issue #8515 Spelling mistakes found checking en-GB to en-US

Spelling corrections, `en-GB` -> `en-US`

AABB_tree/include/CGAL/AABB_tree/internal/AABB_node.h

@@ -56,7 +56,7 @@ class AABB_node
   /**
    * @brief General traversal query
    * @param query the query
-   * @param traits the traversal traits that define the traversal behaviour
+   * @param traits the traversal traits that define the traversal behavior
    * @param nb_primitives the number of primitive
    *
    * General traversal query. The traits class allows using it for the various

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Bitstream_descartes.h

@@ -65,7 +65,7 @@ class Bitstream_descartes;
 
 
 /*
- * \brief Thrown whenever a non-specialised virtual member function is called
+ * \brief Thrown whenever a non-specialized virtual member function is called
  */
 class Virtual_method_exception {};
 
@@ -128,7 +128,7 @@ class Generic_descartes_rep
 
   /*!
    * Constructor computing an interval containing all real roots of \c f,
-   * and initialising the Bitstream Descartes tree
+   * and initializing the Bitstream Descartes tree
    */
   Generic_descartes_rep(Bitstream_descartes_type type,
                         Polynomial f,
@@ -170,7 +170,7 @@ class Generic_descartes_rep
 
   /*!
    * Constructor that copies the Bitstream tree given from outside
-   * and initialising the Bitstream Descartes tree
+   * and initializing the Bitstream Descartes tree
    * The tree must "fit" to the polynomial
    */
   Generic_descartes_rep(Bitstream_descartes_type type,
@@ -367,7 +367,7 @@ class Generic_descartes_rep
   /*!
    * \brief When does the isolation algorithm terminate?
    *
-   * This method must be specialised by derived classes
+   * This method must be specialized by derived classes
    */
   virtual bool termination_condition() {
     throw Virtual_method_exception();
@@ -378,7 +378,7 @@ class Generic_descartes_rep
    * \brief gives an opportunity to process the nodes after
    * the subdivision steps are finished
    *
-   * This method must be specialised by derived classes, but can
+   * This method must be specialized by derived classes, but can
    * remain empty in many cases.
    */
   virtual void process_nodes() {
@@ -389,7 +389,7 @@ class Generic_descartes_rep
   /*! \brief returns whether the \c i th root is definitely a simple root
    * of the isolated polynomial
    *
-   * Must be specialised by derived class
+   * Must be specialized by derived class
    */
   virtual bool is_certainly_simple_root(int) const {
     throw Virtual_method_exception();
@@ -399,7 +399,7 @@ class Generic_descartes_rep
   /*! \brief returns whether the \c i th root is definitely a multiple root
    * of the isolated polynomial
    *
-   * Must be specialised by derived class
+   * Must be specialized by derived class
    */
   virtual bool is_certainly_multiple_root(int) const {
     throw Virtual_method_exception();
@@ -1082,7 +1082,7 @@ class Vert_line_adapter_descartes_rep
  * variant of the Bitstream Descartes method: The Square_free_descartes_tag
  * starts the usual Bitstream method for square free integer polynomials.
  * With the M_k_descartes tag, it is able to handle one multiple root in
- * favourable situations, the Backshear_descartes_tag allows to isolate
+ * favorable situations, the Backshear_descartes_tag allows to isolate
  * even more complicated polynomials, if the multiple roots with even
  * multiplicity can be refined from outside. See the corresponding
  * constructors for more information.

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Bitstream_descartes_rndl_tree.h

@@ -865,7 +865,7 @@ class Bitstream_descartes_rndl_tree_rep {
     by trying randomly and checking.  This randomization means
     the same polynomial and same initial interval may give rise
     to different intervals each time this class is used.
-    As indicated in the paper, we favour subdivision ratios
+    As indicated in the paper, we favor subdivision ratios
     with a small denominator. Hence we first try denominator
     2 (subdivision at midpoint), then denominator 16, and
     only then the "proper" denominator prescribed by theory.

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_analysis_2.h

@@ -469,7 +469,7 @@ class Curve_analysis_2 : public ::CGAL::Handle_with_policy< Rep_ > {
      * (\c SHEAR_ONLY_AT_IRRATIONAL_STRATEGY)
      * is to \c shear the curve
      * if a degenerate situation is detected during the analysis,
-     * except at rational x-coordinates where the curve can be analysed
+     * except at rational x-coordinates where the curve can be analyzed
      * more directly. The analysis
      * is then performed in  the sheared system, and finally translated back
      * into the original system.

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/LRU_hashed_map.h

@@ -140,7 +140,7 @@ class LRU_hashed_map
     virtual ~LRU_hashed_map()
     {  }
 
-    /*! \brief implements cache-like behaviour of the map
+    /*! \brief implements cache-like behavior of the map
     *
     *  If the object is not in the map, it is constructed using \c Creator
     *  and added to the map
@@ -312,7 +312,7 @@ class LRU_hashed_map_with_kernel
     ~LRU_hashed_map_with_kernel()
     {  }
 
-    /*! \brief implements cache-like behaviour of the map
+    /*! \brief implements cache-like behavior of the map
     *
     *  If the object is not in the map, it is constructed using \c Creator
     *  and added to the map

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/exceptions.h

@@ -25,7 +25,7 @@ namespace CGAL {
     /*!
      * \brief Exception class for not sufficiently generic positions.
      *
-     * Must be thrown whenever a curve cannot be analysed because its position
+     * Must be thrown whenever a curve cannot be analyzed because its position
      * is not "good enough".
      */
     class Non_generic_position_exception {
@@ -40,7 +40,7 @@ namespace CGAL {
     /*!
      * \brief Exception class for not sufficiently generic positions.
      *
-     * Must be thrown whenever a curve cannot be analysed because its position
+     * Must be thrown whenever a curve cannot be analyzed because its position
      * is not "good enough".
      */
     template<typename Polynomial>

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/flags.h

@@ -76,7 +76,7 @@
 
 /**
  * If set, the curve and curve pair analysis are using specialized code
- * to analyse conic curves, i.e. curves of degree 2
+ * to analyze conic curves, i.e. curves of degree 2
  */
 #ifndef CGAL_ACK_USE_SPECIAL_TREATMENT_FOR_CONIX
 #define CGAL_ACK_USE_SPECIAL_TREATMENT_FOR_CONIX 0

Algebraic_kernel_d/test/Algebraic_kernel_d/Curve_analysis_2.cpp

@@ -330,7 +330,7 @@ template<typename Arithmetic_kernel> void test_routine() {
 #endif
     }
 
-    { // More tests...just analyse some curves and compute their segments
+    { // More tests...just analyze some curves and compute their segments
         Poly_int2 f = from_string<Poly_int2>("P[8(0,P[8(0,24)(1,-8)(2,-162)(3,204)(4,106)(5,-340)(6,240)(7,-72)(8,8)])(1,P[6(0,-60)(1,8)(2,304)(3,-400)(4,148)(5,8)(6,-8)])(2,P[6(0,18)(1,80)(2,-165)(3,-132)(4,367)(5,-212)(6,38)])(3,P[4(0,-30)(1,-136)(2,264)(3,-72)(4,-26)])(4,P[4(0,-15)(1,36)(2,89)(3,-144)(4,49)])(5,P[2(0,30)(1,-24)(2,-6)])(6,P[2(0,-6)(1,-28)(2,22)])(8,P[0(0,3)])]");
         Curve_analysis_2 curve= construct_curve_2(f);
 #if CGAL_ACK_DEBUG_FLAG

Alpha_shapes_3/include/CGAL/Alpha_shape_3.h

@@ -1638,7 +1638,7 @@ compute_edge_status( const Cell_handle& c,
   last=ccirc;
   while (is_infinite(ccirc) ) ++ccirc; //skip infinite incident cells
   alpha = (*ccirc).get_alpha();
-  as.set_alpha_mid(alpha); // initialise as.alpha_mid to alpha value of an incident cell
+  as.set_alpha_mid(alpha); // initialize as.alpha_mid to alpha value of an incident cell
   as.set_alpha_max(alpha); // same for as.alpha_max
   while (++ccirc != last)
   {

Alpha_shapes_3/test/Alpha_shapes_3/include/CGAL/_count_alpha.h

@@ -218,7 +218,7 @@ test_filtration(AS &A, bool verbose)
     typename AS::NT alpha;
     if(verbose) {
       std::cerr << std::endl;
-      std::cerr << "Analyse filtration " << std::endl;
+      std::cerr << "Analyze filtration " << std::endl;
     }
     for (; filtre_it != filtration.end(); filtre_it++) {
       if(assign(vertex, *filtre_it)) {

Arrangement_on_surface_2/demo/Arrangement_on_surface_2_earth/Aos.cpp

@@ -40,7 +40,7 @@ namespace {
     Flag(bool init) : v{ init } {}
   };
 
-  // EXTENDED AOS for analysing the arrangement
+  // EXTENDED AOS for analyzing the arrangement
   using Ext_dcel = CGAL::Arr_extended_dcel<Geom_traits, Flag, Flag, Flag>;
   using Ext_topol_traits =
     CGAL::Arr_spherical_topology_traits_2<Geom_traits, Ext_dcel>;

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Rational_arc_2.h

@@ -339,7 +339,7 @@ class _Base_rational_arc_2
     if (! valid)
       return;
 
-    // Analyze the behaviour of the rational function at x = -oo (the source).
+    // Analyze the behavior 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 @@ class _Base_rational_arc_2
     else // if (inf_s == ARR_INTERIOR)
       _ps = Point_2 (0, y0);
 
-    // Analyze the behaviour of the rational function at x = +oo (the target).
+    // Analyze the behavior of the rational function at x = +oo (the target).
     const Arr_parameter_space inf_t =
       _analyze_at_plus_infinity (_numer, _denom, y0);
 
@@ -735,7 +735,7 @@ class _Base_rational_arc_2
    */
   Self split_at_pole (const Algebraic& x0)
   {
-    // Analyze the behaviour of the function near the given pole.
+    // Analyze the behavior of the function near the given pole.
     const std::pair<CGAL::Sign, CGAL::Sign>  signs = _analyze_near_pole (x0);
     const CGAL::Sign    sign_left = signs.first;
     const CGAL::Sign    sign_right = signs.second;

Arrangement_on_surface_2/include/CGAL/Arr_rat_arc/Rational_arc_d_1.h

@@ -450,7 +450,7 @@ class Base_rational_arc_d_1
     _info = (_info | IS_DIRECTED_RIGHT);
 
 
-    // Analyze the behaviour of the rational function at x = -oo (the source).
+    // Analyze the behavior of the rational function at x = -oo (the source).
     Algebraic_real_1          y0;
     const Arr_parameter_space inf_s = _analyze_at_minus_infinity(P, Q, y0);
 
@@ -460,7 +460,7 @@ class Base_rational_arc_d_1
       _info = (_info | SRC_AT_Y_PLUS_INFTY);
     else // if (inf_s == ARR_INTERIOR)
       _ps = Algebraic_point_2();   //the point is a dummy
-    //Analyze the behaviour of the rational function at x = +oo (the target).
+    //Analyze the behavior of the rational function at x = +oo (the target).
     const Arr_parameter_space inf_t = _analyze_at_plus_infinity(P, Q, y0);
 
     if (inf_t == ARR_BOTTOM_BOUNDARY)
@@ -949,7 +949,7 @@ class Base_rational_arc_d_1
 
   Self split_at_pole(const Algebraic_real_1& x0)
   {
-    // Analyze the behaviour of the function near the given pole.
+    // Analyze the behavior of the function near the given pole.
     const std::pair<CGAL::Sign, CGAL::Sign>  signs = _analyze_near_pole(x0);
     const CGAL::Sign    sign_left = signs.first;
     const CGAL::Sign    sign_right = signs.second;

Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arr_traits_adaptor_2.h

@@ -1578,7 +1578,7 @@ class Arr_traits_basic_adaptor_2 : public ArrangementBasicTraits_ {
         return res;
       }
 
-      // otherwise: both ends have asymptotic behaviour
+      // otherwise: both ends have asymptotic behavior
       if (ps_y1 == ps_y2) { // need special y-comparison
         if (ce1 == ce2) { // both ends approach asymptote from one side
           Comparison_result res = m_self->compare_x_near_boundary_2_object()(xcv1, xcv2, ce2);

Arrangement_on_surface_2/include/CGAL/Curved_kernel_via_analysis_2/gfx/Curve_renderer_traits.h

@@ -24,7 +24,7 @@
  * \brief
  * defines class Curve_renderer_traits.
  *
- * provides specialisations of Curve_renderer_traits for different number
+ * provides specializations of Curve_renderer_traits for different number
  * types compatible with the curve renderer
 */
 

BGL/include/CGAL/boost/graph/Graph_with_descriptor_with_graph.h

@@ -733,7 +733,7 @@ struct Graph_with_descriptor_with_graph_property_map {
   }
 }; // class Graph_with_descriptor_with_graph_property_map
 
-//specialisation for lvaluepropertymaps
+//specialization for lvaluepropertymaps
 template <typename Graph, typename PM>
 struct Graph_with_descriptor_with_graph_property_map<Graph, PM, boost::lvalue_property_map_tag> {
 

Boolean_set_operations_2/doc/Boolean_set_operations_2/Boolean_set_operations_2.txt

@@ -542,13 +542,13 @@ boundary of each input (linear) polygon as a cyclic sequence of single
 (\f$x\f$-monotone) polylines. By default, `UsePolylines` is set to
 `CGAL::Tag_true`, which implies that the boundary of the each input
 (linear) polygon is treated as a cyclic sequence of (\f$x\f$-monotone)
-polylines. In most cases this behaviour is superior (that is, less
+polylines. In most cases this behavior is superior (that is, less
 time-consuming) because the number of events handled as part of the
 execution of the plane-sweep algorithm is reduced. In cases where the
 boundaries of the input polygons frequently intersect, treating them
 as polylines may become less efficient. In these cases substitute the
 `UsePolylines` template parameter with `CGAL::Tag_false` to restore
-the original behaviour (where the boundary of each input linear
+the original behavior (where the boundary of each input linear
 polygon is treated as a cyclic sequence of single \f$x\f$-monotone
 segments).
 

Bounding_volumes/doc/Bounding_volumes/CGAL/Min_sphere_annulus_d_traits_2.h

@@ -5,7 +5,7 @@ namespace CGAL {
 \ingroup PkgBoundingVolumesRef
 
 The class `Min_sphere_annulus_d_traits_2` is a traits class for the \f$ d\f$-dimensional
-optimisation algorithms using the two-dimensional \cgal kernel.
+optimization algorithms using the two-dimensional \cgal kernel.
 
 \tparam K  must bea model for `Kernel`.
 \tparam ET NT are models for `RingNumberType`. Their default type is `K::RT`.

Bounding_volumes/doc/Bounding_volumes/CGAL/Min_sphere_annulus_d_traits_3.h

@@ -5,7 +5,7 @@ namespace CGAL {
 \ingroup PkgBoundingVolumesRef
 
 The class `Min_sphere_annulus_d_traits_3` is a traits class for the \f$ d\f$-dimensional
-optimisation algorithms using the three-dimensional \cgal kernel.
+optimization algorithms using the three-dimensional \cgal kernel.
 
 \tparam K must be a model for `Kernel`.
 \tparam ET NT are models for `RingNumberType`. Their default type is `K::RT`.

Bounding_volumes/doc/Bounding_volumes/CGAL/Min_sphere_annulus_d_traits_d.h

@@ -5,7 +5,7 @@ namespace CGAL {
 \ingroup PkgBoundingVolumesRef
 
 The class `Min_sphere_annulus_d_traits_d` is a traits class for the \f$ d\f$-dimensional
-optimisation algorithms using the \f$ d\f$-dimensional \cgal kernel.
+optimization algorithms using the \f$ d\f$-dimensional \cgal kernel.
 
 \tparam K must be a model for `Kernel`.
 \tparam ET NT are models for `RingNumberType`. Their default type is `K::RT`.

Bounding_volumes/include/CGAL/Approximate_min_ellipsoid_d/Khachiyan_approximation.h

@@ -71,7 +71,7 @@ namespace CGAL {
     std::vector<const Point *> P;   // input points
     int n;                          // number of input points, i.e., P.size()
 
-    // This class comes in two flavours:
+    // This class comes in two flavors:
     //
     //  (i) When Embed is false, the input points are taken to be
     //    ordinary points in R^{d_P}, where d_P is the dimension of the

Bounding_volumes/include/CGAL/Min_sphere_of_spheres_d/Min_sphere_of_spheres_d_pair.h

@@ -33,7 +33,7 @@ namespace CGAL_MINIBALL_NAMESPACE {
     // they are convertible to double.
     // This is indeed the least invasive fix dropint the function that were
     // defined here and cause linkage bug.
-    // You can still have a behaviour of instantiating only if a type
+    // You can still have a behavior of instantiating only if a type
     // is convertibale to double (by using type_traits together with _if)
     // but until "the whole design should be overhauled at some point"
     // this is fine.

Bounding_volumes/include/CGAL/min_quadrilateral_2.h

@@ -376,7 +376,7 @@ min_rectangle_2(
 
   // quadruple of points defining the current rectangle
   ForwardIterator curr[4];
-  // initialised to the points defining the bounding box
+  // initialized to the points defining the bounding box
   convex_bounding_box_2(f, l, curr, t);
 
   // curr[i] can be advanced (cyclically) until it reaches limit[i]
@@ -482,7 +482,7 @@ min_parallelogram_2(ForwardIterator f,
 
   // quadruple of points defining the bounding box
   ForwardIterator curr[4];
-  // initialised to the points defining the bounding box
+  // initialized to the points defining the bounding box
   convex_bounding_box_2(first, l, curr, t);
 
 
@@ -659,7 +659,7 @@ min_strip_2(ForwardIterator f,
 
   // quadruple of points defining the bounding box
   ForwardIterator curr[4];
-  // initialised to the points defining the bounding box
+  // initialized to the points defining the bounding box
   convex_bounding_box_2(first, l, curr, t);
 
   ForwardIterator low = curr[0];

Bounding_volumes/include/CGAL/rectangular_3_center_2.h

@@ -135,7 +135,7 @@ rectangular_3_center_2_type1(
   rad = sdist(v(r, 2), v(r, 0));
   // init to prevent default constructor requirement
   Point bestpoint = *f;
-  // (initialisation avoids warning)
+  // (initialization avoids warning)
   unsigned int bestrun = 0;
 
   // two cases: top-left & bottom-right or top-right & bottom-left

Bounding_volumes/test/Bounding_volumes/min_sphere_test.cpp

@@ -11,7 +11,7 @@
 // release       : $CGAL_Revision: CGAL-wip $
 // release_date  : $CGAL_Date$
 //
-// chapter       : $CGAL_Chapter: Optimisation $
+// chapter       : $CGAL_Chapter: Geometric Optimization $
 // package       : $CGAL_Package: MinSphere $
 // file          : min_sphere_test.C
 // source        : web/Optimisation/Min_sphere_d.aw

Bounding_volumes/test/Bounding_volumes/min_sphere_traits_2_test.cpp

@@ -12,7 +12,7 @@
 // release       : $CGAL_Revision: CGAL-wip $
 // release_date  : $CGAL_Date$
 //
-// chapter       : $CGAL_Chapter: Optimisation $
+// chapter       : $CGAL_Chapter: Geometric Optimization $
 // package       : $CGAL_Package: MinSphere $
 // file          : min_sphere_traits_2_test.C
 // source        : web/Optimisation/Min_sphere_d.aw

Bounding_volumes/test/Bounding_volumes/min_sphere_traits_3_test.cpp

@@ -11,7 +11,7 @@
 // release       : $CGAL_Revision: CGAL-wip $
 // release_date  : $CGAL_Date$
 //
-// chapter       : $CGAL_Chapter: Optimisation $
+// chapter       : $CGAL_Chapter: Geometric Optimization $
 // package       : $CGAL_Package: MinSphere $
 // file          : min_sphere_traits_3_test.C
 // source        : web/Optimisation/Min_sphere_d.aw

Bounding_volumes/test/Bounding_volumes/test_Min_annulus_d.h

@@ -13,7 +13,7 @@
 //
 // file          : test/Min_annulus_d/test_Min_annulus_d.h
 // package       : $CGAL_Package: Min_annulus_d $
-// chapter       : Geometric Optimisation
+// chapter       : Geometric Optimization
 //
 // source        : web/Min_annulus_d.aw
 // revision      : $Id$