mirror of https://github.com/CGAL/cgal
Minor ref manual improvements
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@ -66,7 +66,7 @@ public:
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introduces an empty triangulation, sets the center and radius of the sphere to `c` and `r` respectively,
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and inserts the point range `[first; beyond[`.
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\tparam PointOnSphereIterator must be a model of `InputIterator` with value type `Point_on_sphere_2`.
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\tparam PointOnSphereIterator must be a model of `InputIterator` with value type `Point_on_sphere_2` or `Point_3`.
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*/
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template <typename PointOnSphereIterator>
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Delaunay_triangulation_on_sphere_2(PointOnSphereIterator first, PointOnSphereIterator beyond,
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@ -78,7 +78,7 @@ public:
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\warning It is the user's responsability to ensure that the center and radius are set as intended in `gt`.
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\tparam PointOnSphereIterator must be a model of `InputIterator` with value type `Point_on_sphere_2`.
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\tparam PointOnSphereIterator must be a model of `InputIterator` with value type `Point_on_sphere_2` or `Point_3`.
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*/
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template <typename PointOnSphereIterator>
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Delaunay_triangulation_on_sphere_2(PointOnSphereIterator first, PointOnSphereIterator beyond,
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@ -183,6 +183,9 @@ public:
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/// Two different embeddings are possible: a "straight" embedding, using line segments living
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/// in Euclidean 3D sphere, and a "curved" embedding, using arc segments on the sphere.
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///
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/// Note that the following operations are constructions, which should be kept in mind in the choice
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/// of the underlying kernel.
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///
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/// @{
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// Straight
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@ -210,22 +213,30 @@ public:
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// Curved
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/*!
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returns the intersection of the dual of the face `f` and the sphere
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returns the intersection of the dual of the face `f` and the sphere.
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\pre `dimension() == 2` and `f` is a solid face.
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*/
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Point dual_on_sphere(const Face_handle f) const;
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/*!
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returns the arc of great circle with endpoints the circumcenters of the faces incident to the edge `e`.
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\pre `dimension() == 2` and `e` is not a ghost edge.
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*/
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Arc_on_sphere_2 dual_on_sphere(const Edge& e) const;
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/*!
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returns the arc of great circle with endpoints the circumcenters of the faces incident to the edge `*ec`.
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\pre `dimension() == 2` and `*ec` is not a ghost edge.
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*/
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Arc_on_sphere_2 dual_on_sphere(const Edge_circulator ec) const;
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/*!
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returns the arc of great circle with endpoints the circumcenters of the faces incident to the edge `*ei`.
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\pre `dimension() == 2` and `*ei` is not a ghost edge.
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*/
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Arc_on_sphere_2 dual_on_sphere(const All_edges_iterator ei) const;
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@ -25,7 +25,7 @@ using the relation above to ensure that a point being inserted is either marked
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and thus not inserted, or guaranteed to not be hidden upon insertion.
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\tparam LK a linear kernel type; it must be a model of `Kernel`.
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\tparam SK a spherical kernel type; it must be a model of `SphericalKernel`.
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\tparam SK a spherical kernel type; it must be a model of `SphericalKernel` refining `LK`.
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\cgalModels `DelaunayTriangulationOnSphereTraits_2`
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@ -31,7 +31,7 @@ are not ghost faces <em>solid faces</em>, and edges of such faces <em>solid edge
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\sa `CGAL::Delaunay_triangulation_on_sphere_2<Traits, TDS>`
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*/
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template< typename Traits, typename TDS >
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template <typename Traits, typename TDS>
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class Triangulation_on_sphere_2
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: public Triangulation_cw_ccw_2
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{
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@ -65,11 +65,6 @@ public:
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*/
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typedef Traits::Point_on_sphere_2 Point;
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/*!
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An arc of a great circle, used to represent a curved segment (Voronoi or Delaunay edge).
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*/
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typedef Traits::Arc_on_sphere_2 Arc_on_sphere_2;
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/*!
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The 3D point type.
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*/
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@ -85,6 +80,11 @@ public:
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*/
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typedef Traits::Triangle_3 Triangle_3;
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/*!
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An arc of a great circle, used to represent a curved segment (Voronoi or Delaunay edge).
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*/
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typedef Traits::Arc_on_sphere_2 Arc_on_sphere_2;
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public:
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/*!
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The vertex type.
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@ -258,12 +258,16 @@ public:
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/*!
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returns `true` if `f` is a ghost face, and `false` otherwise.
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\pre `dimension() == 2`
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*/
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bool is_ghost(const Face_handle f) const;
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/*!
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returns `true` if `e` is a ghost edge, that is if both its incident faces are ghost faces,
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and `false` otherwise.
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\pre `dimension() == 2`
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*/
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bool is_ghost(const Edge& e) const;
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@ -517,6 +521,8 @@ public:
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/*!
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Starts at an arbitrary face incident to the vertex `v`.
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Note that this may contain ghost faces.
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*/
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Face_circulator incident_faces(Vertex_handle v) const;
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@ -545,7 +551,7 @@ public:
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If `true` is returned, the edge with vertices `va` and `vb` is the edge `e=(fr,i)`
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where `fr` is a handle to the face incident to `e` and on the right side of `e` oriented from `va` to `vb`.
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*/
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bool is_edge(Vertex_handle va, Vertex_handle vb, Face_handle& fr, int & i);
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bool is_edge(Vertex_handle va, Vertex_handle vb, Face_handle& fr, int& i);
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/*!
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returns `true` if there exists a face (ghost or solid) having `v1`, `v2` and `v3` as vertices.
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@ -556,7 +562,7 @@ public:
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returns `true` if there exists a face (ghost or solid) having `v1`, `v2` and `v3` as vertices.
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If `true` is returned, `fr` is a handle to the face with `v1`, `v2` and `v3` as vertices.
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*/
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bool is_face(Vertex_handle v1, Vertex_handle v2, Vertex_handle v3, Face_handle &fr);
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bool is_face(Vertex_handle v1, Vertex_handle v2, Vertex_handle v3, Face_handle& fr);
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/// @}
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@ -7,8 +7,9 @@
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The concept `DelaunayTriangulationOnSphereTraits_2` describes the set of requirements
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to be fulfilled by any class used to instantiate the first template
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parameter of the class `CGAL::Delaunay_triangulation_on_sphere_2<Traits, Tds>`.
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This concept provides the types of the geometric primitives used in the
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triangulation and the function object types for the required predicates on those primitives.
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To the requirements listed within the concept `TriangulationOnSphereTraits_2`,
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this concept adds types and functors requirements related to build the dual on the sphere.
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\cgalHasModel `CGAL::Delaunay_triangulation_on_sphere_traits_2`
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\cgalHasModel `CGAL::Projection_on_sphere_traits_3`
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@ -25,7 +26,11 @@ public:
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/// `Point_on_sphere_2 operator()(Point_on_sphere_2 p, Point_on_sphere_2 q, Point_on_sphere_2 r)`
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///
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/// which returns the intersection of the dual of the face defined by the three points `p`, `q`, and `r`,
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/// and the sphere.
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/// and the sphere, on the positive side of the plane defined by `p`, `q`, and `r`. The dual of the face
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/// is the line orthogonal to the face, passing through the center of the smallest circumscribing sphere
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/// of the face.
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///
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/// \pre the center of the sphere is on the negative side of the plane defined by `p`, `q`, and `r`.
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///
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/// \note This type is only required for the computation of dual objects (Voronoi vertices and edges)
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/// and a dummy type can be used otherwise.
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@ -122,9 +122,10 @@ public:
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/// when traversing the great circle counterclockwise seen from the side of the plane
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/// of the great circle pointed by its <I>positive</I> normal vectors.
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///
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/// In this definition, we say that a normal vector \f$ (a,b,c)\f$ is <I>positive</I> if
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/// In this definition, we say that a normal vector \f$ (a,b,c)\f$ is <I>positive</I> if
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/// \f$ (a,b,c)>(0,0,0)\f$ (i.e.\ \f$ (a>0) || (a==0) \&\& (b>0) || (a==0)\&\&(b==0)\&\&(c>0)\f$).
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///
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/// \pre `p` and `q` are not diametrically opposed.
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typedef unspecified_type Construct_arc_on_sphere_2;
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/// Construction object. Must provide the operator:
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