  if(!test_different_scalars())
+  { res=false; }
+
+  if(!res) { return EXIT_FAILURE; }
+
+  std::cout<<"[OK] all tests in Linear_cell_complex_vtk_io_test.cpp"<<std::endl;
+  return EXIT_SUCCESS;
+}