spelling corrections

Some spelling corrections (Directories starting with `A`)

AABB_tree/demo/AABB_tree/Scene.cpp

@@ -334,7 +334,7 @@ void Scene::compute_elements(int mode)
             pos_points.push_back(p.z());
         }
     }
-    //The Segements
+    //The segments
     {
         std::list<Segment>::iterator sit;
         for(sit = m_segments.begin(); sit != m_segments.end(); sit++)

AABB_tree/doc/AABB_tree/aabb_tree.txt

@@ -390,7 +390,7 @@ query and location of query in space.
   number of primitive data (greater than 2M faces in our experiments)
   however we noticed that it is not necessary (and sometimes even
   slower) to use all reference points when constructing the
-  KD-tree. In these cases we recommend to specify trough the function
+  KD-tree. In these cases we recommend to specify through the function
   ` AABB_tree::accelerate_distance_queries()` fewer reference
   points (typically not more than 100K) evenly distributed over the
   input primitives.

AABB_tree/include/CGAL/AABB_traits.h

@@ -213,7 +213,7 @@ public:
   /// Point query type.
   typedef typename GeomTraits::Point_3 Point_3;
 
-  /// additionnal types for the search tree, required by the RangeSearchTraits concept
+  /// additional types for the search tree, required by the RangeSearchTraits concept
   /// \bug This is not documented for now in the AABBTraits concept.
   typedef typename GeomTraits::Iso_cuboid_3 Iso_cuboid_3;
 
@@ -254,7 +254,7 @@ public:
    * @param beyond iterator on beyond element
    * @param bbox the bounding box of [first,beyond[
    *
-   * Sorts the range defined by [first,beyond[. Sort is achieved on bbox longuest
+   * Sorts the range defined by [first,beyond[. Sort is achieved on bbox longest
    * axis, using the comparison function `<dim>_less_than` (dim in {x,y,z})
    */
   class Split_primitives

AABB_tree/test/AABB_tree/aabb_any_all_benchmark.cpp

@@ -131,7 +131,7 @@ std::tuple<std::size_t, std::size_t, std::size_t, long> test(const char* name) {
         tu = std::make_tuple(intersect(lines.begin(), lines.end(), tree, counter),
                                intersect(rays.begin(), rays.end(), tree, counter),
                                intersect(segments.begin(), segments.end(), tree, counter),
-                               // cant use counter here
+                               // can't use counter here
                                0);
         std::get<3>(tu) = counter;
       }

Algebraic_foundations/include/CGAL/Coercion_traits.h

@@ -29,7 +29,7 @@
 
 #include <CGAL/tags.h>
 
-// Makro to define an additional operator for binary functors which takes
+// Macro to define an additional operator for binary functors which takes
 // two number types as parameters that are interoperable with the
 // number type
 #define CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR_WITH_RT( NT, Result_type  ) \

Algebraic_foundations/include/CGAL/Needs_parens_as_product.h

@@ -28,7 +28,7 @@ class Parens_as_product_tag {};
 
 /*! \ingroup NiX_io_parens
  *  \brief decides whether this number requires parentheses
- *  in case it appears within a produkt.
+ *  in case it appears within a product.
  */
 template <class NT>
 struct Needs_parens_as_product{
@@ -37,7 +37,7 @@ struct Needs_parens_as_product{
 
 /*! \ingroup NiX_io_parens
  *  \brief decides whether this number requires parentheses
- *  in case it appears within a produkt.
+ *  in case it appears within a product.
  */
 template <class NT>
 inline bool needs_parens_as_product(const NT& x){

Algebraic_foundations/include/CGAL/Test/_test_rational_traits.h

@@ -39,7 +39,7 @@ void test_rational_traits(){
     assert( Rational_traits().make_rational(std::make_pair(x,x)) == Rational(1));
     assert( Rational_traits().make_rational(std::make_pair(7,RT(2))) == x);
 
-    // gloabal function to_rational
+    // global function to_rational
     x = CGAL::to_rational<Rational>(3.5);
     assert( x == Rational(7)/Rational(2));
 }

Algebraic_foundations/include/CGAL/Test/_test_real_embeddable.h

@@ -84,7 +84,7 @@ namespace CGAL {
             assert(to_interval(Type(42)).first > 41.99);
             assert(to_interval(Type(42)).second < 42.01);
 
-            // test neagtive numbers as well to catch obvious sign
+            // test negative numbers as well to catch obvious sign
             // errors
             assert( -42.0 >= to_interval( -Type(42) ).first );
             assert( -42.0 <= to_interval( -Type(42) ).second );

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Algebraic_curve_kernel_2.h

@@ -840,7 +840,7 @@ public:
         } else {
           // more work! We should not assume that each
           // roots[i].first has f or g as defining polynomial, because
-          // the representation might have been simplifed
+          // the representation might have been simplified
 
           // Here's the safe way: Take the simpler of the curves
           // (but the one without vertical component!)
@@ -922,7 +922,7 @@ public:
      *
      * \attention{This method returns the y-coordinate in isolating interval
      * representation. Calculating such a representation is usually a time-
-     * consuming taks, since it is against the "y-per-x"-view that we take
+     * consuming task, since it is against the "y-per-x"-view that we take
      * in our kernel. Therefore, it is recommended, if possible,
      *  to use the functors
      * \c Approximate_absolute_y_2 and \c Approximate_relative_y_2 that

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Algebraic_real_quadratic_refinement_rep_bfi.h

@@ -494,7 +494,7 @@ public:
         }
     }
 };
-} // namepace internal
+} // namespace internal
 
 } //namespace CGAL
 

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Algebraic_real_rep.h

@@ -38,7 +38,7 @@ namespace internal {
 // sign_at_low_ = polynomial_.evaluate(low_)
 // x is the only root of polynomial_ in the open interval ]low_,high_[
 // low_ != x != high
-// ******************* EXEPTION *******************
+// ******************* EXCEPTION *******************
 // x is rational: in this case low=high=x
 
 template< class Coefficient_, class Rational_>
@@ -135,7 +135,7 @@ protected:
 
         // interval_option left out
 
-        // trys to set rational if degree is 1
+        // tries to set rational if degree is 1
         typedef typename CGAL::Coercion_traits< Coefficient, Rational >::Type RET;
         set_rational(RET());
     }

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Algebraic_real_rep_bfi.h

@@ -52,7 +52,7 @@ namespace internal {
 // sign_at_low_ = polynomial_.evaluate(low_)
 // x is the only root of polynomial_ in the open interval ]low_,high_[
 // low_ != x != high
-// ******************* EXEPTION *******************
+// ******************* EXCEPTION *******************
 // x is rational: in this case low=high=x
 
 

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Bitstream_descartes.h

@@ -1217,7 +1217,7 @@ public:
    *
    * The polynomial \c f must have exactly \c m real roots, counted without
    * multiplicity, and the degree of <tt>gcd(f,f')</tt> must be \c k. In this
-   * case, the constructor either isolates the real roots of \c f sucessfully
+   * case, the constructor either isolates the real roots of \c f successfully
    * or a Non_generic_position_exception is thrown. Such an exception
    * certainly occurs if \c f has more than one multiple real root. If \c f
    * has at most one multiple root over the complex numbers, the roots are

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Bitstream_descartes_E08_tree.h

@@ -443,7 +443,7 @@ private:
     Integer_vector coeff_; // wrt [lower_, upper_], approximate
     int min_var_, max_var_;
     bool coeff_update_delayed_;
-    // "state data" (copied en bloc by .copy_state_from())
+    // "state data" (copied en block by .copy_state_from())
     long subdepth_bound_, subdepth_current_;
     long log_eps_;   // $q - p$
     long log_C_eps_; // $q - p + 4n$

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Bitstream_descartes_rndl_tree.h

@@ -531,7 +531,7 @@ private:
     long log_bdry_den_;
     Integer_vector coeff_; // wrt [lower_, upper_], approximate
     int min_var_, max_var_;
-    // "state data" (copied en bloc by .copy_state_from())
+    // "state data" (copied en block by .copy_state_from())
     long subdiv_tries_, subdiv_fails_;
     long recdepth_;
     long log_sep_, delta_log_sep_, log_eps_, log_C_eps_;
@@ -736,7 +736,7 @@ public:
     <b>Supplying a traits class</b>
 
     This class is actually a class template.
-    To use it, you need to instanciate it with a traits class
+    To use it, you need to instantiate it with a traits class
     that defines the following three types and the various
     functors on them listed below.
      - \c Coefficient: The type of coefficients supplied
@@ -749,7 +749,7 @@ public:
      - \c Bound:  \c lower() and \c upper() return
        interval boundaries in this type.  Must be \c Assignable.
        The canonical choice is \c NiX::Exact_float_number<Integer>.
-       If you never instanciate \c lower() and \c upper()
+       If you never instantiate \c lower() and \c upper()
        (maybe use \c boundaries() instead), you might be lucky
        and get away with typedef'ing this to \c void.
 
@@ -772,7 +772,7 @@ public:
      - \c Lower_bound_log2_abs: A \c UnaryFunction with signature
        <tt>long l = Lower_bound_log2_abs()(Coefficient x)</tt>.
        The result \c l must be a lower bound to log<sub>2</sub>(|<i>x</i>|).
-       If \c Coefficient posesses \c NiX::NT_traits::Floor_log2_abs,
+       If \c Coefficient possesses \c NiX::NT_traits::Floor_log2_abs,
        you can simply use that.
      - \c lower_bound_log2_abs_object(): A \c const member function
        taking no arguments and returning a function object

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_analysis_2.h

@@ -481,7 +481,7 @@ public:
      * \c internal::Zero_resultant_exception<Polynomial_2>,
      * instead of performing a shear.
      *
-     * \Todo Currently the defualt strategy has been changed to SHEAR_STRATEGY
+     * \Todo Currently the default strategy has been changed to SHEAR_STRATEGY
      * because there exist a problem if vertical asymtotes are present at
      * the rational x-coordinate.
      */
@@ -1167,7 +1167,7 @@ public:
 
     /*!
      * \brief returns the status line for the interval
-     * preceeding the <tt>i</tt>th event
+     * preceding the <tt>i</tt>th event
      *
      * Returns a status line for a reference x-coordinate of the <tt>i</tt>th
      * interval of the curve. If called multiple times for the same <tt>i</tt>,
@@ -1827,7 +1827,7 @@ private:
                    static_cast<size_type>(lcoeff_roots.size()) &&
                    event_values[i]==lcoeff_roots[curr_lcoeff_index]) {
                     // We have a root of the leading coefficient
-                    // of the primitve polynomial
+                    // of the primitive polynomial
                     curr_event.index_of_prim_lcoeff_root = curr_lcoeff_index;
                     curr_event.mult_of_prim_lcoeff_root
                         = lcoeff_mults[curr_lcoeff_index];
@@ -1867,7 +1867,7 @@ private:
                    static_cast<size_type>(lcoeff_roots.size()) &&
                    event_values[i]==lcoeff_roots[curr_lcoeff_index]) {
                     // We have a root of the leading coefficient
-                    // of the primitve polynomial
+                    // of the primitive polynomial
                     curr_event.index_of_prim_lcoeff_root = curr_lcoeff_index;
                     curr_event.mult_of_prim_lcoeff_root
                         = lcoeff_mults[curr_lcoeff_index];

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Descartes.h

@@ -328,7 +328,7 @@ private:
             return false;
         return (P[0] != Coeff__(0) && P.evaluate(Coeff__(1)) != Coeff__(0));
     }
-    //! Descartes algoritm to determine isolating intervals for the roots
+    //! Descartes algorithm to determine isolating intervals for the roots
     //! lying in the interval (0,1).
     // The parameters $(i,D)$ describe the interval $(i/2^D, (i+1)/2^D)$.
     // Here $0\leq i < 2^D$.
@@ -389,7 +389,7 @@ private:
     }
 
 
-    //! Strong Descartes algoritm to determine isolating intervals for the
+    //! Strong Descartes algorithm to determine isolating intervals for the
     //! roots lying in the interval (0,1), where the first
     //! derivative have no sign change. \pre $P$ has only one root in the
     //! interval given by $(i,D)$.

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Event_line_builder.h

@@ -118,7 +118,7 @@ public:
      * curve.
      *
      * Additionally, the \c id of the event line to be created has to be
-     * specfied, and
+     * specified, and
      * the number of arcs that are entering from the left and leaving to the
      * right are needed. Furthermore, the flag \c root_of_resultant tells
      * whether \c alpha is a root of the resultant of the specified curve, and
@@ -314,7 +314,7 @@ protected:
      *
      * If the first elements in the sequence are known to be zero,
      * \c first_elements_zero can be set accordingly. The zero test is then
-     * ommitted for that leading elements.
+     * omitted for that leading elements.
      */
     template<typename InputIterator>
     std::pair<int,int> compute_mk(Algebraic_real_1 alpha,

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Float_traits.h

@@ -41,7 +41,7 @@ namespace CGAL {
 
 namespace internal {
 
-// Don't define default, results in more convinient compiler messages
+// Don't define default, results in more convenient compiler messages
 template< class Type > class Float_traits;
 // {
 // public:

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Real_embeddable_extension.h

@@ -54,7 +54,7 @@ namespace internal {
 // TODO: Implement array in source code file
 //    extern const signed char floor_log2_4bit[16]; // see src/floor_log2_4bit.C
 
-// Don't define default, results in more convinient compiler messages
+// Don't define default, results in more convenient compiler messages
 template< class Type > class Real_embeddable_extension;
 // {
 // public:

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Status_line_CA_1.h

@@ -323,7 +323,7 @@ public:
     }
 
     /*!\brief
-     * constructs from a given represenation
+     * constructs from a given representation
      */
     Status_line_CA_1(Rep rep) :
         Base(rep) {

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Status_line_CPA_1.h

@@ -208,7 +208,7 @@ public:
 
 protected:
     /*!\brief
-     * constructs from a given represenation
+     * constructs from a given representation
      */
     Status_line_CPA_1(Rep rep) :
         Base(rep) {

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Xy_coordinate_2.h

@@ -233,7 +233,7 @@ public:
     }
 
     /*!\brief
-     * constructs a point from a given represenation
+     * constructs a point from a given representation
      */
     Xy_coordinate_2(Rep rep) :
         Base(rep) {
@@ -254,7 +254,7 @@ public:
     /*!
      * \brief y-coordinate of this point
      *
-     * Note: In general, this method results in a extremly large polynomial
+     * Note: In general, this method results in a extremely large polynomial
      * for the y-coordinate. It is recommended to use it carefully,
      * and using get_approximation_y() instead whenever approximations suffice.
      */

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/algebraic_curve_kernel_2_tools.h

@@ -157,7 +157,7 @@ template<typename AlgebraicKernel_1> typename AlgebraicKernel_1::Bound
 }
 
 /*!
- * \brief finds a Rational value rightt of an Algebraic real alpha
+ * \brief finds a Rational value right of an Algebraic real alpha
  */
 template<typename AlgebraicKernel_1> typename AlgebraicKernel_1::Bound
   bound_right_of(const AlgebraicKernel_1* kernel,

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/flags.h

@@ -87,10 +87,10 @@
  * (i.e., vertical cusps, isolated points on arcs), and usual regular points.
  * The candidate point on each status line can be checked for being singular
  * using this flag. This gives additional information but increases
- * compuation time
+ * computation time
  *
  * WARNING: Currently, the status line does not store the additional
- * information whether a point is singluar or not.
+ * information whether a point is singular or not.
  * Therefore, there is currently no reasons to set this flag. It is still
  * contained for possible further extension of the status line.
  */
@@ -171,7 +171,7 @@
 /**
  * The algorithm can also handle non-y-regular curves without shearing,
  * in case that the resultant multiplicity at vertical asymptotes is one.
- * This special treatement can be switched off by setting this flag.
+ * This special treatment can be switched off by setting this flag.
  * It is not recommended to do this because of efficiency
  */
 #ifndef CGAL_ACK_SHEAR_ALL_NOT_Y_REGULAR_CURVES

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d_1.h

@@ -111,7 +111,7 @@ public:
 
       void operator()( Type& t, int rel_prec ) const {
         // If t is zero, we can refine the interval to
-        //  infinite precission
+        //  infinite precision
         if( CGAL::is_zero( t ) ) {
           t = Type(0);
         } else {

Algebraic_kernel_d/include/CGAL/RS/algebraic_1.h

@@ -34,7 +34,7 @@ namespace RS_AK1{
 //      Refiner_()(const Polynomial_&,Bound_&,Bound_&,int p);
 //
 // The fourth template argument is a comparator, a function object that
-// receives the polynomials and bounds defining two algebraic numbres and
+// receives the polynomials and bounds defining two algebraic numbers and
 // just compares them, returning a CGAL::Comparison_result. The signature
 // of a comparator must be:
 //      CGAL::Comparison_result

Algebraic_kernel_for_spheres/include/CGAL/Algebraic_kernel_for_spheres/internal_functions_on_roots_and_polynomials_2_3.h

@@ -46,7 +46,7 @@ namespace CGAL {
     typedef typename AK::Polynomial_1_3 Polynomial_1_3;
     // The degenerated cases are 2 tangent spheres
     // os 2 non-intersecting spheres
-    // beacause we cannot have infinitely many solutions
+    // because we cannot have infinitely many solutions
     if(e1 == e2) {
       if(tangent<AK>(e1,e3)) {
         Polynomial_1_3 p = plane_from_2_spheres<AK>(e1,e3);

Alpha_shapes_2/doc/Alpha_shapes_2/CGAL/Alpha_shape_2.h

@@ -47,7 +47,7 @@ how to convert from the camouflaged `CGAL::Point_3` to the two-dimensional point
 of `CGAL::Simple_cartesian<NT>`. In this case, a partial specialization of `Cartesian_converter`
 must be provided by the user. An example of such specialization is given in the example
 \ref Alpha_shapes_2/ex_alpha_projection_traits.cpp "ex_alpha_projection_traits.cpp".
-<li>The tag `ExactAlphaComparisonTag` cannot be used in conjonction with periodic triangulations.
+<li>The tag `ExactAlphaComparisonTag` cannot be used in conjunction with periodic triangulations.
 When the tag `ExactAlphaComparisonTag` is set to \link Tag_true `Tag_true`\endlink,
 the evaluations of predicates such as `Side_of_oriented_circle_2` are done lazily.
 Consequently, the predicates store pointers to the geometrical positions of the

Alpha_shapes_2/include/CGAL/Alpha_shape_2.h

@@ -57,7 +57,7 @@ public:
   typedef typename Dt::Geom_traits Gt;
   typedef typename Dt::Triangulation_data_structure Tds;
 
-  // The Exact Comparison Tag cannot be used in conjonction with periodic triangulations
+  // The Exact Comparison Tag cannot be used in conjunction with periodic triangulations
   // because the periodic triangulations' point() function returns a temporary
   // value while the lazy predicate evaluations that are used when the Exact tag
   // is set to true rely on a permanent and safe access to the points.
@@ -432,7 +432,7 @@ public:
 private:
 
   // the dynamic version is not yet implemented
-  // desactivate the triangulation member functions
+  // deactivate the triangulation member functions
   Vertex_handle insert(const Point& p);
   // Inserts point `p' in the alpha shape and returns the
   // corresponding vertex of the underlying Delaunay triangulation.
@@ -744,7 +744,7 @@ private:
   //---------------------------------------------------------------------
 
 private:
-  // prevent default copy constructor and default assigment
+  // prevent default copy constructor and default assignment
 
   Alpha_shape_2(const Alpha_shape_2& A);
 
@@ -1435,7 +1435,7 @@ template < class Dt, class EACT >
 typename Alpha_shape_2<Dt,EACT>::Type_of_alpha
 Alpha_shape_2<Dt,EACT>::find_alpha_solid() const
 {
-  // compute the minumum alpha such that all data points
+  // compute the minimum alpha such that all data points
   // are either on the boundary or in the interior
   // not necessarily connected
   // starting point for searching

Alpha_shapes_2/include/CGAL/Alpha_shapes_2/internal/Lazy_alpha_nt_2.h

@@ -144,7 +144,7 @@ class Lazy_alpha_nt_2
   typedef typename Types::Exact_point                                      Exact_point;
   typedef typename Types::Input_point                                      Input_point;
 
-  //Convertion functions
+  //Conversion functions
   Approx_point to_approx(const Input_point& wp) const
   {
     // The traits class' Point_2 must be convertible using the Cartesian converter

Alpha_shapes_3/TODO

@@ -1,4 +1,4 @@
-- deprectate the following function 
+- deprecate the following function 
 Classification_type   	  A.classify ( Cell_handle f, int i, FT alpha = get_alpha())
 because it is ambiguous with
 Classification_type   	  A.classify ( Cell_handle f, FT alpha = get_alpha())
@@ -12,7 +12,7 @@ when alpha is given as an int.
   Alpha_shape_3(Dt& dt, bool swap=true, NT alpha = 0, Mode m = REGULARIZED)
   The triangulation is swapped  if swap=true and copied otherwise.
 
-- test the  taking into account of paramater alpha in functions
+- test the taking into account of parameter alpha in functions
 get_alpha_shape_edges
 get_alpha_shape_facets
 get_alpha_shape_vertices

Alpha_shapes_3/demo/Alpha_shapes_3/CMakeLists.txt

@@ -27,7 +27,7 @@ if(CGAL_Qt5_FOUND AND Qt5_FOUND)
   # include(${QT_USE_FILE})
   include_directories(BEFORE ./)
 
-  # ui file, created wih Qt Designer
+  # ui file, created with Qt Designer
   qt5_wrap_ui(uis MainWindow.ui)
 
   # qrc files (resources files, that contain icons, at least)

Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Alpha_shape_3.h

@@ -44,7 +44,7 @@ the basic `Cartesian_converter`, for example when a custom point is used.
 In this case, a partial specialization of `Cartesian_converter`
 must be provided by the user. An example of such specialization is given in the
 two-dimensional Alpha Shapes example \ref Alpha_shapes_2/ex_alpha_projection_traits.cpp "ex_alpha_projection_traits.cpp".
-<li>The tag `ExactAlphaComparisonTag` cannot be used in conjonction with periodic triangulations.
+<li>The tag `ExactAlphaComparisonTag` cannot be used in conjunction with periodic triangulations.
 When the tag `ExactAlphaComparisonTag` is set to \link Tag_true `Tag_true`\endlink,
 the evaluations of predicates such as `Side_of_oriented_sphere_3` are done lazily.
 Consequently, the predicates store pointers to the geometrical positions of the

Alpha_shapes_3/examples/Alpha_shapes_3/ex_alpha_shapes_with_fast_location_3.cpp

@@ -37,7 +37,7 @@ int main()
 
   // compute alpha shape
   Alpha_shape_3 as(dt);
-  std::cout << "Alpha shape computed in REGULARIZED mode by defaut."
+  std::cout << "Alpha shape computed in REGULARIZED mode by default."
             << std::endl;
 
    // find optimal alpha values

Alpha_shapes_3/include/CGAL/Alpha_shape_3.h

@@ -69,7 +69,7 @@ class Alpha_shape_3 : public Dt
   // or INTERIOR with respect to the alpha shape.
   // In GENERAL mode a $k$ simplex is REGULAR if it is on the boundary
   // of the alpha_complex and belongs to a $k+1$ simplex in the complex
-  // and it is SINGULAR simplex if it is  a boundary simplex tht is not
+  // and it is SINGULAR simplex if it is a boundary simplex that is not
   // included in a $k+1$ simplex of the complex.
 
   // In REGULARIZED mode each k-dimensional simplex of the triangulation
@@ -93,7 +93,7 @@ public:
   typedef typename Dt::Geom_traits                  Gt;
   typedef typename Dt::Triangulation_data_structure Tds;
 
-  // The Exact Comparison Tag cannot be used in conjonction with periodic triangulations
+  // The Exact Comparison Tag cannot be used in conjunction with periodic triangulations
   // because the periodic triangulations' point() function returns a temporary
   // value while the lazy predicate evaluations that are used when the Exact tag
   // is set to true rely on a permanent and safe access to the points.
@@ -422,7 +422,7 @@ public:
 private:
 
   // the dynamic version is not yet implemented
-  // desactivate the tetrahedralization member functions
+  // deactivate the tetrahedralization member functions
   void insert(const Point& /*p*/) {}
   // Inserts point `p' in the alpha shape and returns the
   // corresponding vertex of the underlying Delaunay tetrahedralization.
@@ -735,7 +735,7 @@ public:
   // (2) the nb of solid components is equal or less than nb_component
 
   NT find_alpha_solid() const;
-  // compute the minumum alpha such that all data points
+  // compute the minimum alpha such that all data points
   // are either on the boundary or in the interior
   // not necessarily connected
   // starting point for searching
@@ -776,7 +776,7 @@ private:
   //---------------------------------------------------------------------
 
 private:
-  // prevent default copy constructor and default assigment
+  // prevent default copy constructor and default assignment
   Alpha_shape_3(const Alpha_shape_3&);
   void operator=(const Alpha_shape_3&);
 
@@ -1292,7 +1292,7 @@ Alpha_shape_3<Dt,EACT>::initialize_alpha_vertex_maps(bool reinitialize)
                      back_inserter(incidents));
       typename std::list<Cell_handle>::iterator chit=incidents.begin();
       if (is_infinite(*chit)) as->set_is_on_chull(true);
-      while (is_infinite(*chit)) ++chit; //skip infinte cells
+      while (is_infinite(*chit)) ++chit; //skip infinite cells
       alpha = (*chit)->get_alpha();
       as->set_alpha_mid(alpha);
       as->set_alpha_max(alpha);
@@ -1330,7 +1330,7 @@ Alpha_shape_3<Dt,EACT>::initialize_alpha_vertex_maps(bool reinitialize)
       incident_cells(static_cast<Vertex_handle>(vit),
                      back_inserter(incidents));
       typename std::list<Cell_handle>::iterator chit=incidents.begin();
-      while (is_infinite(*chit)) ++chit; //skip infinte cells
+      while (is_infinite(*chit)) ++chit; //skip infinite cells
       alpha = (*chit)->get_alpha();
       as->set_alpha_mid(alpha);
       for( ; chit != incidents.end(); ++chit) {
@@ -1835,7 +1835,7 @@ Alpha_shape_3<Dt,EACT>::find_optimal_alpha(size_type nb_components) const
 template <class Dt,class EACT>
 typename Alpha_shape_3<Dt,EACT>::NT
 Alpha_shape_3<Dt,EACT>::find_alpha_solid() const
-  // compute the minumum alpha such that all data points
+  // compute the minimum alpha such that all data points
   // are either on the boundary or in the interior
   // not necessarily connected
 {

Alpha_shapes_3/include/CGAL/Alpha_shapes_3/internal/Lazy_alpha_nt_3.h

@@ -135,7 +135,7 @@ class Lazy_alpha_nt_3{
   typedef typename Types::Approx_point                                                          Approx_point;
   typedef typename Types::Exact_point                                                           Exact_point;
   typedef typename Types::Input_point                                                           Input_point;
-//Convertion functions
+//Conversion functions
   Approx_point to_approx(const Input_point& wp) const
   {
     // The traits class' Point_3 must be convertible using the Cartesian converter

Alpha_shapes_3/include/CGAL/Fixed_alpha_shape_3.h

@@ -116,7 +116,7 @@ class Fixed_alpha_shape_3 : public Dt
   // or INTERIOR with respect to the alpha shape.
   // A $k$ simplex is REGULAR if it is on the boundary
   // of the alpha_complex and belongs to a $k+1$ simplex in the complex
-  // and it is SINGULAR simplex if it is  a boundary simplex tht is not
+  // and it is SINGULAR simplex if it is a boundary simplex that is not
   // included in a $k+1$ simplex of the complex.
 
   // Roughly, the Fixed_alpha_shape data structure computes and stores,
@@ -280,7 +280,7 @@ public:
       }
     }
     // Erase from edge_status_map, edges that will disappear:
-    // they are not on the boudary of the hole
+    // they are not on the boundary of the hole
     std::set<Edge,Compare_edge> hole_edges;
     std::pair<typename std::set<Edge,Compare_edge>::iterator,bool> it_hedge_and_not_already_seen;
     for (typename std::vector<Cell_handle>::iterator it=cells.begin();it!=cells.end();++it){
@@ -598,7 +598,7 @@ private :
   }
 
 private :
-  // prevent default copy constructor and default assigment
+  // prevent default copy constructor and default assignment
   Fixed_alpha_shape_3(const Fixed_alpha_shape_3&);
   void operator=(const Fixed_alpha_shape_3&);
 

Alpha_shapes_3/test/Alpha_shapes_3/include/CGAL/_test_cls_alpha_shape_3.h

@@ -152,7 +152,7 @@ _test_cls_alpha_shape_3()
   test_filtration(a1,verbose);
 
   std::cout << std::endl;
-  std::cout << "test additionnal creators and set mode" << std::endl;
+  std::cout << "test additional creators and set mode" << std::endl;
   Triangulation dt2( L.begin(), L.end());
   Alpha_shape_3 a2(dt2, 0,  Alpha_shape_3::REGULARIZED);
   if(verbose) show_alpha_values(a2);
@@ -193,10 +193,10 @@ _test_cls_alpha_shape_3()
   Alpha_iterator previous = opt; --previous;
   if(verbose) {
     std::cerr << " optimal  de 1 " << *opt
-              << "nb of componants " << a1.number_of_solid_components(*opt)
+              << "nb of components " << a1.number_of_solid_components(*opt)
               << std::endl;
     std::cerr << " previous        " << *previous
-              << "nb of componants "
+              << "nb of components "
               << a1.number_of_solid_components(*previous) << std::endl;
   }
   assert (a1.number_of_solid_components(*opt) == 1);

Alpha_wrap_3/doc/Alpha_wrap_3/alpha_wrap_3.txt

@@ -332,7 +332,7 @@ and values of alpha smaller than the size of the holes.
 Two-sided wrap.
 (Left) Wrapping a Bunny in 2D, with decreasing values for alpha.
 (Right) Wrapping a defect-laden Bunny in 3D. The rightmost column depicts a clipped visualization
-of the inside. When alpha is small enough with respect the diamater of the holes, the algorithm generates a two-sided wrap.
+of the inside. When alpha is small enough with respect the diameter of the holes, the algorithm generates a two-sided wrap.
 \cgalFigureCaptionEnd
 
 \section aw3_performance Performance

Alpha_wrap_3/include/CGAL/Alpha_wrap_3/internal/Alpha_wrap_3.h

@@ -192,7 +192,7 @@ public:
       m_queue(4096)
   {
     // Due to the Steiner point computation being a dichotomy, the algorithm is inherently inexact
-    // and passing exact kernels is explicitely disabled to ensure no misunderstanding.
+    // and passing exact kernels is explicitly disabled to ensure no misunderstanding.
     CGAL_static_assertion((std::is_floating_point<FT>::value));
   }
 
@@ -944,7 +944,7 @@ private:
       return IRRELEVANT;
     }
 
-    // push if facet is connected to artifical vertices
+    // push if facet is connected to artificial vertices
     for(int i=0; i<3; ++i)
     {
       const Vertex_handle vh = ch->vertex(Dt::vertex_triple_index(id, i));
@@ -1049,7 +1049,7 @@ private:
       check_queue_sanity();
 #endif
 
-      // const& to something that will be poped, but safe as `ch` && `id` are extracted before the pop
+      // const& to something that will be popped, but safe as `ch` && `id` are extracted before the pop
       const Gate& gate = m_queue.top();
       const Facet& f = gate.facet();
       CGAL_precondition(!m_dt.is_infinite(f));

Alpha_wrap_3/include/CGAL/Alpha_wrap_3/internal/splitting_helper.h

@@ -167,7 +167,7 @@ struct AABB_tree_splitter_traits
   // The input face ID serves when traversing the tree, to avoid doing the same intersection()
   // on the same datum seen from different primitives.
   //
-  // Technically, FPM could type-erase the mesh and the VPM, as it currently forces all independant
+  // Technically, FPM could type-erase the mesh and the VPM, as it currently forces all independent
   // inputs to have the same types. This is not such much of an issue for the mesh type,
   // but it can be annoying for the VPM type.
   using ID = std::pair<std::size_t /*primitive ID*/, std::size_t /*input face ID*/>;

Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Apollonius_graph_2_impl.h

@@ -1960,7 +1960,7 @@ template<class Gt, class Agds, class LTag>
 void
 Apollonius_graph_2<Gt,Agds,LTag>::file_output(std::ostream& os) const
 {
-  // ouput to a file
+  // output to a file
   size_type n = this->_tds.number_of_vertices();
   size_type m = this->_tds.number_of_full_dim_faces();
 

Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Apollonius_graph_hierarchy_2_impl.h

@@ -54,7 +54,7 @@ Apollonius_graph_hierarchy_2
 }
 
 
-//Assignement
+//Assignment
 template<class Gt, class Agds, class LTag>
 Apollonius_graph_hierarchy_2<Gt,Agds,LTag> &
 Apollonius_graph_hierarchy_2<Gt,Agds,LTag>::

Apollonius_graph_2/include/CGAL/Apollonius_graph_2/uncertain/Uncertain_vertex_conflict_2.h

@@ -268,7 +268,7 @@ private:
     {
       // NOTE:***************************************
       // * the perturb boolean variable is not used
-      // * for consistancy with Menelaos
+      // * for consistency with Menelaos
       // NOTE:***************************************
       RT x2 = p2.x() - p1.x();
       RT y2 = p2.y() - p1.y();
@@ -298,10 +298,10 @@ private:
           if ( is_indeterminate(s_xw2q) ) { return s_xw2q; }
           power_test = o12 * s_xw2q;
 
-          // this results is consistant with Menelaos
+          // this results is consistent with Menelaos
           if (power_test != ZERO) { return -power_test; }
 
-            // this result is consistant with the perturb on off idea
+            // this result is consistent with the perturb on off idea
             //if (power_test != ZERO || ! perturb) return -power_test;
 
           o1q = CGAL::sign(xq);
@@ -313,10 +313,10 @@ private:
           if ( is_indeterminate(s_yw2q) ) { return s_yw2q; }
           power_test = o12 * s_yw2q;
 
-          // this results is consistant with Menelaos
+          // this results is consistent with Menelaos
           if (power_test != ZERO) { return -power_test; }
 
-          // this result is consistant with the perturb on off idea
+          // this result is consistent with the perturb on off idea
           //if (power_test != ZERO || ! perturb) return -power_test;
 
           o1q = CGAL::sign(yq);
@@ -348,11 +348,11 @@ private:
                    - CGAL::square(xy2q));
       if ( is_indeterminate(radInt) ) { return radInt; }
 
-      // radical intersection degerate
+      // radical intersection degenerate
       if (radInt == ZERO) {
         CGAL_assertion (radSide != ZERO);
 
-        // this result is consistant with the perturb on off idea
+        // this result is consistent with the perturb on off idea
         //if (! perturb) return (radSide == orient) ? ZERO : orient;
 
         RT rs2q1 = (p2.x() - q.x()) * xw2q + (p2.y() - q.y()) * yw2q;

Apollonius_graph_2/test/Apollonius_graph_2/include/test.h

@@ -879,7 +879,7 @@ bool test_algo(InputStream& is)
   // Patch for the Microsoft compiler so that it does not produce the
   // nasty warning about decorated name length
   // Basically what I do here is create typedefs for the default
-  // template paramaters so as to give them shorter names
+  // template parameters so as to give them shorter names
   typedef Apollonius_graph_vertex_base_2<Traits,true>   Vb;
   typedef Triangulation_face_base_2<Traits>             Fb;
   typedef Triangulation_data_structure_2<Vb,Fb>         Agds;
@@ -904,7 +904,7 @@ bool test_hierarchy_algo(InputStream& is)
   // Patch for the Microsoft compiler so that it does not produce the
   // nasty warning about decorated name length
   // Basically what I do here is create typedefs for the default
-  // template paramaters so as to give them shorter names
+  // template parameters so as to give them shorter names
   typedef Apollonius_graph_vertex_base_2<Traits,true>   Vb;
   typedef Apollonius_graph_hierarchy_vertex_base_2<Vb>  HVb;
   typedef Triangulation_face_base_2<Traits>             Fb;
@@ -934,7 +934,7 @@ bool test_filtered_traits_algo(InputStream& is)
   // Patch for the Microsoft compiler so that it does not produce the
   // nasty warning about decorated name length
   // Basically what I do here is create typedefs for the default
-  // template paramaters so as to give them shorter names
+  // template parameters so as to give them shorter names
   typedef Apollonius_graph_vertex_base_2<Traits,true>   Vb;
   typedef Triangulation_face_base_2<Traits>             Fb;
   typedef Triangulation_data_structure_2<Vb,Fb>         Agds;
@@ -961,7 +961,7 @@ bool test_filtered_traits_hierarchy_algo(InputStream& is)
   // Patch for the Microsoft compiler so that it does not produce the
   // nasty warning about decorated name length
   // Basically what I do here is create typedefs for the default
-  // template paramaters so as to give them shorter names
+  // template parameters so as to give them shorter names
   typedef Apollonius_graph_vertex_base_2<Traits,true>   Vb;
   typedef Apollonius_graph_hierarchy_vertex_base_2<Vb>  HVb;
   typedef Triangulation_face_base_2<Traits>             Fb;

Arithmetic_kernel/include/CGAL/CORE_arithmetic_kernel.h

@@ -42,7 +42,7 @@ class CORE_arithmetic_kernel : public internal::Arithmetic_kernel_base {
 public:
     //! exact integers
     typedef CORE::BigInt Integer;
-    //! exact float nummber
+    //! exact float number
     typedef CORE::BigRat Exact_float_number;
     //! exact rationals, constructible from integers
     typedef CORE::BigRat Rational;

Arithmetic_kernel/package_info/Arithmetic_kernel/description.txt

@@ -1,7 +1,7 @@
 An Arithmetic_kernel is required to provide at least the following public types:
-Integer, Rational, Bigfloat_interval. It is guranteed that these types are interoperable. Currently there are:
+Integer, Rational, Bigfloat_interval. It is guaranteed that these types are interoperable. Currently there are:
 Gmp_arithmetic_kernel
 CORE_arithmetic_kernel
 LEDA_arithmetic_kernel
 
-Moreover, the package provides a class template Get_arithmetic_kernel<T>. This cclass provides the corresponding Arithmetic_kernel for T. Note that T may also be a non trivial type such as Sqrt_extension, Polynomial etc.
+Moreover, the package provides a class template Get_arithmetic_kernel<T>. This class provides the corresponding Arithmetic_kernel for T. Note that T may also be a non trivial type such as Sqrt_extension, Polynomial etc.

Arrangement_on_surface_2/benchmark/Arrangement_on_surface_2/Conic_reader.hpp

@@ -69,7 +69,7 @@ public:
     /*! Is a conivs arc currently being processed? */
     bool m_processing_arc;
 
-    /*! A place holder to store the undelying conic of a conic arc */
+    /*! A place holder to store the underlying conic of a conic arc */
     Curve_2 m_conic;
 
     /*! Last orientation */
@@ -263,7 +263,7 @@ public:
   /*! Read the conic curves or arcs of conic curves  from the input file
    * \param filename the name of the input file
    * \param curves_out the iterator of the container of the read curves
-   * \param bbox the counding box of the read curves
+   * \param bbox the bounding box of the read curves
    */
   template<class OutputIterator>
   int read_data(const char * filename, OutputIterator curves_out,

Arrangement_on_surface_2/benchmark/Arrangement_on_surface_2/Double.hpp

@@ -36,7 +36,7 @@ public:
     return(*this);
   }
 
-  // Arithmetic opertors.
+  // Arithmetic operators.
   Double operator+(const Double & x) const { return Double(val + x.val); }
 
   Double operator-(const Double & x) const { return Double(val - x.val); }
@@ -48,7 +48,7 @@ public:
   // Unary minus.
   Double operator-() const { return Double(-val); }
 
-  // Arithmetic opertors and assignment.
+  // Arithmetic operators and assignment.
   void operator+=(const Double & x) { val += x.val; }
 
   void operator-=(const Double & x) { val -= x.val; }

Arrangement_on_surface_2/benchmark/Arrangement_on_surface_2/Point_parser_visitor.hpp

@@ -86,7 +86,7 @@ public:
       std::cout << "Duplicate point: " << point << std::endl;
   }
 
-  /*! Parse a generic Homogenuous point */
+  /*! Parse a generic Homogeneous point */
   virtual void accept_point_2( std::string x, std::string y, std::string w)
   {
     typedef typename Number_type_traits<Rat_number_type>::FT            FT;

Arrangement_on_surface_2/benchmark/Arrangement_on_surface_2/Polyline_reader.hpp

@@ -92,7 +92,7 @@ public:
   /*! Read the segments from the input file
    * \param filename the name of the input file
    * \param curves_out the iterator of the container of the read curves
-   * \param bbox the counding box of the read curves
+   * \param bbox the bounding box of the read curves
    */
   template<class OutputIterator>
   int read_data(const char * filename, OutputIterator curves_out,

Arrangement_on_surface_2/benchmark/Arrangement_on_surface_2/Segment_reader.hpp

@@ -24,7 +24,7 @@ public:
   typedef typename Traits::Point_2              Point_2;
   typedef typename Traits::Curve_2              Curve_2;
 
-  /*! A visitor of the parser that reads segements */
+  /*! A visitor of the parser that reads segments */
   template <class OutputIterator>
   class Segment_parser_visitor :
     public Point_parser_visitor<Kernel, Point_2, Number_type> {
@@ -71,7 +71,7 @@ public:
   /*! Read the segments from the input file
    * \param filename the name of the input file
    * \param curves_out the iterator of the container of the read curves
-   * \param bbox the counding box of the read curves
+   * \param bbox the bounding box of the read curves
    */
   template<class OutputIterator>
   int read_data(const char * filename, OutputIterator curves_out,

Arrangement_on_surface_2/benchmark/Arrangement_on_surface_2/arr_bench.cpp

@@ -590,7 +590,7 @@ void run_bench(Bench_inst & bench_inst, Benchable & benchable,
   if (samples > 0) bench_inst.set_samples(samples);
   else if (iterations > 0) bench_inst.set_iterations(iterations);
 
-  //opertor () in the Bench - does all the work !
+  //operator () in the Bench - does all the work !
   bench_inst();
 }
 
@@ -648,7 +648,7 @@ int main(int argc, char * argv[])
     std::cout << "strategy_mask = " << strategy_mask  << std::endl;
   }
 
-  // Construct Incrementaly  (only if type_code == incremental)
+  // Construct Incrementally  (only if type_code == incremental)
   type_code = Option_parser::TYPE_INCREMENT;
   if (type_mask & (0x1 << type_code)) {
     if (verbose_level > 0) std::cout << "TYPE_INCREMENT " << std::endl;

Arrangement_on_surface_2/demo/Arrangement_on_surface_2/ArrangementGraphicsItem.cpp

@@ -191,7 +191,7 @@ void ArrangementGraphicsItem<Arr_>::paintWithFloodFill(
 
   // paint bounded faces normally?
   // by experimenting it's faster to just paint all using the flood algo
-  // specially with algebraic faces since currenlty all edges have to
+  // specially with algebraic faces since currently all edges have to
   // be recalculated/rendered again for faces
   // this->paintFaces(&painter2);
   this->paintEdges(&painter2, traits);
@@ -588,7 +588,7 @@ void ArrangementGraphicsItem<Arr_>::paintFace(
 
       Halfedge_handle he = cc;
       X_monotone_curve_2 c = he->curve();
-      // Get the co-ordinates of the curve's source and target.
+      // Get the coordinates of the curve's source and target.
       double sx = CGAL::to_double(he->source()->point().x()),
              sy = CGAL::to_double(he->source()->point().y()),
              tx = CGAL::to_double(he->target()->point().x()),
@@ -606,7 +606,7 @@ void ArrangementGraphicsItem<Arr_>::paintFace(
       else
       {
         // If the curve is monotone, than its source and its target has the
-        // extreme x co-ordinates on this curve.
+        // extreme x coordinates on this curve.
         bool is_source_left = (sx < tx);
         int x_min = is_source_left ? coord_source_viewport.x()
                                    : coord_target_viewport.x();

Arrangement_on_surface_2/demo/Arrangement_on_surface_2/ArrangementPainterOstream.cpp

@@ -186,7 +186,7 @@ ArrangementPainterOstream<CGAL::Arr_conic_traits_2<
   QGraphicsView* view = this->scene->views().first();
   int xmin = view->mapFromScene(bb.xmin(), bb.ymin()).x();
   int xmax = view->mapFromScene(bb.xmax(), bb.ymin()).x();
-  // can be negitive due to rotation trasnformation
+  // can be negative due to rotation transformation
   size_t n = static_cast<size_t>(std::abs(xmax - xmin));
   if (n == 0) { return *this; }
 

Arrangement_on_surface_2/demo/Arrangement_on_surface_2/FloodFill.h

@@ -26,7 +26,7 @@ class FloodFill
 public:
   // this currently assumes that there is a "border" in the boundaries that
   // will prevent the flood fill from going there
-  // this way we don't check bounadry conditions!
+  // this way we don't check boundary conditions!
   void
   operator()(QRgb* raw_img, uint16_t width, uint16_t x, uint16_t y, QRgb color);
 

Arrangement_on_surface_2/demo/Arrangement_on_surface_2/GraphicsSceneMixin.h

@@ -21,7 +21,7 @@ class QGraphicsView;
 class GraphicsSceneMixin
 {
 public:
-  /*! Costructor */
+  /*! Constructor */
   GraphicsSceneMixin(QGraphicsScene* scene_ = nullptr);
 
   /*! Destructor (virtual) */

Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils/Utils.cpp

@@ -93,7 +93,7 @@ double Compute_squared_distance_2<
   CGAL::Arr_conic_traits_2<RatKernel, AlgKernel, NtTraits>>::
 operator()(const Point_2& p, const X_monotone_curve_2& c) const
 {
-  // Get the co-ordinates of the curve's source and target.
+  // Get the coordinates of the curve's source and target.
   // double sx = CGAL::to_double( c.source( ).x( ) );
   // double sy = CGAL::to_double( c.source( ).y( ) );
   // double tx = CGAL::to_double( c.target( ).x( ) );
@@ -111,7 +111,7 @@ operator()(const Point_2& p, const X_monotone_curve_2& c) const
   else
   {
     // If the curve is monotone, than its source and its target has the
-    // extreme x co-ordinates on this curve.
+    // extreme x coordinates on this curve.
     // bool is_source_left = (sx < tx);
     // int  x_min = is_source_left ? (*w).x_pixel(sx) : (*w).x_pixel(tx);
     // int  x_max = is_source_left ? (*w).x_pixel(tx) : (*w).x_pixel(sx);

Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils/Utils.h

@@ -281,7 +281,7 @@ public:
   double operator()(const Point_2& p, const X_monotone_curve_2& c) const;
 };
 
-// chcek if arrangement is a model of the concept ArrangementOpenBoundaryTraits_2
+// check if arrangement is a model of the concept ArrangementOpenBoundaryTraits_2
 template <typename ArrTraits>
 struct IsOpenBoundaryArrangement :
     public CGAL::Boolean_tag<

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_conic_traits_2.h

@@ -376,7 +376,7 @@ public:
      */
     Point_2(const typename Alg_kernel::Point_2& p);
 
-    /*! constructs from homegeneous coordinates.
+    /*! constructs from homogeneous coordinates.
      */
     Point_2(const Algebraic& hx, const Algebraic& hy, const Algebraic& hz);
 

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h

@@ -22,7 +22,7 @@ namespace CGAL {
    * We use the following parameterization of the unit sphere \f$S =
    * \phi_S(\Phi)\f$: \f$\Phi = [\alpha, 2\pi + \alpha] \times [-\frac{\pi}{2},
    * \frac{\pi}{2}]\f$, \f$\phi_S(x, y) = (\cos y \cos x, \sin y \cos x, \sin
-   * x)\f$, where \f$\alpha = \arctan(X, Y)\f$. By deafult, \f$X = -1, Y = 0\f$,
+   * x)\f$, where \f$\alpha = \arctan(X, Y)\f$. By default, \f$X = -1, Y = 0\f$,
    * which implies \f$\alpha = \pi\f$, and a default parameterization \f$\Phi =
    * [-\pi, \pi] \times [-\frac{\pi}{2}, \frac{\pi}{2}]\f$. The equator curve,
    * for example, is given by \f$\gamma(t) = (\pi(2t - 1) + \alpha, 0)\f$, for
@@ -365,7 +365,7 @@ namespace CGAL {
       X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q);
 
       /*! Construct a full great circle from a normal to a plane.
-       * Observe that the constrcted arc has one endpoint that lies on
+       * Observe that the constructed arc has one endpoint that lies on
        * the identification curve. This point is considered both the source and
        * target (and also the left and right) point of the arc.
        * \param normal the normal to the plane containing the great circle.

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_overlay_2.h

@@ -72,4 +72,4 @@ void overlay (const Arrangement_with_history_2<Traits,Dcel1>& arr1,
 
 
 
-} /* end namesapce CGAL */
+} /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_polycurve_traits_2.h

@@ -10,7 +10,7 @@ namespace CGAL {
    * or line segments. We call such a compound curve a polycurve.  A polycurve
    * is a chain of subcurves, where each two neighboring subcurves in the chain
    * share a common endpoint; that is, the polycurve is continuous. Furthermore,
-   * the target of the \f$i\f$th segement of a polycurve has to coincide with
+   * the target of the \f$i\f$th segment of a polycurve has to coincide with
    * the source of the \f$i+1\f$st segment; that is, the polycurve has to be
    * \a well-oriented. Note that it is possible to construct general polycurves
    * that are neither continuous nor well-oriented, as it is impossible to
@@ -231,7 +231,7 @@ namespace CGAL {
     public:
       /*! Obtain a trimmed version of the polycurve with src and tgt as end
         * vertices.
-        * Src and tgt will be swaped if they do not conform to the direction of
+        * Src and tgt will be swapped if they do not conform to the direction of
         * the polycurve.
         */
       X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv,
@@ -424,7 +424,7 @@ namespace CGAL {
       /// @{
 
       /*! Append a subcurve to the polycurve at the back.
-       * \a Warning: This function does not preform the precondition test
+       * \a Warning: This function does not perform the precondition test
        *             that the `Push_back_2` functor does. Thus, it is
        *             recommended to use the latter.
        * \param subcurve The new subcurve to be appended to the polycurve.

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_polyline_traits_2.h

@@ -15,7 +15,7 @@ namespace CGAL {
  * curves, commonly referred to as polylines. Each polyline is a
  * chain of segments, where each two neighboring segments in the
  * chain share a common endpoint; that is, the polyline is
- * continuous. Furthermore, the target of the \f$i\f$th segement of
+ * continuous. Furthermore, the target of the \f$i\f$th segment of
  * a polyline has to coincide with the source of the \f$i+1\f$st
  * segment; that is, the polyline has to be \a well-oriented. Note
  * that it is possible to construct general polylines that are

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_triangulation_point_location.h

@@ -8,9 +8,9 @@ namespace CGAL {
  * The `Arr_triangulation_point_location` class template implements a
  * point-location (and vertical ray-shooting) strategy that is based on
  * triangulation. In particular, the algorithm uses a constrained triangulation,
- * provided by the 2D Triangulations package, as a search strcture. Every time
+ * provided by the 2D Triangulations package, as a search structure. Every time
  * the arrangement is modified the constrained triangulation search-structure is
- * reconstructed from scrach, where the edges of the arrangement are set to be
+ * reconstructed from scratch, where the edges of the arrangement are set to be
  * the constrained edges of the triangulation. This strategy is inefficient
  * (especially when the number of modifications applied to the arrangement is
  * high) and provided only for educational purposes.

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_2.h

@@ -282,7 +282,7 @@ void insert_non_intersecting_curves(Arrangement_2<Traits,Dcel>& arr,
  *
  * Inserts a given point into a given arrangement.  It uses a given
  * point-location object to locate the given point in the given arrangement. If
- * the point conincides with an existing vertex, there is nothing left to do; if
+ * the point coincides with an existing vertex, there is nothing left to do; if
  * it lies on an edge, the edge is split at the point. Otherwise, the point is
  * contained inside a face, and is inserted as an isolated vertex inside this
  * face.  By default, the function uses the "walk along line" point-location

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_on_surface_2.h

@@ -1185,7 +1185,7 @@ void insert_non_intersecting_curves
  *
  * Inserts a given point into a given arrangement.  It uses a given
  * point-location object to locate the given point in the given arrangement. If
- * the point conincides with an existing vertex, there is nothing left to do; if
+ * the point coincides with an existing vertex, there is nothing left to do; if
  * it lies on an edge, the edge is split at the point. Otherwise, the point is
  * contained inside a face, and is inserted as an isolated vertex inside this
  * face.  By default, the function uses the "walk along line" point-location

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrTraits--CompareXOnBoundaryOfCurveEnd_2.h

@@ -20,7 +20,7 @@ public:
    * enumeration `ce` that specifies either the minimum or the maximum end of
    * the curve where the curve has a vertical asymptote, compares the \f$
    * x\f$-coordinate of `p` and the \f$x\f$-coordinate of the limit of the
-   * curve at its specificed end. The variable `xcv` identifies the parametric
+   * curve at its specified end. The variable `xcv` identifies the parametric
    * curve \f$c(t) = (x(t), y(t))\f$ defined over an open or half-open interval
    * with endpoints \f$ 0\f$ and \f$ 1\f$. The enumeration `ce` identifies an
    * open end \f$d \in\{0,1\}\f$ of \f$c\f$.  Formally, compares the \f$
@@ -40,7 +40,7 @@ public:
 /*! Given two \f$ x\f$-monotone curves `xcv1` and `xcv2` and two indices `ce1`
  * and `ce2` that specify either the minimum or the maximum ends of `xcv1` and
  * `xcv2`, respectively, where the curves have vertical asymptotes, compares the
- * \f$ x\f$-coordinates of the limits of the curves at their specificed
+ * \f$ x\f$-coordinates of the limits of the curves at their specified
  * ends. The variables `xcv1` and `xcv2` identify the parametric curves \f$
  * c_1(t) = (x_1(t),y_1(t))\f$ and \f$ c_2(t) = (x_2(t),y_2(t))\f$,
  * respectively, defined over open or half-open intervals with endpoints \f$

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrTraits--Merge_2.h

@@ -15,7 +15,7 @@ public:
   /// @{
 
   /*! accepts two <I>mergeable</I> \f$ x\f$-monotone curves `xc1` and `xc2`
-   * and asigns `xc` with the merged curve.
+   * and assigns `xc` with the merged curve.
    *
    * \pre `are_mergeable_2`(`xc1`, `xc2`) is true.
    */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementDcelFace.h

@@ -8,7 +8,7 @@
  * (CCB). A face may be unbounded. Otherwise, it has one or more outer CCBs. A
  * face may also be bounded by inner CCBs, and it may contain isolated vertices
  * in its interior. A planar face may have only one outer CCBs and its inner
- * CCBs are refered to as holes.
+ * CCBs are referred to as holes.
  *
  * \sa `ArrangementDcel`
  * \sa `ArrangementDcelVertex`

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementDcelWithRebind.h

@@ -39,7 +39,7 @@ typedef unspecified_type template <class T> rebind;
 /// @{
 
 /*!
-constructs an empty \dcel with one unbouned face.
+constructs an empty \dcel with one unbounded face.
 */
 Arr_dcel();
 

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementOpenBoundaryTraits_2.h

@@ -11,7 +11,7 @@
  * `ArrangementBasicTraits_2`. The arrangement template instantiated with a
  * traits class that models this concept can handle \f$ x\f$-monotone curves
  * that are unbounded in any direction. The concept
- * `ArrangementOpenBoundaryTraits_2`, nontheless, also supports planar \f$
+ * `ArrangementOpenBoundaryTraits_2`, nonetheless, also supports planar \f$
  * x\f$-monotone curves that reach the boundary of an open yet bounded parameter
  * space.
  *

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementTopologyTraits.h

@@ -15,7 +15,7 @@
  * <li> `CGAL::Arr_bounded_planar_topology_traits_2`&mdash;can serve as a topology traits
  * for an arrangement of planar unbounded curves.
  * <li> `CGAL::Arr_unb_planar_topology_traits_2`&mdash;can serve as a topology traits
- * for an arrangement of arcs of great circles embeded on a sphere.
+ * for an arrangement of arcs of great circles embedded on a sphere.
  * </ul>
  *
  * At this point we do not expose all the requirements of this concept.
@@ -46,7 +46,7 @@ public:
   /*! constructs default. */
   Arr_topology_traits();
 
-  /*! construcs from a geometry-traits object. */
+  /*! constructs from a geometry-traits object. */
   Arr_topology_traits(const Geometry_traits_2* geometry_traits);
 
   /// @}

Arrangement_on_surface_2/examples/Arrangement_on_surface_2/conics.cpp

@@ -37,7 +37,7 @@ int main() {
 
   // Insert a parabolic arc (C6) supported by the parabola y = -x^2 with
   // endpoints (-sqrt(3),-3) (~(-1.73,-3)) and (sqrt(2),-2) (~(1.41,-2)).
-  // Since the x-coordinates of the endpoints cannot be acccurately represented,
+  // Since the x-coordinates of the endpoints cannot be accurately represented,
   // we specify them as the intersections of the parabola with the lines
   // y = -3 and y = -2, respectively. The arc is clockwise-oriented.
   Conic_arc c6 =

Arrangement_on_surface_2/examples/Arrangement_on_surface_2/overlay_unbounded.cpp

@@ -11,7 +11,7 @@
 
 #include "arr_linear.h"
 
-// Define a functor for creating a label from a characer and an integer.
+// Define a functor for creating a label from a character and an integer.
 struct Overlay_label {
   std::string operator()(char c, unsigned int i) const
   { return c + boost::lexical_cast<std::string>(i); }

Arrangement_on_surface_2/examples/Arrangement_on_surface_2/polycurve_circular_arc.cpp

@@ -103,12 +103,12 @@ int main() {
   X_monotone_polycurve x_polycurve_1 =
     ctr_xcurve(x_curves.begin(), x_curves.end());
 
-  // Insert polycurves to Arangment and print.
+  // Insert polycurves to Arrangement and print.
   Polycurve_circ_arc_arrangment polycurve_arrangment(&traits);
   insert(polycurve_arrangment, polycurve_1);
   insert(polycurve_arrangment, polycurve_2);
   insert(polycurve_arrangment, x_polycurve_1);
-  std::cout << "Arrangment Statistics:\n";
+  std::cout << "Arrangement Statistics:\n";
   print_arrangement(polycurve_arrangment);
 
   return 0;

Arrangement_on_surface_2/examples/Arrangement_on_surface_2/polycurve_conic.cpp

@@ -108,7 +108,7 @@ int main() {
   X_monotone_polycurve conic_x_mono_polycurve_2 =
     ctr_xpolycurve(xmono_conic_curves_2.begin(), xmono_conic_curves_2.end());
 
-  // Insert the Polycurves into arrangment and print.
+  // Insert the Polycurves into arrangement and print.
   Polycurve_conic_arrangment x_pc_arrangment(&traits);
   insert(x_pc_arrangment, conic_x_mono_polycurve_1);
   insert(x_pc_arrangment, conic_x_mono_polycurve_2);

Arrangement_on_surface_2/include/CGAL/Arr_Bezier_curve_traits_2.h

@@ -138,7 +138,7 @@ public:
     m_owner (false)
   {}
 
-  /*! Assignmnet operator. */
+  /*! Assignment operator. */
   Self& operator= (const Self& tr)
   {
     if (this == &tr)
@@ -809,7 +809,7 @@ public:
                              m_traits.compare_y_at_x_2_object());
       CGAL_precondition_code(Equal_2 equal_2 = m_traits.equal_2_object());
       Compare_x_2 compare_x_2 = m_traits.compare_x_2_object();
-      // Check whether source and taget are two distinct points and they lie
+      // Check whether source and taeget are two distinct points and they lie
       // on the line.
       CGAL_precondition(compare_y_at_x_2(src, xcv) == EQUAL);
       CGAL_precondition(compare_y_at_x_2(tgt, xcv) == EQUAL);

Arrangement_on_surface_2/include/CGAL/Arr_accessor.h

@@ -430,7 +430,7 @@ public:
    * Insert an x-monotone curve into the arrangement, such that one of its
    * endpoints corresponds to a given arrangement vertex, given the exact
    * place for the curve in the circular list around this vertex. The other
-   * endpoint corrsponds to a free vertex (a newly created vertex or an
+   * endpoint corresponds to a free vertex (a newly created vertex or an
    * isolated vertex).
    * \param he_to The reference halfedge. We should represent cv as a pair
    *              of edges, one of them should become he_to's successor.
@@ -792,7 +792,7 @@ public:
   const Dcel& dcel() const { return (p_arr->_dcel()); }
 
   /*!
-   * Clear the entire arrangment.
+   * Clear the entire arrangement.
    */
   void clear_all()
   {

Arrangement_on_surface_2/include/CGAL/Arr_algebraic_segment_traits_2.h

@@ -61,7 +61,7 @@ public:
     // Copy constructor
     Arr_algebraic_segment_traits_2 (const  Self& /* s */) { /* No state...*/}
 
-    // Assignement operator
+    // Assignment operator
     const Self& operator= (const Self& s)
         {return s;}
 
@@ -254,7 +254,7 @@ public:
             return std::make_pair(std::make_pair(0,0),vertical);
         }
 
-        // abbrevation for convenience
+        // abbreviation for convenience
         bool is_one_one(Curve_2 cv, Point_2 p) const {
 
             std::pair<std::pair<int,int>,bool> branches

Arrangement_on_surface_2/include/CGAL/Arr_circle_segment_traits_2.h

@@ -20,7 +20,7 @@
 #include <CGAL/disable_warnings.h>
 
 /*! \file
- * The header file for the Arr_circle_segment_traits_2<Kenrel> class.
+ * The header file for the Arr_circle_segment_traits_2<Kernel> class.
  */
 
 #include <CGAL/tags.h>
@@ -421,7 +421,7 @@ public:
         return oi;
       }
 
-      // Check the case of a degenrate circle (a point).
+      // 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_precondition (sign_rad != NEGATIVE);
@@ -702,7 +702,7 @@ public:
                              m_traits.compare_y_at_x_2_object());
       CGAL_precondition_code(Equal_2 equal_2 = m_traits.equal_2_object());
       Compare_x_2 compare_x_2 = m_traits.compare_x_2_object();
-      // Check whether source and taget are two distinct points and they lie
+      // Check whether source and target are two distinct points and they lie
       // on the line.
       CGAL_precondition(compare_y_at_x_2(src, xcv) == EQUAL);
       CGAL_precondition(compare_y_at_x_2(tgt, xcv) == EQUAL);

Arrangement_on_surface_2/include/CGAL/Arr_conic_traits_2.h

@@ -843,7 +843,7 @@ public:
                              m_traits.compare_y_at_x_2_object());
       CGAL_precondition_code(Equal_2 equal_2 = m_traits.equal_2_object());
       Compare_x_2 compare_x_2 = m_traits.compare_x_2_object();
-      // Check  whether source and taget are two distinct points and they lie
+      // Check  whether source and target are two distinct points and they lie
       // on the line.
       CGAL_precondition(compare_y_at_x_2(src, xcv) == EQUAL);
       CGAL_precondition(compare_y_at_x_2(tgt, xcv) == EQUAL);

Arrangement_on_surface_2/include/CGAL/Arr_counting_traits_2.h

@@ -21,7 +21,7 @@
  * A counting traits-class for the arrangement package.
  * This is a meta-traits class. It is parameterized with another traits class
  * and inherits from it. For each traits method it maintains a counter that
- * counts the number of invokations into the method.
+ * counts the number of invocations into the method.
  */
 
 #include <iostream>

Arrangement_on_surface_2/include/CGAL/Arr_curve_data_traits_2.h

@@ -79,10 +79,10 @@ public:
   typedef typename internal::Arr_complete_right_side_category<Base_traits_2>::
   Category                                           Right_side_category;
 
-  // Representation of a curve with an addtional data field:
+  // Representation of a curve with an additonal data field:
   typedef _Curve_data_ex<Base_curve_2, Curve_data>   Curve_2;
 
-  // Representation of an x-monotone curve with an addtional data field:
+  // Representation of an x-monotone curve with an additonal data field:
   typedef _Curve_data_ex<Base_x_monotone_curve_2, X_monotone_curve_data>
                                                      X_monotone_curve_2;
 
@@ -99,7 +99,7 @@ public:
   Arr_curve_data_traits_2(const Base_traits_2& traits) : Base_traits_2(traits) {}
   //@}
 
-  /// \name Overriden functors.
+  /// \name Overridden functors.
   //@{
 
   //! \name Intersections & subdivisions

Arrangement_on_surface_2/include/CGAL/Arr_geodesic_arc_on_sphere_partition_traits_2.h

@@ -87,7 +87,7 @@ public:
 
     /*! Compare two points lexigoraphically: by x, then by y.
      *  We actually reversing the order, so x <--> y.
-     * \param p1 the first enpoint directional point.
+     * \param p1 the first endpoint directional point.
      * \param p2 the second endpoint directional point.
      * \return true - y(p1) < y(p2);
      *         true - y(p1) = y(p2) and x(p1) < x(p2);
@@ -129,7 +129,7 @@ public:
 
     /*! Compare two points lexigoraphically: by y, then by x.
      *  We actually reversing the order, so x <--> y.
-     * \param p1 the first enpoint directional point.
+     * \param p1 the first endpoint directional point.
      * \param p2 the second endpoint directional point.
      * \return true - x(p1) < x(p2);
      *         true - x(p1) = x(p2) and y(p1) < y(p2);
@@ -250,7 +250,7 @@ public:
 
     /*! Compare two points by y coordinate.
      *  We actually reversing the order, so x <--> y.
-     * \param p1 the first enpoint directional point.
+     * \param p1 the first endpoint directional point.
      * \param p2 the second endpoint directional point.
      * \return SMALLER - x(p1) < x(p2);
      *         EQUAL   - x(p1) = x(p2);
@@ -395,7 +395,7 @@ public:
 
     /*! Compare two points lexigoraphically: by x, then by y.
      *  We actually reversing the order, so x <--> y.
-     * \param p1 the first enpoint directional point.
+     * \param p1 the first endpoint directional point.
      * \param p2 the second endpoint directional point.
      * \return true - y(p1) < y(p2);
      *         true - y(p1) = y(p2) and x(p1) < x(p2);
@@ -436,7 +436,7 @@ public:
 
     /*! Compare two points lexigoraphically: by y, then by x.
      *  We actually reversing the order, so x <--> y.
-     * \param p1 the first enpoint directional point.
+     * \param p1 the first endpoint directional point.
      * \param p2 the second endpoint directional point.
      * \return true - x(p1) < x(p2);
      *         true - x(p1) = x(p2) and y(p1) < y(p2);
@@ -556,7 +556,7 @@ public:
 
     /*! Compare two points by y coordinate.
      *  We actually reversing the order, so x <--> y.
-     * \param p1 the first enpoint directional point.
+     * \param p1 the first endpoint directional point.
      * \param p2 the second endpoint directional point.
      * \return SMALLER - x(p1) < x(p2);
      *         EQUAL   - x(p1) = x(p2);

Arrangement_on_surface_2/include/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h

@@ -231,7 +231,7 @@ protected:
 
 public:
   /*! Compare two endpoint directions by v.
-   * \param d1 the first enpoint direction.
+   * \param d1 the first endpoint direction.
    * \param d2 the second endpoint direction.
    * \return SMALLER - v(d1) < v(d2);
    *         EQUAL   - v(d1) = v(d2);
@@ -283,7 +283,7 @@ public:
   }
 
   /*! Compare two endpoint directions by u.
-   * \param d1 the first enpoint direction.
+   * \param d1 the first endpoint direction.
    * \param d2 the second endpoint direction.
    * \return SMALLER - u(d1) < u(d2);
    *         EQUAL   - u(d1) = u(d2);
@@ -301,7 +301,7 @@ public:
   }
 
   /*! Compare two endpoint directions lexigoraphically: by u, then by v.
-   * \param d1 the first enpoint direction.
+   * \param d1 the first endpoint direction.
    * \param d2 the second endpoint direction.
    * \return SMALLER - u(d1) < u(d2);
    *         SMALLER - u(d1) = u(d2) and v(d1) < v(d2);
@@ -640,7 +640,7 @@ public:
         return;
       }
 
-      // None of the enpoints coincide with a pole:
+      // None of the endpoints coincide with a pole:
       Direction_2 s = Traits::project_xy(source);
       Direction_2 t = Traits::project_xy(target);
 
@@ -763,7 +763,7 @@ public:
         return cv;
       }
 
-      // None of the enpoints coincide with a pole:
+      // None of the endpoints coincide with a pole:
       if (z_sign(normal) == ZERO) {
         // The arc is vertical
         cv.set_is_vertical(true);
@@ -992,8 +992,8 @@ public:
   };
 
 protected:
-  /*! Obtain the possitive (north) pole
+  /*! Obtain the positive (north) pole
-   * \return the possitive (north) pole
+   * \return the positive (north) pole
    */
   inline static const Point_2& pos_pole()
   {
@@ -1033,7 +1033,7 @@ public:
 
   public:
     /*! Compare two directional points lexigoraphically: by x, then by y.
-     * \param p1 the first enpoint directional point.
+     * \param p1 the first endpoint directional point.
      * \param p2 the second endpoint directional point.
      * \return SMALLER - x(p1) < x(p2);
      *         SMALLER - x(p1) = x(p2) and y(p1) < y(p2);
@@ -2140,7 +2140,7 @@ public:
           return oi;
         }
 
-        // None of the enpoints coincide with a pole.
+        // None of the endpoints coincide with a pole.
         bool s_is_positive, t_is_positive, plane_is_positive;
         CGAL::Sign xsign = Traits::x_sign(normal);
         if (xsign == ZERO) {
@@ -2172,7 +2172,7 @@ public:
         return oi;
       }
 
-      // The curve is not vertical, (none of the enpoints coincide with a pole)
+      // The curve is not vertical, (none of the endpoints coincide with a pole)
       Direction_3 dp;
       m_traits.intersection_with_identification(c, dp, Zero_atan_y());
       Point_2 p(dp, Point_2::MID_BOUNDARY_LOC);
@@ -2589,7 +2589,7 @@ public:
             return oi;
           }
 
-          /*! If the endpoints of one arc coinside with the 2 poles resp,
+          /*! If the endpoints of one arc coincide with the 2 poles resp,
            * the other arc is completely overlapping.
            */
           if (xc1.left().is_min_boundary() && xc1.right().is_max_boundary()) {
@@ -3166,7 +3166,7 @@ public:
       return;
     }
 
-    // None of the enpoints coincide with a pole:
+    // None of the endpoints coincide with a pole:
     Direction_2 s = Traits::project_xy(m_source);
     Direction_2 t = Traits::project_xy(m_target);
 

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Arr_plane_3.h

@@ -211,7 +211,7 @@ intersect(const Arr_plane_3<Kernel> & plane1,
   typedef typename Kernel::FT           FT;
   typedef boost::variant<Line_3, Arr_plane_3<Kernel> >  Intersection_result;
 
-  // We know that the plane goes throgh the origin
+  // We know that the plane goes through the origin
   const FT& a1 = plane1.a();
   const FT& b1 = plane1.b();
   const FT& c1 = plane1.c();

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_bounding_rational_traits.h

@@ -719,7 +719,7 @@ public:
 
   /*!
    * Construct a bounding box for the given control polygon.
-   * \param cp A sequence of control point (the control polgon).
+   * \param cp A sequence of control point (the control polygon).
    * \param bbox Output: The bounding box.
    * \pre cp is not empty.
    */
@@ -776,7 +776,7 @@ private:
     Comparison_result                  res = EQUAL;
 
     // Look for the first pair of consecutive points whose x-coordinate
-    // (or y-coordinate) are not equal. Their comparsion result will be
+    // (or y-coordinate) are not equal. Their comparison result will be
     // set as the "reference" comparison result.
     typename Control_points::const_iterator  pt_curr = cp.begin();
     typename Control_points::const_iterator  pt_end = cp.end();
@@ -1054,7 +1054,7 @@ private:
     const Point_2&  s2 = cp2.front();
     const Point_2&  t2 = cp2.back();
 
-    // Check whether any pair of these endpoints conincide.
+    // Check whether any pair of these endpoints coincide.
     NT      x, y;               // Coordinate of a common endpoint.
     NT      t_val1, t_val2;     // Its respective parameters.
 
@@ -1114,7 +1114,7 @@ private:
   }
 
   /*!
-   * An auxilary recursive function for computing the approximated
+   * An auxiliary recursive function for computing the approximated
    * intersection points between two Bezier curves.
    * \param cp1 The control points of the first curve.
    * \param t_min1 The lower bound of the parameter range of the first curve.
@@ -1369,7 +1369,7 @@ private:
   }
 
   /*!
-   * An auxilary recursive function for computing the approximated vertical
+   * An auxiliary recursive function for computing the approximated vertical
    * tangency points of a Bezier curves.
    * \param cp The control points of the curve.
    * \param t_min The lower bound of the parameter range of the curve.

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_cache.h

@@ -822,7 +822,7 @@ _Bezier_cache<NtTraits>::_compute_resultant
         }
 
         // We multiplied the current row by the i'th diagonal entry, thus
-        // multipling the determinant value by it. We therefore increment
+        // multiplying the determinant value by it. We therefore increment
         // the exponent of mat[i][i] in the normalization factor.
         exp_fact[i] = exp_fact[i] + 1;
       }

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_curve_2.h

@@ -162,7 +162,7 @@ public:
 
     for (k = 0; pts_begin != pts_end; ++pts_begin, k++)
     {
-//SL: Acccording to the fact that all operations are based on polynomials
+//SL: According to the fact that all operations are based on polynomials
 //    duplicated control points can be allowed.
 //      // Make sure that we do not have two identical consecutive control
 //      // points.
@@ -423,7 +423,7 @@ public:
   }
 
   /*!
-   * Get an interator for the first control point.
+   * Get an iterator for the first control point.
    */
   Control_point_iterator control_points_begin () const
   {
@@ -431,7 +431,7 @@ public:
   }
 
   /*!
-   * Get a past-the-end interator for control points.
+   * Get a past-the-end iterator for control points.
    */
   Control_point_iterator control_points_end () const
   {

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_point_2.h

@@ -88,7 +88,7 @@ private:
     unsigned int        _xid;       /*!< Serial number of the originating
                                          x-monotone curve. */
     Bez_point_bound     _bpb;       /*!< Bounding information for the
-                                         point: bouding control polygon,
+                                         point: bounding control polygon,
                                          point type, etc. */
     Algebraic          *p_t;        /*!< The algebraic parameter for the
                                          point (if available). */
@@ -240,7 +240,7 @@ private:
      * Set the serial number of the originating x-monotone curve.
      * \param xid the new serial number of the originating x-monotone curve.
      * \pre The current xid() is 0.
-     * \pre xid is possitive.
+     * \pre xid is positive.
      */
     void set_xid (unsigned int xid)
     {
@@ -253,7 +253,7 @@ private:
   };
 
   /*! \struct Subcurve
-   * Auxilary structure for the vertical_position() function.
+   * Auxiliary structure for the vertical_position() function.
    */
   typedef typename Bounding_traits::Control_points   Control_points;
   typedef typename Bounding_traits::NT               BoundNT;
@@ -1421,7 +1421,7 @@ bool _Bezier_point_2_rep<RatKer, AlgKer, NtTrt, BndTrt>::_refine ()
     CGAL_assertion(_origs.size() == 2);
 
     // Obtain the other curve that originates the intersection point and use
-    // it to refine its reprsentation.
+    // it to refine its representation.
     Orig_iter    org_it = _origs.begin();
     ++org_it;
     Originator&  orig2 = *org_it;

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_x_monotone_2.h

@@ -533,7 +533,7 @@ private:
   /*! Compute the exact vertical position of the given point with respect to
    * the x-monotone curve.
    * \param p The point.
-   * \param force_exact Sould we force an exact result.
+   * \param force_exact Should we force an exact result.
    * \return SMALLER if the point is below the curve;
    *         LARGER if the point is above the curve;
    *         EQUAL if p lies on the curve.
@@ -751,7 +751,7 @@ point_position(const Point_2& p, Bezier_cache& cache) const
     in_range = _is_in_range(p, correct_res);
 
     if (! correct_res) {
-      // Perform the comparsion in an exact manner.
+      // Perform the comparison in an exact manner.
       if (! p.is_exact())
         p.make_exact(cache);
 
@@ -764,7 +764,7 @@ point_position(const Point_2& p, Bezier_cache& cache) const
   }
 
   // Call the vertical-position function that uses the bounding-boxes
-  // to evaluate the comparsion result.
+  // to evaluate the comparison result.
   typename Bounding_traits::Control_points cp;
 
   std::copy(_curve.control_points_begin(), _curve.control_points_end(),
@@ -1192,7 +1192,7 @@ _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::compare_to_left
     return (slope_res);
 
   // Compare the two subcurves by choosing some point to the left of p
-  // and compareing the vertical position there.
+  // and comparing the vertical position there.
   Comparison_result   left_res;
 
   if (left().compare_x(cv.left(), cache) != SMALLER)
@@ -1376,7 +1376,7 @@ _is_in_range(const Algebraic& t, Bezier_cache& cache) const
     return (false);
   }
 
-  // Obtain the exact t-range of the curve and peform an exact comparison.
+  // Obtain the exact t-range of the curve and perform an exact comparison.
   std::pair<Algebraic, Algebraic> range = _t_range (cache);
   const Algebraic&                t_src = range.first;
   const Algebraic&                t_trg = range.second;
@@ -1923,7 +1923,7 @@ _clip_control_polygon(typename Bounding_traits::Control_points& ctrl,
   if (! (org_min->point_bound().type == Bez_point_bound::RATIONAL_PT &&
          CGAL::sign(org_min->point_bound().t_min) == CGAL::ZERO))
   {
-    // It is possible that the paramater range of the originator is too large.
+    // It is possible that the parameter range of the originator is too large.
     // We therefore make sure it fits the current bounding box of the point
     // (which we know is tight enough).
     p_min.fit_to_bbox();
@@ -1951,7 +1951,7 @@ _clip_control_polygon(typename Bounding_traits::Control_points& ctrl,
   if (! (org_max->point_bound().type == Bez_point_bound::RATIONAL_PT &&
          CGAL::compare (org_max->point_bound().t_max, 1) == CGAL::EQUAL))
   {
-    // It is possible that the paramater range of the originator is too large.
+    // It is possible that the parameter range of the originator is too large.
     // We therefore make sure it fits the current bounding box of the point
     // (which we know is tight enough).
     p_max.fit_to_bbox();
@@ -2435,7 +2435,7 @@ _exact_vertical_position(const Point_2& p,
 #endif
                          ) const
 {
-  // If it is a rational point, obtain its rational reprsentation.
+  // If it is a rational point, obtain its rational representation.
   Rat_point_2              rat_p;
 
   if (p.is_rational())

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Circle_segment_2.h

@@ -1705,7 +1705,7 @@ protected:
   }
 
   /*! Compute the intersections between the supporting circle of (*this) and
-   * the supporting line of the segement cv.
+   * the supporting line of the segment cv.
    */
   void _circ_line_intersect(const Self& cv,
                             Intersection_list& inter_list) const

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Conic_arc_2.h

@@ -182,7 +182,7 @@ public:
     _target (target),
     _extra_data_P (nullptr)
   {
-    // Make sure that the source and the taget are not the same.
+    // Make sure that the source and the target are not the same.
     CGAL_precondition (Alg_kernel().compare_xy_2_object() (source,
                                                            target) != EQUAL);
 
@@ -249,7 +249,7 @@ public:
     _source = Point_2 (nt_traits.convert (x1), nt_traits.convert (y1));
     _target = Point_2 (nt_traits.convert (x2), nt_traits.convert (y2));
 
-    // Make sure that the source and the taget are not the same.
+    // Make sure that the source and the target are not the same.
     CGAL_precondition (Alg_kernel().compare_xy_2_object() (_source,
                                                            _target) != EQUAL);
 
@@ -300,7 +300,7 @@ public:
     Rational          y0 = center.y();
     Rational          R_sqr = ker.compute_squared_radius_2_object() (circ);
 
-    // Produce the correponding conic: if the circle center is (x0,y0)
+    // Produce the corresponding conic: if the circle center is (x0,y0)
     // and its squared radius is R^2, that its equation is:
     //   x^2 + y^2 - 2*x0*x - 2*y0*y + (x0^2 + y0^2 - R^2) = 0
     // Note that this equation describes a curve with a negative (clockwise)
@@ -338,7 +338,7 @@ public:
     _target(target),
     _extra_data_P (nullptr)
   {
-    // Make sure that the source and the taget are not the same.
+    // Make sure that the source and the target are not the same.
     CGAL_precondition (Alg_kernel().compare_xy_2_object() (source,
                                                            target) != EQUAL);
     CGAL_precondition (orient != COLLINEAR);
@@ -350,7 +350,7 @@ public:
     Rational          y0 = center.y();
     Rational          R_sqr = ker.compute_squared_radius_2_object() (circ);
 
-    // Produce the correponding conic: if the circle center is (x0,y0)
+    // Produce the corresponding conic: if the circle center is (x0,y0)
     // and it squared radius is R^2, that its equation is:
     //   x^2 + y^2 - 2*x0*x - 2*y0*y + (x0^2 + y0^2 - R^2) = 0
     // Since this equation describes a curve with a negative (clockwise)
@@ -412,7 +412,7 @@ public:
     _source = Point_2 (nt_traits.convert (x1), nt_traits.convert (y1));
     _target = Point_2 (nt_traits.convert (x3), nt_traits.convert (y3));
 
-    // Make sure that the source and the taget are not the same.
+    // Make sure that the source and the target are not the same.
     CGAL_precondition (Alg_kernel().compare_xy_2_object() (_source,
                                                            _target) != EQUAL);
 
@@ -440,7 +440,7 @@ public:
 
     if (points_collinear)
     {
-      _info = 0;           // Inavlid arc.
+      _info = 0;           // Invalid arc.
       return;
     }
 
@@ -506,7 +506,7 @@ public:
 
     if (point_collinear)
     {
-      _info = 0;           // Inavlid arc.
+      _info = 0;           // Invalid arc.
       return;
     }
 
@@ -943,7 +943,7 @@ public:
     }
     else
     {
-      // Use the source and target to initialize the exterme points.
+      // Use the source and target to initialize the extreme points.
       bool   source_left =
         CGAL::to_double(_source.x()) < CGAL::to_double(_target.x());
       x_min = source_left ?
@@ -1270,7 +1270,7 @@ private:
       else
       {
         // The sign of (4rs - t^2) detetmines the conic type:
-        // - if it is possitive, the conic is an ellipse,
+        // - if it is positive, the conic is an ellipse,
         // - if it is negative, the conic is a hyperbola,
         // - if it is zero, the conic is a parabola.
         CGAL::Sign   sign_conic = CGAL::sign (4*_r*_s - _t*_t);
@@ -1371,7 +1371,7 @@ private:
   }
 
   /*!
-   * Build the data for hyperbolic arc, contaning the characterization of the
+   * Build the data for hyperbolic arc, containing the characterization of the
    * hyperbolic branch the arc is placed on.
    */
   void _build_hyperbolic_arc_data ()
@@ -1626,7 +1626,7 @@ protected:
   }
 
   /*!
-   * Find the vertical tangency points of the undelying conic.
+   * Find the vertical tangency points of the underlying conic.
    * \param ps The output points of vertical tangency.
    *           This area must be allocated at the size of 2.
    * \return The number of vertical tangency points.
@@ -1709,7 +1709,7 @@ protected:
   }
 
   /*!
-   * Find the horizontal tangency points of the undelying conic.
+   * Find the horizontal tangency points of the underlying conic.
    * \param ps The output points of horizontal tangency.
    *           This area must be allocated at the size of 2.
    * \return The number of horizontal tangency points.

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Conic_point_2.h

@@ -111,12 +111,12 @@ private:
     Base()
   {}
 
-  /*! Constrcutor from the base class. */
+  /*! Constructor from the base class. */
   _Conic_point_2 (const Base& p) :
     Base (p)
   {}
 
-  /*! Constructor with homegeneous coordinates. */
+  /*! Constructor with homogeneous coordinates. */
   _Conic_point_2 (const Algebraic& hx,
                   const Algebraic& hy,
                   const Algebraic& hz) :

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Conic_x_monotone_arc_2.h

@@ -106,7 +106,7 @@ protected:
 
 public:
 
-  /// \name Constrcution methods.
+  /// \name Construction methods.
   //@{
 
   /*!
@@ -945,7 +945,7 @@ public:
 
   /*!
    * Flip the arc.
-   * \return An arc with swapped source and target and a reverse orienation.
+   * \return An arc with swapped source and target and a reverse orientation.
    */
   Self flip() const
   {
@@ -1218,7 +1218,7 @@ private:
 
     // Check whether the conic is facing up or facing down:
     // Check whether the arc (which is x-monotone of degree 2) lies above or
-    // below the segement that contects its two end-points (x1,y1) and (x2,y2).
+    // below the segment that connects its two end-points (x1,y1) and (x2,y2).
     // To do that, we find the y coordinate of a point on the arc whose x
     // coordinate is (x1+x2)/2 and compare it to (y1+y2)/2.
     Comparison_result res = ker.compare_y_2_object() (p_arc_mid, p_mid);
@@ -1239,7 +1239,7 @@ private:
 
   /*!
    * Check if the arc is a special segment connecting two algebraic endpoints
-   * (and has no undelying integer conic coefficients).
+   * (and has no underlying integer conic coefficients).
    */
   bool _is_special_segment () const
   {
@@ -1679,7 +1679,7 @@ private:
   }
 
   /*!
-   * Intersect the supporing conic curves of this arc and the given arc.
+   * Intersect the supporting conic curves of this arc and the given arc.
    * \param arc The arc to intersect with.
    * \param inter_list The list of intersection points.
    */
@@ -1703,7 +1703,7 @@ private:
     if (arc._is_special_segment()) {
       // The second arc is a special segment (a*x + b*y + c = 0).
       if (_is_special_segment()) {
-        // Both arc are sepcial segment, so they have at most one intersection
+        // Both arc are special segment, so they have at most one intersection
         // point.
         Algebraic denom = this->_extra_data_P->a * arc._extra_data_P->b -
           this->_extra_data_P->b * arc._extra_data_P->a;

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/One_root_number.h

@@ -474,7 +474,7 @@ CGAL::Comparison_result compare (const _One_root_number<NT, FL>& x,
       sign_right = ZERO;
   }
 
-  // Check whether on of the terms is zero. In this case, the comparsion
+  // Check whether on of the terms is zero. In this case, the comparison
   // result is simpler:
   if (sign_left == ZERO)
   {
@@ -507,7 +507,7 @@ CGAL::Comparison_result compare (const _One_root_number<NT, FL>& x,
   // We now square both terms and look at the sign of the one-root number:
   //   ((a1 - a2)^2 - (b1^2*c1 + b2^2*c2)) + 2*b1*b2*sqrt(c1*c2)
   //
-  // If both signs are negative, we should swap the comparsion result
+  // If both signs are negative, we should swap the comparison result
   // we eventually compute.
   const NT          A = diff_alpha*diff_alpha - (x_sqr + y_sqr);
   const NT          B = 2 * x.beta() * y.beta();

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Rational_arc_2.h

@@ -95,7 +95,7 @@ protected:
 
 public:
 
-  /// \name Constrcution methods.
+  /// \name Construction methods.
   //@{
 
   /*!
@@ -339,7 +339,7 @@ public:
     if (! valid)
       return;
 
-    // Analyze the bahaviour of the rational function at x = -oo (the source).
+    // Analyze the behaviour of the rational function at x = -oo (the source).
     Algebraic           y0;
     const Arr_parameter_space inf_s =
       _analyze_at_minus_infinity (_numer, _denom, y0);
@@ -351,7 +351,7 @@ public:
     else // if (inf_s == ARR_INTERIOR)
       _ps = Point_2 (0, y0);
 
-    // Analyze the bahaviour of the rational function at x = +oo (the target).
+    // Analyze the behaviour of the rational function at x = +oo (the target).
     const Arr_parameter_space inf_t =
       _analyze_at_plus_infinity (_numer, _denom, y0);
 
@@ -989,7 +989,7 @@ public:
 
     // Both arcs are defined to the same side (left or right) of the vertical
     // asymptote. If one is defined at y = -oo and the other at y = +oo, we
-    // preform a "lexicographic" comparison.
+    // perform a "lexicographic" comparison.
     const Arr_parameter_space  inf_y1 =
       (ind1 == ARR_MIN_END ? left_infinite_in_y() : right_infinite_in_y());
     const Arr_parameter_space  inf_y2 = (ind2 == ARR_MIN_END) ?
@@ -1833,7 +1833,7 @@ public:
   typedef std::pair<Point_2,Multiplicity>        Intersection_point;
 
 
-  /// \name Constrcution methods.
+  /// \name Construction methods.
   //@{
 
   /*!
@@ -1844,7 +1844,7 @@ public:
   {}
 
   /*!
-   * Constrcutor from a base arc.
+   * Constructor from a base arc.
    */
   _Continuous_rational_arc_2 (const Base& arc) :
     Base (arc)
@@ -2346,7 +2346,7 @@ public:
   typedef typename Base::Rat_vector                     Rat_vector;
   typedef typename Base::Polynomial                     Polynomial;
 
-  /// \name Constrcution methods.
+  /// \name Construction methods.
   //@{
 
   /*!

Arrangement_on_surface_2/include/CGAL/Arr_landmarks_point_location.h

@@ -262,7 +262,7 @@ protected:
    * \param new_vertex Output: if found a closer vertex to the query point.
    * \param cv_is_contained_in_seg Output: Whether cv is contained inside seg.
    * \return A handle to the halfedge (if no intersecting edge is found, the
-   *         function returns an ivalid halfedge handle).
+   *         function returns an invalid halfedge handle).
    */
   Halfedge_const_handle
   _intersection_with_ccb(Ccb_halfedge_const_circulator circ,