CGAL Namespace Reference

Namespaces
	Euler

Classes
class	halfedge_graph_traits< Polyhedron_3< Traits > >
class	HalfedgeDS_face_max_base_with_id
	The class HalfedgeDS_face_max_base_with_id is a model of the HalfedgeDSFace concept. More...
class	HalfedgeDS_halfedge_max_base_with_id
	The class HalfedgeDS_halfedge_max_base_with_id is a model of the HalfedgeDSHalfedge concept. More...
class	HalfedgeDS_vertex_max_base_with_id
	The class HalfedgeDS_vertex_max_base_with_id is a model of the HalfedgeDSVertex concept. More...
class	Polyhedron_items_with_id_3
	The class Polyhedron_items_with_id_3 is a model of the PolyhedronItems_3 concept. More...
class	Triangulation_vertex_base_with_id_2
	The class Triangulation_vertex_base_with_id_2 is a model of the concept TriangulationVertexBase_2, the base vertex of a 2D-triangulation. More...
class	Halfedge_around_source_iterator
	A bidirectional iterator with value type boost::graph_traits<Graph>::halfedge_descriptor over all halfedges having the same vertex as source. More...
class	Halfedge_around_target_iterator
	A bidirectional iterator with value type boost::graph_traits<Graph>::halfedge_descriptor over all halfedges having the same vertex as target. More...
class	Halfedge_around_face_iterator
	A bidirectional iterator with value type boost::graph_traits<Graph>::halfedge_descriptor over all halfedges incident to the same face or border. More...
class	Halfedge_around_target_circulator
	A bidirectional circulator with value type boost::graph_traits<Graph>::halfedge_descriptor over all halfedges having the same vertex as target. More...
class	Halfedge_around_source_circulator
	A bidirectional circulator with value type boost::graph_traits<Graph>::halfedge_descriptor over all halfedges having the same vertex as source. More...
class	Face_around_target_circulator
	A bidirectional circulator with value type boost::graph_traits<Graph>::face_descriptor over all faces incident to the same vertex. More...
class	Halfedge_around_face_circulator
	A bidirectional circulator with value type boost::graph_traits<Graph>::halfedge_descriptor over all halfedges incident to the same face or border. More...
class	Face_around_face_iterator
	A bidirectional iterator with value type boost::graph_traits<Graph>::face_descriptor. More...
class	Face_around_face_circulator
	A bidirectional circulator with value type boost::graph_traits<Graph>::face_descriptor. More...
class	Face_around_target_iterator
class	Vertex_around_face_circulator
class	Vertex_around_face_iterator
	A bidirectional iterator with value type boost::graph_traits<Graph>::vertex_descriptor over all vertices incident to the same face or border. More...
class	Opposite_edge_around_face_iterator
class	Vertex_around_target_circulator
	A bidirectional circulator with value type boost::graph_traits<Graph>::vertex_descriptor over all vertices adjacent to the same vertex. More...
class	Vertex_around_target_iterator
class	Out_edge_iterator
class	In_edge_iterator

Enumerations
enum	vertex_is_border_t { vertex_is_border }
	The constant vertex_is_border is a property tag which refers to the property of a vertex of being a border vertex. More...
enum	vertex_point_t { vertex_point }
	The constant vertex_point is a property tag which refers to the geometric embedding property of a vertex of a HalfedgeGraph. More...

Functions
template<class HalfedgeDS_with_id >
void	set_halfedgeds_items_id (HalfedgeDS_with_id &hds)
	Given a CGAL::Polyhedron_3 or more generally a model of HalfedgeDS, for each simplex type (vertex, halfedge, facet) associates an index from 0 to the number of simplices minus 1 to each simplex of hds. More...
template<typename Graph >
Iterator_range < Halfedge_around_source_iterator < Graph > >	halfedges_around_source (typename boost::graph_traits< Graph >::halfedge_descriptor h, Graph &g)
	returns an iterator range over all halfedges with vertex source(h,g) as source.
template<typename Graph >
Iterator_range < Halfedge_around_source_iterator < Graph > >	halfedges_around_source (typename boost::graph_traits< Graph >::vertex_descriptor v, Graph &g)
	returns an iterator range over all halfedges with vertex v as source.
template<typename Graph >
Iterator_range < Halfedge_around_target_iterator < Graph > >	halfedges_around_target (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
	returns an iterator range over all halfedges with vertex target(h,g) as target.
template<typename Graph >
Iterator_range < Halfedge_around_target_iterator < Graph > >	halfedges_around_target (typename boost::graph_traits< Graph >::vertex_descriptor v, Graph &g)
	returns an iterator range over all halfedges with vertex v as target.
template<typename Graph >
Iterator_range < Halfedge_around_face_iterator < Graph > >	halfedges_around_face (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
	returns an iterator range over all halfedges incident to the same face or border as h.
template<typename Graph >
Iterator_range < Face_around_target_iterator < Graph > >	faces_around_target (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
	returns an iterator range over all faces around vertex target(h,g).
template<typename Graph >
Iterator_range < Face_around_face_iterator < Graph > >	faces_around_face (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
	returns an iterator range over all edge-adjacent faces to the same face face(h,g).
template<typename Graph >
Iterator_range < Opposite_edge_around_face_iterator < Graph > >	opposite_edges_around_face (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
template<typename Graph >
Iterator_range < Vertex_around_target_iterator < Graph > >	adjacent_vertices (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
template<typename Graph >
Iterator_range < Vertex_around_target_iterator < Graph > >	adjacent_vertices (typename boost::graph_traits< Graph >::vertex_descriptor v, const Graph &g)
template<typename Graph >
Iterator_range < Vertex_around_target_iterator < Graph > >	vertices_around_target (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
	returns an iterator range over all vertices adjacent to the vertex target(h,g).
template<typename Graph >
Iterator_range < Vertex_around_target_iterator < Graph > >	vertices_around_target (typename boost::graph_traits< Graph >::vertex_descriptor v, const Graph &g)
template<typename Graph >
Iterator_range < Vertex_around_face_iterator < Graph > >	vertices_around_face (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
	returns an iterator range over all vertices adjacent to the face face(h,g).
template<typename FaceGraph >
bool	is_border (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
	returns true if the halfedge hd is on a border.
template<typename FaceGraph >
bool	is_border_edge (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
	returns true if the halfedge hd or the opposite halfedge is on a border.
template<typename FaceGraph >
bool	is_border (typename boost::graph_traits< FaceGraph >::edge_descriptor ed, const FaceGraph &g)
	returns true if the edge e is on a border.
template<typename FaceGraph >
boost::optional< typename boost::graph_traits< FaceGraph > ::halfedge_descriptor >	is_border (typename boost::graph_traits< FaceGraph >::vertex_descriptor vd, const FaceGraph &g)
	returns a halfedge which is on a border and whose target vertex is vd, if such a halfedge exists.
template<typename FaceGraph >
bool	is_closed (const FaceGraph &g)
	returns true if there are no border edges.
template<typename FaceGraph >
bool	is_bivalent (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
	returns true if the target of hd has exactly two incident edges.
template<typename FaceGraph >
bool	is_bivalent_mesh (const FaceGraph &g)
	returns true if all vertices have exactly two incident edges.
template<typename FaceGraph >
bool	is_trivalent (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
	returns true if the target of hd has exactly three incident edges.
template<typename FaceGraph >
bool	is_trivalent_mesh (const FaceGraph &g)
	returns true if all vertices have exactly three incident edges.
template<typename FaceGraph >
bool	is_isolated_triangle (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
	returns true iff the connected component denoted by hd is a triangle. More...
template<typename FaceGraph >
bool	is_triangle (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
	returns true iff the face denoted by hd is a triangle, that is it has three incident halfedges.
template<typename FaceGraph >
bool	is_triangle_mesh (const FaceGraph &g)
	returns true if all faces are triangles.
template<typename FaceGraph >
bool	is_isolated_quad (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
	returns true iff the connected component denoted by hd is a quadrilateral.
template<typename FaceGraph >
bool	is_quad (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
	returns true iff the face denoted by hd is a quad, that is it has four incident halfedges.
template<typename FaceGraph >
bool	is_quad_mesh (const FaceGraph &g)
	returns true if all faces are quadrilaterals.
template<typename FaceGraph >
bool	is_tetrahedron (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
	returns true iff the connected component denoted by hd is a tetrahedron.
template<typename FaceGraph >
bool	is_valid_halfedge_descriptor (typename boost::graph_traits< FaceGraph >::halfedge_descriptor h, const FaceGraph &g)
template<typename FaceGraph >
bool	is_valid_vertex_descriptor (typename boost::graph_traits< FaceGraph >::vertex_descriptor v, const FaceGraph &g)
template<typename FaceGraph >
bool	is_valid_face_descriptor (typename boost::graph_traits< FaceGraph >::face_descriptor f, const FaceGraph &g)
template<typename FaceGraph >
bool	is_valid_polygon_mesh (const FaceGraph &g)
template<typename FaceGraph >
bool	is_hexahedron (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
	returns true iff the connected component denoted by hd is a hexahedron.
template<typename Graph , typename P >
boost::graph_traits< Graph > ::halfedge_descriptor	make_triangle (const P &p0, const P &p1, const P &p2, Graph &g)
	Creates an isolated triangle with border edges in g having p0, p1, and p2 as points and adds it to the graph g. More...
template<typename Graph , typename P >
boost::graph_traits< Graph > ::halfedge_descriptor	make_quad (const P &p0, const P &p1, const P &p2, const P &p3, Graph &g)
	Creates an isolated quad with border edges in g having p0, p1, p2, and p3 as points and adds it to the graph g. More...
template<typename Graph , typename P >
boost::graph_traits< Graph > ::halfedge_descriptor	make_hexahedron (const P &p0, const P &p1, const P &p2, const P &p3, const P &p4, const P &p5, const P &p6, const P &p7, Graph &g)
	Creates an isolated hexahedron in g having p0, p1, ... , and p7 as points and adds it to the graph g. More...
template<typename Graph , typename P >
boost::graph_traits< Graph > ::halfedge_descriptor	make_tetrahedron (const P &p0, const P &p1, const P &p2, const P &p3, Graph &g)
	Creates an isolated tetrahedron in g having p0, p1, p2, and p3 as points and adds it to the graph g. More...
template<typename HalfedgeGraph , typename PositionMap , typename NormalMap >
void	calculate_face_normals (const HalfedgeGraph &g, PositionMap pm, NormalMap nm)
template<typename HalfedgeGraph , typename Position , typename Normal , typename Boundary >
void	calculate_vertex_normals (const HalfedgeGraph &g, Position position_map, Normal normal_map, Boundary boundary_map)
template<typename HalfedgeGraph >
Kernel_traits< typename boost::property_traits < typename boost::property_map < HalfedgeGraph, CGAL::vertex_point_t > ::const_type >::value_type > ::Kernel::Triangle_3	triangle (const HalfedgeGraph &g, typename boost::graph_traits< HalfedgeGraph >::halfedge_descriptor h)
	Convenience function that calls triangle() with the property map obtained by get(CGAL::vertex_point, g). More...
template<typename HalfedgeGraph , typename PositionMap >
Kernel_traits< typename boost::property_traits < PositionMap >::value_type > ::Kernel::Triangle_3	triangle (const HalfedgeGraph &g, typename boost::graph_traits< HalfedgeGraph >::halfedge_descriptor h, const PositionMap &pm)
	triangle() returns a Triangle_3 constructed from the positions of the vertex_descriptors around the face incident to h in counter-clockwise direction. More...

Enumeration Type Documentation

enum CGAL::vertex_is_border_t

The constant vertex_is_border is a property tag which refers to the property of a vertex of being a border vertex.

vertex_is_border is an interior property, that is, a property map for vertex_is_border can be extracted from any model of a HalfedgeGraph using the Bgl PropertyGraph interface: boost::get(vertex_is_border,graph)

The Boolean flag that indicates if the vertex is a border can be directly accessed via: boost::get(vertex_is_border,graph,edge)

Enumerator
vertex_is_border

enum CGAL::vertex_point_t

The constant vertex_point is a property tag which refers to the geometric embedding property of a vertex of a HalfedgeGraph.

A vertex_point is an interior property, that is, a property map for a vertex_point can be extracted from any model of a HalfedgeGraph using the Bgl PropertyGraph interface: boost::get(vertex_point,graph)

A point of a vertex can be directly accessed via:

• boost::get(vertex_point,graph,vertex)
• boost::put(vertex_point,graph,vertex,newpoint)

Enumerator
vertex_point

Function Documentation

template<typename HalfedgeGraph >

Kernel_traits< typename boost::property_traits< typename boost::property_map< HalfedgeGraph, CGAL::vertex_point_t>::const_type >::value_type >::Kernel::Triangle_3 CGAL::triangle	(	const HalfedgeGraph &	g,
		typename boost::graph_traits< HalfedgeGraph >::halfedge_descriptor	h
	)

Convenience function that calls triangle() with the property map obtained by get(CGAL::vertex_point, g).

template<typename HalfedgeGraph , typename PositionMap >

Kernel_traits<typename boost::property_traits<PositionMap>::value_type>::Kernel::Triangle_3 CGAL::triangle	(	const HalfedgeGraph &	g,
		typename boost::graph_traits< HalfedgeGraph >::halfedge_descriptor	h,
		const PositionMap &	pm
	)

triangle() returns a Triangle_3 constructed from the positions of the vertex_descriptors around the face incident to h in counter-clockwise direction.

The Kernel of the returned Triangle_3 is the same as the Kernel of the value_type of the.

Precondition

The face incident to h is triangular.

Template Parameters

PositionMap	must be a model of ReadablePropertyMap. Its value_type must be a model of Kernel::Point_3
HalfedgeGraph	must be a model of HalfedgeGraph.

Parameters

g	The graph
h	The halfedge
pm	The map used to find the vertices of the triangle.