Spelling corrections (#7624)

Spelling corrections `a e...` -> `an e...`

Algebraic_foundations/doc/Algebraic_foundations/Concepts/EuclideanRing.h

@@ -3,7 +3,7 @@
 \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
 \cgalConcept
 
-A model of `EuclideanRing` represents an euclidean ring (or Euclidean domain).
+A model of `EuclideanRing` represents a Euclidean ring (or Euclidean domain).
 It is an `UniqueFactorizationDomain` that affords a suitable notion of minimality of remainders
 such that given \f$ x\f$ and \f$ y \neq 0\f$ we obtain an (almost) unique solution to
 \f$ x = qy + r \f$ by demanding that a solution \f$ (q,r)\f$ is chosen to minimize \f$ r\f$.

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_pair_analysis_2.h

@@ -613,7 +613,7 @@ public:
     /*
      * \brief returns the indices of the <tt>i</tt>th event value
      *
-     * Returns a Event_indices <tt>(fg,ffy,ggy)</tt> such that
+     * Returns an `Event_indices` <tt>(fg,ffy,ggy)</tt> such that
      * the <tt>i</tt>th event root is the <tt>fg</tt>th root of the
      * resultant of \c f and \c g, the <tt>ffy</tt>th root of the
      * discriminant of \c f, and  the <tt>ggy</tt>th root of the

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Xy_coordinate_2.h

@@ -254,7 +254,7 @@ public:
     /*!
      * \brief y-coordinate of this point
      *
-     * Note: In general, this method results in a extremely large polynomial
+     * Note: In general, this method results in an extremely large polynomial
      * for the y-coordinate. It is recommended to use it carefully,
      * and using get_approximation_y() instead whenever approximations suffice.
      */

Arrangement_on_surface_2/include/CGAL/Arr_batched_point_location.h

@@ -105,7 +105,7 @@ locate(const Arrangement_on_surface_2<GeometryTraits_2, TopologyTraits>& arr,
     }
   }
 
-  // Obtain a extended traits-class object.
+  // Obtain an extended traits-class object.
   const Gt2* geom_traits = arr.geometry_traits();
 
   /* We would like to avoid copy construction of the geometry traits class.

Arrangement_on_surface_2/include/CGAL/Arr_circular_line_arc_traits_2.h

@@ -459,7 +459,7 @@ namespace CGAL {
   }
 
 
-  // a empty class used to have different types between Curve_2 and X_monotone_curve_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{
     struct Not_X_Monotone{};

Arrangement_on_surface_2/include/CGAL/Arr_overlay_2.h

@@ -231,7 +231,7 @@ overlay(const Arrangement_on_surface_2<GeometryTraitsA_2, TopologyTraitsA>& arr1
     xcvs_vec[i] = Ovl_x_monotone_curve_2(eit2->curve(), invalid_he1, he2);
   }
 
-  // Obtain a extended traits-class object and define the sweep-line visitor.
+  // Obtain an extended traits-class object and define the sweep-line visitor.
   const typename Arr_res::Traits_adaptor_2* traits_adaptor =
     arr.traits_adaptor();
 

Arrangement_on_surface_2/include/CGAL/Arr_point_location/Arr_batched_point_location_traits_2.h

@@ -411,7 +411,7 @@ public:
     }
   };
 
-  /*! Obtain a Equal_2 function object. */
+  /*! Obtain an `Equal_2` function object. */
   Equal_2 equal_2_object() const
   { return (Equal_2(m_base_traits->equal_2_object())); }
 

Arrangement_on_surface_2/include/CGAL/Arr_vertical_decomposition_2.h

@@ -109,7 +109,7 @@ decompose(const Arrangement_on_surface_2<GeometryTraits_2, TopologyTraits>& arr,
     }
   }
 
-  // Obtain a extended traits-class object.
+  // Obtain an extended traits-class object.
   const Gt2* geom_traits = arr.geometry_traits();
 
   /* We would like to avoid copy construction of the geometry traits class.

Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arrangement_on_surface_2_global.h

@@ -737,7 +737,7 @@ insert_non_intersecting_curve
 
   if (vh1 != nullptr) {
     if (vh2 != nullptr) {
-      // Both endpoints are associated with a existing vertices.
+      // Both endpoints are associated with existing vertices.
       // In this case insert_at_vertices() already returns a halfedge
       // directed from left to right.
       new_he = arr.insert_at_vertices(c,

Arrangement_on_surface_2/include/CGAL/IO/Arr_text_formatter.h

@@ -524,7 +524,7 @@ public:
 /*! \class
  * A class defining a textual (\ascii) input/output format for arrangements
  * that store auxiliary dat with all their DCEL records, as they are templated
- * by a extended DCEL class.
+ * by an extended DCEL class.
  */
 template <class Arrangement_>
 class Arr_extended_dcel_text_formatter :

Arrangement_on_surface_2/include/CGAL/Surface_sweep_2/Arr_basic_insertion_traits_2.h

@@ -440,7 +440,7 @@ public:
     { return (m_base_eq(p1.base(), p2.base())); }
   };
 
-  /*! Obtain a Equal_2 function object */
+  /*! Obtain an `Equal_2` function object */
   Equal_2 equal_2_object() const
   { return (Equal_2(m_base_traits->equal_2_object())); }
 

Arrangement_on_surface_2/include/CGAL/Surface_sweep_2/Arr_no_intersection_insertion_ss_visitor.h

@@ -23,7 +23,7 @@
  * This class can be further split into two, where one derives from the other,
  * such that the derived class handles the case of inserting non-intersecting
  * curves into a non-empty arrangement, and the base class handles the case of
- * inserting non-intersecting curves into a empty arrangement.
+ * inserting non-intersecting curves into an empty arrangement.
  */
 
 #include <CGAL/Surface_sweep_2/Arr_construction_ss_visitor.h>

Arrangement_on_surface_2/include/CGAL/Surface_sweep_2/Arr_overlay_traits_2.h

@@ -705,7 +705,7 @@ public:
     { return m_base_equal(xcv1.base(), xcv2.base()); }
   };
 
-  /*! Obtain a Equal_2 functor object. */
+  /*! Obtain an `Equal_2` functor object. */
   Equal_2 equal_2_object() const
   { return Equal_2(m_base_traits->equal_2_object()); }
 

BGL/test/BGL/test_Gwdwg.cpp

@@ -22,7 +22,7 @@ int main()
   Mesh mesh2(sm2);
   try {
     if( target( *(halfedges(mesh).first), mesh2) == *(vertices(mesh).first)){
-      CGAL_error_msg("The previous lie should have throw a exception");
+      CGAL_error_msg("The previous line should have throw an exception");
     }
   } catch(...){
     std::cerr << "we caught it" << std::endl;

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_traits_decorator.h

@@ -387,7 +387,7 @@ public:
     }
   };
 
-  /*! Get a Equal_2 functor object. */
+  /*! Get an `Equal_2` functor object. */
   Equal_2 equal_2_object() const
   {
     return Equal_2(m_base_traits->equal_2_object());

Circulator/doc/Circulator/CGAL/circulator.h

@@ -246,7 +246,7 @@ Circulator_from_iterator();
 /*!
 a circulator `c` initialized to refer to the element
 `*cur` in a range `[begin, end)`.
-The circulator `c` refers to a empty sequence
+The circulator `c` refers to an empty sequence
 if `begin==end`.
 
 */
@@ -255,7 +255,7 @@ const I& end, const I& cur = begin);
 
 /*!
 a copy of circulator `d` referring to the element `*cur`.
-The circulator `c` refers to a empty sequence
+The circulator `c` refers to an empty sequence
 if `d` does so.
 
 */

Cone_spanners_2/doc/Cone_spanners_2/Cone_spanners_2.txt

@@ -304,7 +304,7 @@ and `Construct_yao_graph_2` construct full Theta and Yao graphs. They also provi
 to compute Half Theta and Yao graphs. As mentioned in Section \ref sec_CBS_mydefinitions,
 only the edges for the odd or even cones are added to the graph in an Half Theta and Yao
 graph. To do so, the constructor of the functors provides a parameter of type
-`Cones_selected` which is a enumeration that contains the following possible values:
+`Cones_selected` which is an enumeration that contains the following possible values:
 `ALL_CONES`, `EVEN_CONES` and `ODD_CONES`. Users should include the
 `CGAL/Cone_spanners_enum_2.h` header file to use these enum values. The following are the
 examples on the functor constructions for Half Theta and Yao Graphs.

GraphicsView/include/CGAL/Qt/qglviewer_impl.h

@@ -194,7 +194,7 @@ This method is automatically called once, before the first call to paintGL().
 
 Overload init() instead of this method to modify viewer specific OpenGL state.
 
-If a 4.3 context could not be set, a ES 2.0 context will be used instead.
+If a 4.3 context could not be set, an ES 2.0 context will be used instead.
  \see `isOpenGL_4_3()`
 */
 CGAL_INLINE_FUNCTION

Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/CGAL/Hyperbolic_Delaunay_triangulation_2.h

@@ -208,7 +208,7 @@ public:
   /// @{
     /*!
       Inserts the point `p` in the triangulation.
-      If the point `p` coincides with a existing vertex, then the vertex is returned
+      If the point `p` coincides with an existing vertex, then the vertex is returned
       and the triangulation is not modified. The optional parameter `start` is used
       to initialize the location of `p`.
     */

Hyperbolic_triangulation_2/include/CGAL/Hyperbolic_Delaunay_triangulation_2.h

@@ -880,7 +880,7 @@ public:
 
   Face_handle locate(const Point& query, Locate_type& lt, int &li, Face_handle hint = Face_handle()) const
   {
-    // Perform an Euclidean location first and get close to the hyperbolic face containing the query point
+    // Perform a Euclidean location first and get close to the hyperbolic face containing the query point
     typename Base::Locate_type blt;
     Face_handle fh = Base::locate(query, blt, li, hint);
 
@@ -901,7 +901,7 @@ public:
 
     CGAL_assertion(!is_infinite(fh));
 
-    // This case corresponds to when the point is located on an Euclidean edge.
+    // This case corresponds to when the point is located on a Euclidean edge.
     if(lt == EDGE)
     {
       // Here because the call to `side_of_hyperbolic_triangle` might change `li`

Installation/cmake/modules/CGAL_SetupCGALDependencies.cmake

@@ -15,7 +15,7 @@
 # .. variable:: CGAL_DISABLE_GMP
 #
 #    If set, the `GMP` library will not be used. If
-#    :variable:`WITH_LEDA` is not used either, a efficient exact
+#    :variable:`WITH_LEDA` is not used either, an efficient exact
 #    number types are used by CGAL kernels for exact computation.
 #
 # .. variable:: WITH_LEDA

Installation/cmake/modules/FindTBB.cmake

@@ -84,7 +84,7 @@ function(tbb_extract_real_library library real_library)
   set(_elf_magic "7f454c46")
   file(READ ${library} _hex_data OFFSET 0 LIMIT 4 HEX)
   if(_hex_data STREQUAL _elf_magic)
-    #we have opened a elf binary so this is what
+    #we have opened an elf binary so this is what
     #we should link to
     set(${real_library} "${library}" PARENT_SCOPE)
     return()

Nef_S2/include/CGAL/Nef_S2/SM_io_parser.h

@@ -34,7 +34,7 @@ namespace CGAL {
 /*{\Manpage {SM_io_parser}{Decorator_}{IO of embedded maps}{IO}}*/
 
 /*{\Mdefinition An instance |\Mvar| of the data type |\Mname| is a
-decorator to provide input and output of a embedded map.  |\Mtype| is
+decorator to provide input and output of an embedded map.  |\Mtype| is
 generic with respect to the |Decorator_| parameter.  |Decorator_| has
 to be a decorator model of our |SM_decorator| concept.}*/
 

Number_types/include/CGAL/Sqrt_extension/Fraction_traits.h

@@ -41,9 +41,9 @@ namespace Intern{
  *
  *  Extensions provide suitable specializations of \c CGAL::Fraction_traits.
  *  They are decomposable iff their coefficient type is.
- *  The denominator \e d of a Extension \e ext is a low common multiple
+ *  The denominator \e d of an extension \e ext is a low common multiple
  *  (see \c CGAL::Fraction_traits::Common_factor for details) of the
- *  denominators of its coefficients.  The numerator is the Extenion
+ *  denominators of its coefficients.  The numerator is the extenion
  *  \e d*ext with a fraction-free coefficient type.
  *
  *  This works for nested Sqrt_extensions, too.

Polynomial/include/CGAL/Polynomial_traits_d.h

@@ -462,7 +462,7 @@ private:
 
 
   // We use our own Strict Weak Ordering predicate in order to avoid
-  // problems when calling sort for a Exponents_coeff_pair where the
+  // problems when calling sort for an `Exponents_coeff_pair` where the
   // coeff type has no comparison operators available.
 private:
   struct Compare_exponents_coeff_pair

Spatial_searching/doc/Spatial_searching/Concepts/OrthogonalDistance.h

@@ -4,7 +4,7 @@
 
 Requirements of an orthogonal distance class supporting incremental distance updates.
 To optimize distance computations transformed distances are used.
-E.g., for an Euclidean distance the transformed distance is the squared Euclidean distance.
+E.g., for a Euclidean distance the transformed distance is the squared Euclidean distance.
 
 \cgalRefines{GeneralDistance}
 

Spatial_searching/doc/Spatial_searching/Spatial_searching.txt

@@ -282,7 +282,7 @@ scenarios for different splitter types.
 
 \subsection Spatial_searchingExampleforKNeighborSearching Example for K Neighbor Searching
 
-The first example illustrates k neighbor searching with an Euclidean
+The first example illustrates k neighbor searching with a Euclidean
 distance and 2-dimensional points. The generated random
 data points are inserted in a search tree. We then initialize
 the k neighbor search object with the origin as query. Finally, we

Straight_skeleton_2/doc/Straight_skeleton_2/Concepts/PolygonOffsetBuilderTraits_2.h

@@ -41,7 +41,7 @@ Must provide
 `boost::optional<Point_2> operator()(const FT& t, const Segment_2& e0, const Segment_2& e1, const Trisegment_2_ptr& et) const`,
 
 which constructs the point of intersection of the lines obtained by offsetting
-the oriented lines given by `e0` and `e0` an Euclidean distance `t`.
+the oriented lines given by `e0` and `e0` a Euclidean distance `t`.
 
 If `e0` and `e1` are collinear, if `et` is not specified (`nullptr`), then the midpoint should be returned,
 otherwise, the event point of `et` should be returned.

Straight_skeleton_2/doc/Straight_skeleton_2/Concepts/StraightSkeletonBuilderTraits_2.h

@@ -67,8 +67,8 @@ Must provide
 `bool operator()( const Trisegment_2_ptr& tri_segment, boost::optional<FT> max_time ) const`,
 
 which determines if, given the three <I>oriented</I> lines defined by the three input edges,
-there exists an Euclidean distance `t >= 0` and `t <= max_time` for which the corresponding three
+there exists a Euclidean distance `t >= 0` and `t <= max_time` for which the corresponding three
-<I>offset lines at `t`</I> (parallel lines at an Euclidean distance of `t`) intersect in a single point.
+<I>offset lines at `t`</I> (parallel lines at a Euclidean distance of `t`) intersect in a single point.
 
 \pre Each edge in the triple must properly define an oriented line, that is, its points cannot be coincident.
 */

Straight_skeleton_2/doc/Straight_skeleton_2/Concepts/StraightSkeletonVertex_2.h

@@ -26,7 +26,7 @@ The type of the 2D point being the geometric embedding of the vertex
 typedef unspecified_type Point_2;
 
 /*!
-A model of the `FieldWithSqrt` concept representing the time of a vertex (an Euclidean distance)
+A model of the `FieldWithSqrt` concept representing the time of a vertex (a Euclidean distance)
 */
 typedef unspecified_type FT;
 

Straight_skeleton_2/include/CGAL/constructions/Straight_skeleton_cons_ftC2.h

@@ -328,7 +328,7 @@ construct_trisegment ( Segment_2_with_ID<K> const& e0,
 // If the lines do not intersect, for example, for collinear edges, or parallel edges but with the same orientation,
 // returns 0 (the actual distance is undefined in this case, but 0 is a useful return)
 //
-// NOTE: The result is a explicit rational number returned as a tuple (num,den); the caller must check that den!=0 manually
+// NOTE: The result is an explicit rational number returned as a tuple (num,den); the caller must check that den!=0 manually
 // (a predicate for instance should return indeterminate in this case)
 //
 // PRECONDITION: None of e0, e1 and e2 are collinear (but two of them can be parallel)
@@ -596,7 +596,7 @@ compute_artifical_isec_timeC2 ( Trisegment_2_ptr< Trisegment_2<K, Segment_2_with
 // returns the OFFSET DISTANCE (n/d) at which a line perpendicular to the collinear edge passing through
 // the degenerate seed point intersects the offset line of the non collinear edge
 //
-// NOTE: The result is a explicit rational number returned as a tuple (num,den); the caller must check that den!=0 manually
+// NOTE: The result is an explicit rational number returned as a tuple (num,den); the caller must check that den!=0 manually
 // (a predicate for instance should return indeterminate in this case)
 //
 // POSTCONDITION: In case of overflow an empty optional is returned.

Surface_mesh/include/CGAL/Surface_mesh/Properties.h

@@ -67,7 +67,7 @@ public:
     /// Return a deep copy of self.
     virtual Base_property_array* clone () const = 0;
 
-    /// Return a empty copy of self.
+    /// Return an empty copy of self.
     virtual Base_property_array* empty_clone () const = 0;
 
     /// Return the type_info of the property

Surface_mesh_parameterization/doc/Surface_mesh_parameterization/Surface_mesh_parameterization.txt

@@ -441,7 +441,7 @@ Orbifold-Tutte Planar Embedding was introduced by Aigerman and Lipman \cgalCite{
 and is a generalization of Tutte’s embedding to other topologies, and in particular
 spheres, which we consider here. The orbifold-Tutte embedding bijectively maps
 the original surface, that is required to be a topological ball, to a canonical,
-topologically equivalent, two-dimensional flat surface called an Euclidean orbifold.
+topologically equivalent, two-dimensional flat surface called a Euclidean orbifold.
 There are 17 Euclidean orbifolds, of which only the 4 sphere orbifolds are currently implemented
 in CGAL.
 

Surface_mesh_segmentation/include/CGAL/Surface_mesh_segmentation/internal/auxiliary/graph.h

@@ -661,7 +661,7 @@ private:
   DBlock<nodeptr>                *nodeptr_block;
 
   void        (*error_function)(const char
-                          *);        /* this function is called if a error occurs,
+                          *);        /* this function is called if an error occurs,
                                                                                    with a corresponding error message
                                                                                    (or exit(1) is called if it's nullptr) */
 

Surface_mesh_topology/doc/Surface_mesh_topology/CGAL/Curves_on_surface_topology.h

@@ -91,7 +91,7 @@ namespace Surface_mesh_topology {
     /// Number type of the weights.
     using Weight_t=double;
 
-    /// creates an Euclidean_length_weight_functor given a mesh.
+    /// creates a Euclidean_length_weight_functor given a mesh.
     Euclidean_length_weight_functor(const Mesh& m);
   };