diff --git a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Boolean_set_operations_2.txt b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Boolean_set_operations_2.txt index adfd0e20e78..2a3b938bf2f 100644 --- a/Boolean_set_operations_2/doc/Boolean_set_operations_2/Boolean_set_operations_2.txt +++ b/Boolean_set_operations_2/doc/Boolean_set_operations_2/Boolean_set_operations_2.txt @@ -116,7 +116,7 @@ In our context, a polygon must uphold the following conditions:
  1. Closed Boundary - the polygon's outer boundary must be a connected sequence of curves, that start and end at the same vertex.
  2. Simplicity - the polygon must be simple. -
  3. Orientation - the polygon's outer boundary must be counter-clockwise oriented. +
  4. Orientation - the polygon's outer boundary must be counterclockwise oriented.
\subsection bso_ssecpolygon_with_holes_validation Conditions for Valid Polygons with Holes diff --git a/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h b/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h index a4069a1168a..7a4021cfafe 100644 --- a/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h +++ b/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h @@ -137,7 +137,7 @@ public: The direction of the first ray can be specified by the parameter initial_direction, which allows the first ray to start at any direction. - The remaining directions are calculated in counter-clockwise order. + The remaining directions are calculated in counterclockwise order. \param cone_number The number of cones \param initial_direction The direction of the first ray diff --git a/Cone_spanners_2/include/CGAL/Construct_theta_graph_2.h b/Cone_spanners_2/include/CGAL/Construct_theta_graph_2.h index 5a6a73299fb..cd71ce6d04d 100644 --- a/Cone_spanners_2/include/CGAL/Construct_theta_graph_2.h +++ b/Cone_spanners_2/include/CGAL/Construct_theta_graph_2.h @@ -169,7 +169,7 @@ protected: /* Construct edges in one cone bounded by two directions. \param cwBound The direction of the clockwise boundary of the cone. - \param ccwBound The direction of the counter-clockwise boundary. + \param ccwBound The direction of the counterclockwise boundary. \param g The Theta graph to be built. */ void add_edges_in_cone(const Direction_2& cwBound, const Direction_2& ccwBound, Graph_& g) { diff --git a/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h b/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h index 58090bdd506..640bb25a299 100644 --- a/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h +++ b/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h @@ -164,7 +164,7 @@ protected: /* Construct edges in one cone bounded by two directions. \param cwBound The direction of the clockwise boundary of the cone. - \param ccwBound The direction of the counter-clockwise boundary. + \param ccwBound The direction of the counterclockwise boundary. \param g The Yao graph to be built. */ void add_edges_in_cone(const Direction_2& cwBound, const Direction_2& ccwBound, Graph_& g) { diff --git a/Heat_method_3/doc/Heat_method_3/Heat_method_3.txt b/Heat_method_3/doc/Heat_method_3/Heat_method_3.txt index 99ad2fb4344..3c637a18bfd 100644 --- a/Heat_method_3/doc/Heat_method_3/Heat_method_3.txt +++ b/Heat_method_3/doc/Heat_method_3/Heat_method_3.txt @@ -149,7 +149,7 @@ Next, the gradient in a given triangle can be expressed as \f$\nabla u = \frac{1}{2 A_f} \sum_i u_i ( N \times e_i ) \f$ -where \f$A_f\f$ is the area of the triangle, \f$N\f$ is its outward unit normal, \f$e_i\f$ is the \f$i\f$th edge vector (oriented counter-clockwise), and \f$u_i\f$ is the value of \f$u\f$ at the opposing vertex. The integrated divergence associated with vertex \f$i\f$ can be written as +where \f$A_f\f$ is the area of the triangle, \f$N\f$ is its outward unit normal, \f$e_i\f$ is the \f$i\f$th edge vector (oriented counterclockwise), and \f$u_i\f$ is the value of \f$u\f$ at the opposing vertex. The integrated divergence associated with vertex \f$i\f$ can be written as \f$\nabla \cdot X = \frac{1}{2} \sum_j cot\theta_1 (e_1 \cdot X_j) + cot \theta_2 (e_2 \cdot X_j)\f$ diff --git a/Mesh_2/include/CGAL/Mesh_2/Refine_edges_visitor.h b/Mesh_2/include/CGAL/Mesh_2/Refine_edges_visitor.h index 216ed38c035..e6cbe9320d7 100644 --- a/Mesh_2/include/CGAL/Mesh_2/Refine_edges_visitor.h +++ b/Mesh_2/include/CGAL/Mesh_2/Refine_edges_visitor.h @@ -98,7 +98,7 @@ public: // set fh to the face at the right of [va,v] typename Tr::Face_circulator fc = tr.incident_faces(v, fh), fcbegin(fc); - // circulators are counter-clockwise, so we start at the right of + // circulators are counterclockwise, so we start at the right of // [va,v] do { if( !tr.is_infinite(fc) ) diff --git a/Nef_2/include/CGAL/Nef_2/PM_checker.h b/Nef_2/include/CGAL/Nef_2/PM_checker.h index 89d60c6cd7e..ae92226feb8 100644 --- a/Nef_2/include/CGAL/Nef_2/PM_checker.h +++ b/Nef_2/include/CGAL/Nef_2/PM_checker.h @@ -95,12 +95,12 @@ bool is_forward(Halfedge_const_handle e) const void check_order_preserving_embedding(Vertex_const_handle v) const; /*{\Mop checks if the embedding of the targets of the edges in -the adjacency list |A(v)| is counter-clockwise order-preserving with +the adjacency list |A(v)| is counterclockwise order-preserving with respect to the order of the edges in |A(v)|.}*/ void check_order_preserving_embedding() const; /*{\Mop checks if the embedding of all vertices of |P| is -counter-clockwise order-preserving with respect to the adjacency +counterclockwise order-preserving with respect to the adjacency list ordering of all vertices.}*/ void check_forward_prefix_condition(Vertex_const_handle v) const; diff --git a/Nef_S2/include/CGAL/Nef_S2/SM_checker.h b/Nef_S2/include/CGAL/Nef_S2/SM_checker.h index dd659105e70..c5e82ea46ca 100644 --- a/Nef_S2/include/CGAL/Nef_S2/SM_checker.h +++ b/Nef_S2/include/CGAL/Nef_S2/SM_checker.h @@ -79,12 +79,12 @@ bool is_forward(Halfedge_const_handle e) const void check_order_preserving_embedding(Vertex_const_handle v) const; /*{\Mop checks if the embedding of the targets of the edges in -the adjacency list |A(v)| is counter-clockwise order-preserving with +the adjacency list |A(v)| is counterclockwise order-preserving with respect to the order of the edges in |A(v)|.}*/ void check_order_preserving_embedding() const; /*{\Mop checks if the embedding of all vertices of |P| is -counter-clockwise order-preserving with respect to the adjacency +counterclockwise order-preserving with respect to the adjacency list ordering of all vertices.}*/ void check_forward_prefix_condition(Vertex_const_handle v) const; diff --git a/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/CGAL/Periodic_2_Delaunay_triangulation_2.h b/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/CGAL/Periodic_2_Delaunay_triangulation_2.h index 279f21dec86..e4c592a7ce7 100644 --- a/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/CGAL/Periodic_2_Delaunay_triangulation_2.h +++ b/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/CGAL/Periodic_2_Delaunay_triangulation_2.h @@ -212,7 +212,7 @@ public: contains `p`. It outputs in the container pointed to by `eit` the boundary of the zone in conflict with `p`. The boundary edges of the conflict zone are output in - counter-clockwise order and each edge is described through its + counterclockwise order and each edge is described through its incident face which is not in conflict with `p`. The function returns in a std::pair the resulting output iterators. \pre `start` is in conflict with `p` and `p` lies in the original domain `domain`. diff --git a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/CGAL/Hyperbolic_octagon_translation.h b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/CGAL/Hyperbolic_octagon_translation.h index 026bb2efaa2..add3cf68651 100644 --- a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/CGAL/Hyperbolic_octagon_translation.h +++ b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/CGAL/Hyperbolic_octagon_translation.h @@ -124,7 +124,7 @@ public: Comparison operator. Each translation \f$g\f$ of \f$\mathcal G\f$, when applied to the octagon \f$\mathcal D_O\f$, produces a copy of \f$\mathcal D_O\f$ labeled by the translation \f$g\f$. The copies of - \f$\mathcal D_O\f$ incident to \f$\mathcal D_O\f$ are naturally ordered counter-clockwise around + \f$\mathcal D_O\f$ incident to \f$\mathcal D_O\f$ are naturally ordered counterclockwise around \f$\mathcal D_O\f$. The comparison operator compares two translations based on the ordering of the copies of \f$\mathcal D_O\f$ that they produce. For more details, see Section \ref P4HT2_representation of the User manual. diff --git a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationFaceBase_2.h b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationFaceBase_2.h index 2ebf4a74bbd..d2f106c51a4 100644 --- a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationFaceBase_2.h +++ b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationFaceBase_2.h @@ -11,7 +11,7 @@ A refinement of the concept `TriangulationFaceBase_2` that adds an interface for At the base level, a face stores handles to its incident vertices and to its neighboring faces. Compare with Section \ref Section_2D_Triangulations_Software_Design of the 2D Triangulations -package. The vertices and neighbors are indexed counter-clockwise 0, 1, and 2. Neighbor `i` lies +package. The vertices and neighbors are indexed counterclockwise 0, 1, and 2. Neighbor `i` lies opposite to vertex `i`. For periodic hyperbolic triangulations, the face base class needs to store three hyperbolic diff --git a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/PackageDescription.txt b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/PackageDescription.txt index f5b7200ee7e..1384fcdc8af 100644 --- a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/PackageDescription.txt +++ b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/PackageDescription.txt @@ -54,7 +54,7 @@ Each face gives access to its three incident vertices and to its three adjacent to store additionally three hyperbolic translations. When applied to the three points stored in the vertices of the face, these translations produce the canonical representative of the face in the hyperbolic plane. -The three vertices of a face are indexed with 0, 1, and 2 in positive (counter-clockwise) orientation. The +The three vertices of a face are indexed with 0, 1, and 2 in positive (counterclockwise) orientation. The orientation of faces on the Bolza surface is defined as the orientation of their canonical representatives in the hyperbolic plane. diff --git a/Polygon_repair/doc/Polygon_repair/Polygon_repair.txt b/Polygon_repair/doc/Polygon_repair/Polygon_repair.txt index f837f18e9eb..34e7145d474 100644 --- a/Polygon_repair/doc/Polygon_repair/Polygon_repair.txt +++ b/Polygon_repair/doc/Polygon_repair/Polygon_repair.txt @@ -123,7 +123,7 @@ strict criteria: - Adjacent collinear edges touching at vertices of degree two are merged - The sequence of vertices representing a boundary starts from its lexicographically smallest vertex -- Outer boundaries are oriented counter-clockwise and inner boundaries are +- Outer boundaries are oriented counterclockwise and inner boundaries are oriented clockwise - The inner boundaries of a polygon with holes are stored in lexicographic order diff --git a/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Concepts/SegmentDelaunayGraphDataStructure_2.h b/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Concepts/SegmentDelaunayGraphDataStructure_2.h index 88e901da204..5ee787b77f3 100644 --- a/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Concepts/SegmentDelaunayGraphDataStructure_2.h +++ b/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Concepts/SegmentDelaunayGraphDataStructure_2.h @@ -21,7 +21,7 @@ reverses the action of the other. The join and split operations. Left to right: The vertex `v` is split into \f$ v_1\f$ and \f$ v_2\f$. The faces \f$ f\f$ and \f$ g\f$ are inserted after \f$ f_1\f$ and \f$ f_2\f$, respectively, in the -counter-clockwise sense. The vertices \f$ v_1\f$, \f$ v_2\f$ and the +counterclockwise sense. The vertices \f$ v_1\f$, \f$ v_2\f$ and the faces \f$ f\f$ and \f$ g\f$ are returned as a `boost::tuple` in that order. Right to left: The edge `(f,i)` is collapsed, and thus the vertices \f$ v_1\f$ and \f$ v_2\f$ are joined. The vertex `v` is @@ -60,7 +60,7 @@ Vertex_handle join_vertices(Face_handle f, int i); /*! Splits the vertex `v` into two vertices `v1` and `v2`. The common faces `f` and `g` of `v1` and -`v2` are created after (in the counter-clockwise sense) the +`v2` are created after (in the counterclockwise sense) the faces `f1` and `f2`. The 4-tuple `(v1,v2,f,g)` is returned (see \cgalFigureRef{figsdgdssplitjoin}). */ diff --git a/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Concepts/SegmentDelaunayGraphTraits_2.h b/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Concepts/SegmentDelaunayGraphTraits_2.h index 933124e25d1..ecb00ed9b23 100644 --- a/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Concepts/SegmentDelaunayGraphTraits_2.h +++ b/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Concepts/SegmentDelaunayGraphTraits_2.h @@ -206,7 +206,7 @@ returns the sign of the distance of `q` from the Voronoi circle of `s1`, `s2`, `s3` (the Voronoi circle of three sites `s1`, `s2`, `s3` is a circle co-tangent to all three sites, that touches them in that order as we walk on its circumference -in the counter-clockwise sense). +in the counterclockwise sense). \pre the Voronoi circle of `s1`, `s2`, `s3` must exist. Must also provide `Sign operator()(Site_2 s1, Site_2 s2, Site_2 q)`, which returns the sign of the distance of diff --git a/Segment_Delaunay_graph_Linf_2/doc/Segment_Delaunay_graph_Linf_2/Concepts/SegmentDelaunayGraphLinfTraits_2.h b/Segment_Delaunay_graph_Linf_2/doc/Segment_Delaunay_graph_Linf_2/Concepts/SegmentDelaunayGraphLinfTraits_2.h index 62c9a4f8f5b..bbef09563ef 100644 --- a/Segment_Delaunay_graph_Linf_2/doc/Segment_Delaunay_graph_Linf_2/Concepts/SegmentDelaunayGraphLinfTraits_2.h +++ b/Segment_Delaunay_graph_Linf_2/doc/Segment_Delaunay_graph_Linf_2/Concepts/SegmentDelaunayGraphLinfTraits_2.h @@ -78,7 +78,7 @@ segment Voronoi diagram. /*! A constructor for the point \f$ v \f$ at which the three \f$ L_{\infty} \f$ bisectors between the three given sites `s1`, `s2` and `s3` intersect -and the regions of `s1`, `s2` and `s3` appear in the counter-clockwise order +and the regions of `s1`, `s2` and `s3` appear in the counterclockwise order `s1`, `s2`, `s3` around \f$ v\f$. Point \f$ v \f$ is equidistant @@ -116,7 +116,7 @@ of `s1`, `s2`, `s3`. The \f$ L_{\infty} \f$ Voronoi square of three sites `s1`, `s2`, `s3` is an axis-parallel square which is passing through all three sites and touches them in the `s1`, `s2`, `s3` -order as we walk on the square in the counter-clockwise sense. +order as we walk on the square in the counterclockwise sense. The center of the square is at the intersection of the three \f$ L_{\infty} \f$ bisectors of the three sites. @@ -256,7 +256,7 @@ Since CGAL segments have also an orientation, we also orient For an oriented segment \f$ s \f$, we orient its \f$L_{\infty}\f$-perpendicular lines so that the lines' orientation is closest to the following orientation: -the orientation of \f$ s \f$ rotated counter-clockwise by +the orientation of \f$ s \f$ rotated counterclockwise by \f$ \pi/2 \f$. Let `s` be a segment and `p` a point contained in its interior. diff --git a/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Polygon_offset_builder_2.h b/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Polygon_offset_builder_2.h index 65cbf5cbb71..939e0817de3 100644 --- a/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Polygon_offset_builder_2.h +++ b/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Polygon_offset_builder_2.h @@ -70,7 +70,7 @@ For any given input polygon, its offset polygons at a certain distance are compo This method returns all such contours in an unspecified order and with no parental relationship between them (that is why it is called `construct_offset_contours()` and not `construct_offset_polygons()`). -Those offset contours in the resulting sequence which are oriented counter-clockwise are outer contours +Those offset contours in the resulting sequence which are oriented counterclockwise are outer contours and those oriented clockwise are holes. It is up to the user to match each hole to its parent in order to reconstruct the parent-hole relationship of the conceptual output. It is sufficient to test each hole against each parent as there won't be a hole inside a hole, a parent inside any other contour, diff --git a/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Straight_skeleton_2.h b/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Straight_skeleton_2.h index 727da054561..9b19a44c449 100644 --- a/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Straight_skeleton_2.h +++ b/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Straight_skeleton_2.h @@ -96,10 +96,10 @@ of the straight skeleton HDS, such border halfedges are oriented such that their outwards the polygon. Therefore, the opposite halfedge of any border halfedge is oriented such that its left side faces inward the polygon. -This \cgal package requires the input polygon (with holes) to be weakly simple and oriented counter-clockwise. +This \cgal package requires the input polygon (with holes) to be weakly simple and oriented counterclockwise. The skeleton halfedges are oriented such that their left side faces inward the region they bound. -That is, the vertices (both contour and skeleton) of a face are circulated in counter-clockwise order. +That is, the vertices (both contour and skeleton) of a face are circulated in counterclockwise order. There is one and only one contour halfedge incident upon any face. The contours of the input polygon are traced by the border halfedges of the HDS (those facing outward), @@ -115,7 +115,7 @@ Thus, the 2 opposite halfedges of a skeleton edge link the edge to its 2 definin Starting from any border contour halfedge, circulating the structure walks through border counter halfedges and traces the vertices of the polygon's contours (in opposite order). -Starting from any non-border but contour halfedge, circulating the structure walks counter-clockwise +Starting from any non-border but contour halfedge, circulating the structure walks counterclockwise around the face corresponding to that contour halfedge. The vertices around a face always describe a non-convex weakly simple polygon. diff --git a/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Straight_skeleton_builder_2.h b/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Straight_skeleton_builder_2.h index 1331edf5f38..2226c78af51 100644 --- a/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Straight_skeleton_builder_2.h +++ b/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Straight_skeleton_builder_2.h @@ -169,7 +169,7 @@ whose straight skeleton is to be built. Each contour must be input in turn starting with the outer contour and following with the holes (if any). The order of the holes is unimportant but the outer contour must be entered first. -The outer contour must be oriented counter-clockwise while holes must be oriented clockwise. +The outer contour must be oriented counterclockwise while holes must be oriented clockwise. It is an error to enter more than one outer contour, to enter a hole which is not inside the outer contour, to enter a hole that is inside another hole, or to enter a contour which crosses diff --git a/Straight_skeleton_2/doc/Straight_skeleton_2/Straight_skeleton_2.txt b/Straight_skeleton_2/doc/Straight_skeleton_2/Straight_skeleton_2.txt index 9686bdf2e97..1c183705474 100644 --- a/Straight_skeleton_2/doc/Straight_skeleton_2/Straight_skeleton_2.txt +++ b/Straight_skeleton_2/doc/Straight_skeleton_2/Straight_skeleton_2.txt @@ -175,7 +175,7 @@ for each boundary that does not contain the defining contour edge of its inciden \cgalFigureCaptionBegin{SLSArtificial} A polygon with four holes (black) and its straight skeleton (red). -Three artificial bisectors (green) are added in a post-processing step to recover the simply-connected +Three artificial bisectors (green) are added in a postprocessing step to recover the simply-connected property for the straight skeleton face (gray) of the rightmost vertical contour edge. \cgalFigureCaptionEnd @@ -454,7 +454,7 @@ To construct the straight skeleton of a polygon the user must:
  • Instantiate the straight skeleton builder.
  • Enter one contour at a time, starting from the outer contour, via the method `Straight_skeleton_builder_2::enter_contour()`. The input polygon must be - weakly simple and counter-clockwise oriented (see the definitions at the beginning + weakly simple and counterclockwise oriented (see the definitions at the beginning of this chapter). Collinear edges are allowed. The insertion order of each hole is unimportant but the outer contour must be entered first.
  • Call `Straight_skeleton_builder_2::construct_skeleton()` once all the contours @@ -480,18 +480,18 @@ The resulting sequence of offset contours can contain both outer and inner conto However, this algorithm returns a sequence of contours in arbitrary order and there is no indication whatsoever of the parental relationship between inner and outer contours. -On the other hand, each outer contour is counter-clockwise oriented while each hole is clockwise-oriented. +On the other hand, each outer contour is counterclockwise oriented while each hole is clockwise-oriented. And since offset contours do form simple polygons, it is guaranteed that no hole will be inside another hole, no outer contour will be inside any other contour, and each hole will be inside exactly 1 outer contour. Parental relationships are not automatically reconstructed by this algorithm because -this relation is not directly given by the input polygon and must be done as a post-processing +this relation is not directly given by the input polygon and must be done as a postprocessing step. The function `CGAL::arrange_offset_polygons_2()` can be used to do that efficiently. A user can reconstruct the parental relationships as a post processing operation by testing each inner contour (which is identified by being clockwise) against each outer contour (identified -as being counter-clockwise) for insideness. +as being counterclockwise) for insideness. This algorithm requires exact predicates but not exact constructions. Therefore, the `Exact_predicates_inexact_constructions_kernel` should be used. diff --git a/Stream_support/doc/Stream_support/File_formats/Supported_file_formats.txt b/Stream_support/doc/Stream_support/File_formats/Supported_file_formats.txt index 8f9a99e0877..84a23f73a67 100644 --- a/Stream_support/doc/Stream_support/File_formats/Supported_file_formats.txt +++ b/Stream_support/doc/Stream_support/File_formats/Supported_file_formats.txt @@ -106,7 +106,7 @@ which offers combinatorial repairing while reading bad inputs. \section IOStreamOBJ Wavefront Advanced Visualizer Object Format (OBJ) The `OBJ` file format, using the file extension `.obj`, is a simple \ascii data format that represents 3D geometry. -Vertices are stored in a counter-clockwise order by default, making explicit declaration of face normals unnecessary. +Vertices are stored in a counterclockwise order by default, making explicit declaration of face normals unnecessary. A precise specification of the format is available here. diff --git a/TDS_2/doc/TDS_2/CGAL/Triangulation_data_structure_2.h b/TDS_2/doc/TDS_2/CGAL/Triangulation_data_structure_2.h index 5c076eed68f..327d5c1b910 100644 --- a/TDS_2/doc/TDS_2/CGAL/Triangulation_data_structure_2.h +++ b/TDS_2/doc/TDS_2/CGAL/Triangulation_data_structure_2.h @@ -134,7 +134,7 @@ Vertex_handle join_vertices(Edges_circulator ec); /*! splits the vertex `v` into two vertices `v1` and `v2`. -The common faces `f` and `g` of `v1` and `v2` are created after (in the counter-clockwise sense) the +The common faces `f` and `g` of `v1` and `v2` are created after (in the counterclockwise sense) the faces `f1` and `f2`. The 4-tuple `(v1,v2,f,g)` is returned (see Fig. \ref figtdssplitjoin). \pre `dimension()` must be equal to `2`, `f1` and `f2` must be different from `Face_handle()` and `v` must be a vertex of both `f1` and `f2`. diff --git a/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_Delaunay_triangulation_2.h b/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_Delaunay_triangulation_2.h index d0c228c5880..3ba65d37b27 100644 --- a/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_Delaunay_triangulation_2.h +++ b/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_Delaunay_triangulation_2.h @@ -305,7 +305,7 @@ outputs the boundary edges of the conflict zone of point `p` into an output iter This functions outputs in the container pointed to by `eit`, the boundary of the zone in conflict with `p`. The boundary edges -of the conflict zone are output in counter-clockwise order +of the conflict zone are output in counterclockwise order and each edge is described through the incident face which is not in conflict with `p`. The function returns the resulting output iterator. diff --git a/Triangulation_2/doc/Triangulation_2/CGAL/Delaunay_triangulation_2.h b/Triangulation_2/doc/Triangulation_2/CGAL/Delaunay_triangulation_2.h index ec43542e73f..6779a7eb4df 100644 --- a/Triangulation_2/doc/Triangulation_2/CGAL/Delaunay_triangulation_2.h +++ b/Triangulation_2/doc/Triangulation_2/CGAL/Delaunay_triangulation_2.h @@ -221,7 +221,7 @@ i. e., the faces whose circumcircle contains `p`. It outputs in the container pointed to by `eit` the the boundary of the zone in conflict with `p`. The boundary edges -of the conflict zone are output in counter-clockwise order +of the conflict zone are output in counterclockwise order and each edge is described through its incident face which is not in conflict with `p`. The function returns in a `std::pair` the resulting output iterators. diff --git a/Triangulation_2/doc/Triangulation_2/CGAL/Regular_triangulation_2.h b/Triangulation_2/doc/Triangulation_2/CGAL/Regular_triangulation_2.h index 2c9bf5384ae..7005ff7f1b0 100644 --- a/Triangulation_2/doc/Triangulation_2/CGAL/Regular_triangulation_2.h +++ b/Triangulation_2/doc/Triangulation_2/CGAL/Regular_triangulation_2.h @@ -295,7 +295,7 @@ have negative power wrt. `p`. It outputs in the container pointed to by `eit` the boundary of the zone in conflict with `p`. It inserts the vertices that would be hidden by `p` into the container pointed to by `vit`. The boundary edges of -the conflict zone are output in counter-clockwise order and each edge +the conflict zone are output in counterclockwise order and each edge is described through its incident face which is not in conflict with `p`. The function returns in a `CGAL::Triple` the resulting output iterators. diff --git a/Triangulation_on_hyperbolic_surface_2/doc/Triangulation_on_hyperbolic_surface_2/Triangulation_on_hyperbolic_surface_2.txt b/Triangulation_on_hyperbolic_surface_2/doc/Triangulation_on_hyperbolic_surface_2/Triangulation_on_hyperbolic_surface_2.txt index 17c1cac5374..781793b956d 100644 --- a/Triangulation_on_hyperbolic_surface_2/doc/Triangulation_on_hyperbolic_surface_2/Triangulation_on_hyperbolic_surface_2.txt +++ b/Triangulation_on_hyperbolic_surface_2/doc/Triangulation_on_hyperbolic_surface_2/Triangulation_on_hyperbolic_surface_2.txt @@ -60,9 +60,9 @@ In order to perform fast and exact computations with a fundamental domain, every \subsection Subsection_Hyperbolic_Surface_Triangulations_DS_Domains Data Structure for Domains -We represent every fundamental domain as a polygon in the PoincarĂ© disk, given by the list of its vertices in counter-clockwise order and by the list of its side pairings. +We represent every fundamental domain as a polygon in the PoincarĂ© disk, given by the list of its vertices in counterclockwise order and by the list of its side pairings. This package can generate a random convex fundamental domain \f$ P \f$ of a surface of genus two, with eight vertices \f$ z_0, \dots, z_7 \in \mathbb{C} \f$. -The vertices and the sides are in counter-clockwise order, the side between \f$ z_0 \f$ and \f$ z_1 \f$ is \f$ A \f$, the side between \f$ z_4 \f$ and \f$ z_5 \f$ is \f$ \overline{A} \f$ and so on as on \cgalFigureRef{THS2-octagon}. The side pairings are \f$ A \f$ with \f$\overline{A} \f$ , \f$ B \f$ with \f$ \overline{B} \f$ , \f$ C \f$ with \f$ \overline{C} \f$ and \f$ D \f$ with \f$ \overline{D} \f$. +The vertices and the sides are in counterclockwise order, the side between \f$ z_0 \f$ and \f$ z_1 \f$ is \f$ A \f$, the side between \f$ z_4 \f$ and \f$ z_5 \f$ is \f$ \overline{A} \f$ and so on as on \cgalFigureRef{THS2-octagon}. The side pairings are \f$ A \f$ with \f$\overline{A} \f$ , \f$ B \f$ with \f$ \overline{B} \f$ , \f$ C \f$ with \f$ \overline{C} \f$ and \f$ D \f$ with \f$ \overline{D} \f$. These octagons are symmetric, i.e. \f$ z_i = -z_{i+4} \f$ for every \f$ i \f$, where indices are modulo eight. Such octagons are described in \cgalCite{aigon2005hyperbolic}. diff --git a/Triangulation_on_hyperbolic_surface_2/include/CGAL/Triangulation_on_hyperbolic_surface_2.h b/Triangulation_on_hyperbolic_surface_2/include/CGAL/Triangulation_on_hyperbolic_surface_2.h index c592f4d17a2..4112762f5cd 100644 --- a/Triangulation_on_hyperbolic_surface_2/include/CGAL/Triangulation_on_hyperbolic_surface_2.h +++ b/Triangulation_on_hyperbolic_surface_2/include/CGAL/Triangulation_on_hyperbolic_surface_2.h @@ -35,7 +35,7 @@ namespace CGAL { Represents a geodesic triangulation of a closed orientable hyperbolic surface. The triangulation is stored as combinatorial map decorated with one cross-ratio per edge. It is also possible to specify an anchor for the triangulation. An anchor consists in 1) a dart of the combinatorial map, belonging by definition to a vertex V and a triangle T, together with -2) three points A,B,C in the hyperbolic plane. The points A,B,C are the three vertices in counter-clockwise order of a triangle. This triangle is a lift +2) three points A,B,C in the hyperbolic plane. The points A,B,C are the three vertices in counterclockwise order of a triangle. This triangle is a lift of T, and A is a lift of V. */ template diff --git a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_on_sphere_2.h b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_on_sphere_2.h index b8dd0b0678c..72908531f39 100644 --- a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_on_sphere_2.h +++ b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_on_sphere_2.h @@ -157,7 +157,7 @@ public: This function outputs in the container pointed to by `fit` the faces which are in conflict with point `p`, i. e., the faces whose circumcircle contains `p`. It outputs in the container pointed to by `eit` the boundary of the zone in conflict with `p`. The boundary edges of the conflict zone - are output in counter-clockwise order and each edge is described through its incident face + are output in counterclockwise order and each edge is described through its incident face which is not in conflict with `p`. The function returns in a `std::pair` the resulting output iterators. \tparam OutItFaces is an output iterator with `Face_handle` as value type. diff --git a/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h b/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h index fd7bfd719a8..a2bf487b43f 100644 --- a/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h +++ b/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h @@ -806,7 +806,7 @@ private: } //for face query: traverse the face to get all edges - //and sort vertices in counter-clockwise order. + //and sort vertices in counterclockwise order. void input_face (Face_const_handle fh) const { Ccb_halfedge_const_circulator curr = fh->outer_ccb(); @@ -840,7 +840,7 @@ private: } } //for vertex or edge query: traverse the face to get all edges - //and sort vertices in counter-clockwise order. + //and sort vertices in counterclockwise order. void input_face (Face_const_handle fh, EHs& good_edges, Arrangement_2& bbox) const