Fix various grammar issues

Algebraic_foundations/doc/Algebraic_foundations/CGAL/number_utils.h

@@ -22,7 +22,7 @@ namespace CGAL {
 \ingroup PkgAlgebraicFoundationsRef
 
 The template function `compare()` compares the first argument with respect to
-the second, i.e.\ it returns `CGAL::LARGER` if \f$ x\f$ is larger then \f$ y\f$.
+the second, i.e.\ it returns `CGAL::LARGER` if \f$ x\f$ is larger than \f$ y\f$.
 
 In case the argument types `NT1` and `NT2` differ,
 `compare` is performed with the semantic of the type determined via

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_analysis_2.h

@@ -2007,7 +2007,7 @@ public:
      *
      * For each status line at an event and each status line that represents
      * an interval, all y-coordinates are approximated such that their
-     * isolating interval has absolute size smaller then \c precision.
+     * isolating interval has absolute size smaller than \c precision.
      */
     void refine_all(Bound precision) {
 

Apollonius_graph_2/doc/Apollonius_graph_2/CGAL/Apollonius_graph_2.h

@@ -721,7 +721,7 @@ Checks the validity of the Apollonius graph. If `verbose` is
 is 0, only the data structure is validated. If `level` is 1, then
 both the data structure and the Apollonius graph are
 validated. Negative values of `level` always return true, and
-values greater then 1 are equivalent to `level` being 1.
+values greater than 1 are equivalent to `level` being 1.
 */
 bool is_valid(bool verbose = false, int level = 1);
 

Apollonius_graph_2/doc/Apollonius_graph_2/CGAL/Apollonius_graph_hierarchy_2.h

@@ -209,7 +209,7 @@ is validated, as well as the inter-level pointers. If `level` is
 1, then the data structure at all levels is validated, the inter-level
 pointers are validated and all levels of the Apollonius graph
 hierarchy are also validated. Negative values of `level` always
-return `true`, and values greater then 1 are equivalent to
+return `true`, and values greater than 1 are equivalent to
 `level` being 1.
 */
 bool is_valid(bool verbose = false, int level = 1) const;

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt

@@ -3728,7 +3728,7 @@ of the general ones; e.g., `insert()`.
 
 <LI>When the curves to be inserted into an arrangement are segments that
 are pairwise disjoint in their interior, it is more efficient to use
-the traits class `Arr_non_caching_segment_traits_2` rather then
+the traits class `Arr_non_caching_segment_traits_2` rather than
 the default one (`Arr_segment_traits_2`).
 
 If the segments may intersect each other, the default traits class

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_polycurve_traits_2.h

@@ -408,7 +408,7 @@ namespace CGAL {
       size_type number_of_subcurves() const;
 
       /*! Obtain the \f$ k\f$th subcurve of the polycurve.
-       * \pre \f$k\f$ is not greater then or equal to \f$n-1\f$, where
+       * \pre \f$k\f$ is not greater than or equal to \f$n-1\f$, where
        *      \f$n\f$ is the number of subcurves.
        */
       typename SubcurveTraits_2::X_monotone_curve_2

Arrangement_on_surface_2/include/CGAL/Arr_overlay_2.h

@@ -168,7 +168,7 @@ overlay(const Arrangement_on_surface_2<GeometryTraitsA_2, TopologyTraitsA>& arr1
   typedef Arrangement_on_surface_2<Rgt2, Rtt>                   Arr_res;
   typedef typename Arr_res::Allocator                           Allocator;
 
-  // some type assertions (not all, but better then nothing).
+  // some type assertions (not all, but better than nothing).
 #if !defined(CGAL_NO_ASSERTIONS)
   typedef typename Agt2::Point_2                                A_point;
   typedef typename Bgt2::Point_2                                B_point;

Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arrangement_on_surface_2_impl.h

@@ -4042,7 +4042,7 @@ _defines_outer_ccb_of_new_face(const DHalfedge* he_to,
     //   - No smallest has bin recorded so far, or
     //   - The current target vertex and the recorded vertex are the same and
     //       * The current curve is smaller than the recorded curve, or
-    //   - The current curve end is smaller then the recorded curve end.
+    //   - The current curve end is smaller than the recorded curve end.
     // smaller than its source, so we should check whether it is also smaller
     // Note that we compare the vertices lexicographically: first by the
     // indices, then by x, then by y.

GraphicsView/demo/L1_Voronoi_diagram_2/include/CGAL/L1_voronoi_traits_2.h

@@ -88,7 +88,7 @@ public:
 
     // Walk on the horizontal edge of the rectangle and then on the vertical.
 
-    // There is a chance that the width of the rectangle is smaller then the mid-dist.
+    // There is a chance that the width of the rectangle is smaller than the mid-dist.
     FT walk_x = (CGAL::min)(abs_x, dist);
     mid_x += sign_x * walk_x;
     dist -= walk_x;

GraphicsView/include/CGAL/Qt/keyFrameInterpolator_impl.h

@@ -320,7 +320,7 @@ qreal KeyFrameInterpolator::keyFrameTime(int index) const {
 /*! Returns the duration of the KeyFrameInterpolator path, expressed in seconds.
 
  Simply corresponds to lastTime() - firstTime(). Returns 0.0 if the path has
- less than 2 keyFrames. See also keyFrameTime(). */
+ fewer than 2 keyFrames. See also keyFrameTime(). */
 CGAL_INLINE_FUNCTION
 qreal KeyFrameInterpolator::duration() const {
   return lastTime() - firstTime();

Interpolation/TODO

@@ -181,6 +181,6 @@ long and hold to much information at once for a manual. For example:
 predicate you have to read at least twice before getting the meaning. 
 More, but simpler sentences would do a lot, especially as people look up 
 the manual on the web. Partly it just simply reads more like a
-scientific paper then like a manual.
+scientific paper than like a manual.
 
 ===================

Linear_cell_complex/include/CGAL/Linear_cell_complex_constructors.h

@@ -207,7 +207,7 @@ namespace CGAL {
          std::cerr << " " << std::endl;
          std::cerr << "Polyhedron_scan_OFF<Traits>::" << std::endl;
          std::cerr << "operator()(): input error: facet " << i
-         << " has less than 3 vertices." << std::endl;
+         << " has fewer than 3 vertices." << std::endl;
          }
          B.rollback();
          in.clear( std::ios::badbit);

Polygon/include/CGAL/Polygon_2/Polygon_2_algorithms_impl.h

@@ -519,7 +519,7 @@ Orientation orientation_2(ForwardIterator first,
   if (next == last)
     next = first;
 
-  // if the range [first,last) contains less than three points, then some
+  // if the range [first,last) contains fewer than three points, then some
   // of the points (prev,i,next) will coincide
 
   // return the orientation of the triple (prev,i,next)

Polygonal_surface_reconstruction/include/CGAL/internal/hypothesis.h

@@ -680,7 +680,7 @@ namespace CGAL {
                 template <typename Kernel>
                 void Hypothesis<Kernel>::compute_triplet_intersections() {
                         triplet_intersections_.clear();
-                        if (supporting_planes_.size() < 4) // no closed surface will be constructed from less than 4 planes
+                        if (supporting_planes_.size() < 4) // no closed surface will be constructed from fewer than 4 planes
                                 return;
 
                         for (std::size_t i = 0; i < supporting_planes_.size(); ++i) {

Polyhedron/demo/Polyhedron/Plugins/PMP/Hole_filling_plugin.cpp

@@ -939,7 +939,7 @@ void Polyhedron_demo_hole_filling_plugin::hole_filling_polyline_action() {
       continue;
     }
     if(it->size() < 4) { // no triangle, skip it (needs at least 3 + 1 repeat)
-      print_message("Warning: skipping polyline which has less than 4 points!");
+      print_message("Warning: skipping polyline which has fewer than 4 points!");
       continue;
     }
 

Polyhedron_IO/include/CGAL/IO/Polyhedron_scan_OFF.h

@@ -105,7 +105,7 @@ Polyhedron_scan_OFF<HDS>:: operator()( HDS& target) {
                 std::cerr << " " << std::endl;
                 std::cerr << "Polyhedron_scan_OFF<Traits>::" << std::endl;
                 std::cerr << "operator()(): input error: facet " << i
-                     << " has less than 3 vertices." << std::endl;
+                     << " has fewer than 3 vertices." << std::endl;
             }
             B.rollback();
             m_in.clear( std::ios::badbit);

STL_Extension/include/CGAL/Multiset.h

@@ -1196,7 +1196,7 @@ public:
 
   /*!
    * Split the tree such that all remaining objects are less than a given
-   * key, and all objects greater then (or equal to) this key form
+   * key, and all objects greater than (or equal to) this key form
    * a new output tree. [takes O(log n) operations]
    * \param key The split key.
    * \param comp_key A comparison functor for comparing keys and objects.

Spatial_sorting/doc/Spatial_sorting/CGAL/Multiscale_sort.h

@@ -8,7 +8,7 @@ Given a range of `n` points:
 <OL>
 <LI>it applies `Sort` on the last `(1 - ratio) * n` points,
 <LI>it recurses on the first `ratio * n` points,
-stopping when there are less than `threshold` points.
+stopping when there are fewer than `threshold` points.
 </OL>
 
 */

Spatial_sorting/include/CGAL/Hilbert_sort_median_d.h

@@ -114,7 +114,7 @@ public:
       current_dir = (current_dir +1) % _dimension;
     }while (current_dir != last_dir);
 
-    if ( end-begin < two_to_dim) return; // less than 2^dim points
+    if ( end-begin < two_to_dim) return; // fewer than 2^dim points
 
     /////////////start recursive calls
     last_dir = (direction + _dimension -1) % _dimension;

Straight_skeleton_2/doc/Straight_skeleton_2/Straight_skeleton_2.txt

@@ -266,7 +266,7 @@ If `Polygon_with_holes_2` is used, you can pass an instance of it directly to th
 
 \subsection Straight_skeleton_2CreateOffsetPolygonsfrom Create Offset Polygons from a Straight Skeleton
 
-If you already have a straight skeleton instance, the simpler way to generate offset polygons is to call `create_offset_polygons_2()` as shown in the next example, passing the desired offset and the straight skeleton. You can reuse the same skeleton to generate offsets at a different distance, which is recommended because producing the straight skeleton is much slower then generating offset polygons.
+If you already have a straight skeleton instance, the simpler way to generate offset polygons is to call `create_offset_polygons_2()` as shown in the next example, passing the desired offset and the straight skeleton. You can reuse the same skeleton to generate offsets at a different distance, which is recommended because producing the straight skeleton is much slower than generating offset polygons.
 
 \cgalExample{Straight_skeleton_2/Create_offset_polygons_2.cpp}
 

Straight_skeleton_2/include/CGAL/Straight_skeleton_builder_2.h

@@ -1325,7 +1325,7 @@ public:
       }
       else
       {
-        CGAL_STSKEL_BUILDER_TRACE(0,"Degenerate contour (less than 3 non-degenerate vertices).");
+        CGAL_STSKEL_BUILDER_TRACE(0,"Degenerate contour (fewer than 3 non-degenerate vertices).");
       }
     }
     else

Stream_support/include/CGAL/IO/write_3mf.h

@@ -243,7 +243,7 @@ bool write_points(const PointRange& points,
     NMR::lib3mf_release(pModel);
     return false;
   }
-  //add 3 demmy vertices to be sure to have a valid triangle and accept point sets with less than 3 vertices.
+  //add 3 demmy vertices to be sure to have a valid triangle and accept point sets with fewer than 3 vertices.
   for(int i = 0; i< 3; ++i)
     pVertices.push_back(tmf_internal::fnCreateVertex(0,0,0));
   for( auto point : points)

TDS_2/doc/TDS_2/TDS_2.txt

@@ -74,7 +74,7 @@ equivalent to a two-dimensional triangulated sphere.
 
 This rules extends to lower dimensional triangulation data structure
 arising in degenerate cases or when the triangulations
-have less than three vertices.
+have fewer than three vertices.
 A one dimensional triangulation structure maintains a set of vertices
 and edges which forms a ring
 topologically equivalent to a \f$ 1\f$-sphere.

Three/include/CGAL/Three/Scene_draw_interface.h

@@ -63,13 +63,13 @@ public:
    * \return true if the TextItem is visible. */
   virtual bool  testDisplayId(double x, double y, double z, CGAL::Three::Viewer_interface* viewer) = 0;
 
-  ///\brief displays all the vertices ids if there are less than max_textItems.
+  ///\brief displays all the vertices ids if there are fewer than max_textItems.
   virtual void printVertexIds() = 0;
-  ///\brief displays all the edges ids if there are less than max_textItems.
+  ///\brief displays all the edges ids if there are fewer than max_textItems.
   virtual void printEdgeIds() = 0;
-  ///\brief displays all the faces ids if there are less than max_textItems.
+  ///\brief displays all the faces ids if there are fewer than max_textItems.
   virtual void printFaceIds() = 0;
-  ///\brief displays all the primitive ids if there are less than max_textItems.
+  ///\brief displays all the primitive ids if there are fewer than max_textItems.
   virtual void printAllIds() = 0;
 
   //!\brief moves the camera orthogonally to the picked face.

Triangulation_2/doc/Triangulation_2/Triangulation_2.txt

@@ -165,7 +165,7 @@ Infinite vertex and infinite faces
 
 This extends to lower dimensional triangulations
 arising in degenerate cases or when the triangulations
-as less than three vertices.
+has fewer than three vertices.
 Including the infinite faces,
 a one dimensional triangulation
 is a ring of edges and vertices