Generic convenience functions for testing if an edge is a border edge, if a mesh is triangular, for conversion between models of different FaceGraph concepts, etc.

Most functions are in the header file <CGAL/boost/graph/helpers.h>

Functions
template<typename FaceGraph >
bool	CGAL::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	CGAL::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	CGAL::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 >	CGAL::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	CGAL::is_closed (const FaceGraph &g)
	returns `true` if there are no border edges.

template<typename FaceGraph >
bool	CGAL::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	CGAL::is_bivalent_mesh (const FaceGraph &g)
	returns `true` if all vertices have exactly two incident edges.

template<typename FaceGraph >
bool	CGAL::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	CGAL::is_trivalent_mesh (const FaceGraph &g)
	returns `true` if all vertices have exactly three incident edges.

template<typename FaceGraph >
bool	CGAL::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	CGAL::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	CGAL::is_triangle_mesh (const FaceGraph &g)
	returns `true` if all faces are triangles.

template<typename FaceGraph >
bool	CGAL::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	CGAL::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	CGAL::is_quad_mesh (const FaceGraph &g)
	returns `true` if all faces are quadrilaterals.

template<typename FaceGraph >
bool	CGAL::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 Graph >
bool	CGAL::is_valid_halfedge_graph (const Graph &g, bool verb=false)
	checks the integrity of `g`. More...

template<typename Graph >
bool	CGAL::is_valid_face_graph (const Graph &g, bool verb=false)
	checks the integrity of `g`. More...

template<typename Mesh >
bool	CGAL::is_valid_polygon_mesh (const Mesh &g, bool verb=false)
	checks the integrity of `g`. More...

template<typename FaceGraph >
bool	CGAL::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 FaceGraph >
void	CGAL::clear (FaceGraph &g)
	removes all vertices, faces and halfedges from a graph. More...

template<typename FaceGraph >
bool	CGAL::is_empty (const FaceGraph &g)
	checks whether the graph is empty, by checking that it does not contain any vertex. More...

template<typename Graph >
int	CGAL::vertex_index_in_face (const typename boost::graph_traits< Graph >::vertex_descriptor vd, const typename boost::graph_traits< Graph >::face_descriptor fd, const Graph &g)
	returns the number of calls to `next()` one has to apply to the halfedge `hd` for `source(hd, mesh) == vd` to be true, starting from `hd = halfedge(fd, tm)`. More...

template<typename Graph >
int	CGAL::halfedge_index_in_face (typename boost::graph_traits< Graph >::halfedge_descriptor he, const Graph &g)
	returns the number of calls to `next(hd, tm)` one has to apply to `hd` for `hd == he` to be true, starting from `hd = halfedge(face(he, tm), tm)`. More...

template<typename Graph , typename P >
boost::graph_traits< Graph >::halfedge_descriptor	CGAL::make_triangle (const P &p0, const P &p1, const P &p2, Graph &g)
	Creates an isolated triangle with its vertices initialized to `p0`, `p1` and `p2`, and adds it to the graph `g`. More...

template<typename Graph , typename P >
boost::graph_traits< Graph >::halfedge_descriptor	CGAL::make_quad (const P &p0, const P &p1, const P &p2, const P &p3, Graph &g)
	Creates an isolated quad with its vertices initialized to `p0`, `p1`, `p2`, and `p3`, and adds it to the graph `g`. More...

template<typename Graph , typename P >
boost::graph_traits< Graph >::halfedge_descriptor	CGAL::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 with its vertices initialized to `p0`, `p1`, ... , and `p7`, and adds it to the graph `g`. More...

template<typename Graph , typename P >
boost::graph_traits< Graph >::halfedge_descriptor	CGAL::make_tetrahedron (const P &p0, const P &p1, const P &p2, const P &p3, Graph &g)
	Creates an isolated tetrahedron with its vertices initialized to `p0`, `p1`, `p2`, and `p3`, and adds it to the graph `g`. More...

template<class Graph , class P >
boost::graph_traits< Graph >::halfedge_descriptor	CGAL::make_regular_prism (typename boost::graph_traits< Graph >::vertices_size_type nb_vertices, Graph &g, const P &base_center=P(0, 0, 0), typename CGAL::Kernel_traits< P >::Kernel::FT height=1.0, typename CGAL::Kernel_traits< P >::Kernel::FT radius=1.0, bool is_closed=true)
	Creates a triangulated regular prism, outward oriented, having `nb_vertices` vertices in each of its bases and adds it to the graph `g`. More...

template<class Graph , class P >
boost::graph_traits< Graph >::halfedge_descriptor	CGAL::make_pyramid (typename boost::graph_traits< Graph >::vertices_size_type nb_vertices, Graph &g, const P &base_center=P(0, 0, 0), typename CGAL::Kernel_traits< P >::Kernel::FT height=1.0, typename CGAL::Kernel_traits< P >::Kernel::FT radius=1.0, bool is_closed=true)
	Creates a pyramid, outward oriented, having `nb_vertices` vertices in its base and adds it to the graph `g`. More...

template<class Graph , class P >
boost::graph_traits< Graph >::halfedge_descriptor	CGAL::make_icosahedron (Graph &g, const P &center=P(0, 0, 0), typename CGAL::Kernel_traits< P >::Kernel::FT radius=1.0)
	Creates an icosahedron, outward oriented, centered in `center` and adds it to the graph `g`. More...

template<class Graph , class CoordinateFunctor >
boost::graph_traits< Graph >::halfedge_descriptor	CGAL::make_grid (typename boost::graph_traits< Graph >::vertices_size_type i, typename boost::graph_traits< Graph >::vertices_size_type j, Graph &g, const CoordinateFunctor &calculator, bool triangulated=false)
	Creates a row major ordered grid with `i` cells along the width and `j` cells along the height and adds it to the graph `g`. More...

template<typename SourceMesh , typename TargetMesh , typename NamedParameters1 , typename NamedParameters2 >
void	CGAL::copy_face_graph (const SourceMesh &sm, TargetMesh &tm, const NamedParameters1 &np1, const NamedParameters2 &np2)
	copies a source model of `FaceListGraph` into a target model of a `FaceListGraph`. More...

Function Documentation

◆ clear()

template<typename FaceGraph >

void CGAL::clear ( FaceGraph & g )

#include <CGAL/boost/graph/helpers.h>

removes all vertices, faces and halfedges from a graph.

Calls remove_edge(), remove_vertex(), and remove_face() for each edge, vertex or face.

If the graph has a member function clear(), it will be called instead.

Template Parameters

FaceGraph model of MutableHalfedgeGraph and MutableFaceGraph

Parameters

g	the graph to clear

◆ copy_face_graph()

template<typename SourceMesh , typename TargetMesh , typename NamedParameters1 , typename NamedParameters2 >

void CGAL::copy_face_graph	(	const SourceMesh &	sm,
		TargetMesh &	tm,
		const NamedParameters1 &	np1,
		const NamedParameters2 &	np2
	)

#include <CGAL/boost/graph/copy_face_graph.h>

copies a source model of FaceListGraph into a target model of a FaceListGraph.

OutputIterators can be provided to produce a mapping between source and target elements. The target graph is not cleared.

Template Parameters

SourceMesh	a model of `FaceListGraph`. The descriptor types `boost::graph_traits<SourceMesh>::vertex_descriptor` and `boost::graph_traits<SourceMesh>::face_descriptor` must be models of `Hashable`.
TargetMesh	a model of `FaceListGraph`
NamedParameters1	a sequence of Named Parameters
NamedParameters2	a sequence of Named Parameters

The types sm_vertex_descriptor and sm_face_descriptor must be models of the concept Hashable.

Parameters

sm	the source mesh
tm	the target mesh
np1	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

a property map associating points to the vertices of `sm` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<SourceMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, sm)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` must be available in `SourceMesh`.
an `OutputIterator` containing the pairs source-vertex, target-vertex. Type: a class model of `OutputIterator` accepting `std::pair<`boost::graph_traits<SourceMesh>::vertex_descriptor, `boost::graph_traits<TargetMesh>::vertex_descriptor>` Default: `Emptyset_iterator` Extra: If this parameter is given, then `vertex_to_vertex_map` cannot be used.
an `OutputIterator` containing the pairs source-halfedge, target-halfedge. Type: a class model of `OutputIterator` accepting `std::pair<`boost::graph_traits<SourceMesh>::halfedge_descriptor, `boost::graph_traits<TargetMesh>::halfedge_descriptor>` Default: `Emptyset_iterator` Extra: If this parameter is given, then `halfedge_to_halfedge_map` cannot be used.
an `OutputIterator` containing the pairs source-face, target-face. Type: a class model of `OutputIterator` accepting `std::pair<`boost::graph_traits<SourceMesh>::face_descriptor, `boost::graph_traits<TargetMesh>::face_descriptor>` Default: `Emptyset_iterator` Extra: If this parameter is given, then `face_to_face_map` cannot be used.
a property map storing for each vertex of a source mesh the corresponding vertex of another mesh Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<SourceMesh>::vertex_descriptor` as key type and `boost::graph_traits<TargetMesh>::vertex_descriptor` as value type. Default: unused Extra: A typical use case is mapping the vertices from a source mesh to its copy's after a `copy_face_graph()` operation.
a property map storing for each halfedge of a source mesh the corresponding halfedge of another mesh Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<SourceMesh>::halfedge_descriptor` as key type and `boost::graph_traits<TargetMesh>::halfedge_descriptor` as value type Default: unused Extra: A typical use case is mapping the halfedges from a source mesh to its copy's after a `copy_face_graph()`operation.
a property map storing for each face of a source mesh the corresponding face of another mesh Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<SourceMesh>::face_descriptor` as key type and `boost::graph_traits<TargetMesh>::face_descriptor` as value type Default: unused Extra: A typical use case is mapping the faces from a source mesh to its copy's after a `copy_face_graph()` operation

Parameters

np2	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

a property map associating points to the vertices of tm
Type: a class model of ReadWritePropertyMap with boost::graph_traits<TargetMesh>::vertex_descriptor as key type and Point_3 as value type
Default: boost::get(CGAL::vertex_point, tm)
Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in TargetMesh.

The points from sm to tm are converted using CGAL::Cartesian_converter<SourceKernel, TargetKernel>. SourceKernel and TargetKernel are deduced using CGAL::Kernel_traits from the value types of the vertex point maps.

Other properties are not copied.

Examples:: BGL_polyhedron_3/copy_polyhedron.cpp, BGL_surface_mesh/surface_mesh_partition.cpp, and Surface_mesh_segmentation/extract_segmentation_into_mesh_example.cpp.

◆ halfedge_index_in_face()

template<typename Graph >

int CGAL::halfedge_index_in_face	(	typename boost::graph_traits< Graph >::halfedge_descriptor	he,
		const Graph &	g
	)

#include <CGAL/boost/graph/helpers.h>

returns the number of calls to next(hd, tm) one has to apply to hd for hd == he to be true, starting from hd = halfedge(face(he, tm), tm).

Template Parameters

Graph a model of FaceGraph.

Parameters

he	a halfedge of `g` whose index in `face(he, tm)` is sought
g	an object of type `Graph`

◆ is_empty()

template<typename FaceGraph >

bool CGAL::is_empty ( const FaceGraph & g )

#include <CGAL/boost/graph/helpers.h>

checks whether the graph is empty, by checking that it does not contain any vertex.

Template Parameters

FaceGraph model of FaceGraph

Parameters

g	the graph to test

◆ is_isolated_triangle()

template<typename FaceGraph >

bool CGAL::is_isolated_triangle	(	typename boost::graph_traits< FaceGraph >::halfedge_descriptor	hd,
		const FaceGraph &	g
	)

#include <CGAL/boost/graph/helpers.h>

returns true iff the connected component denoted by hd is a triangle.

Precondition: g must be valid.

◆ is_valid_face_graph()

template<typename Graph >

bool CGAL::is_valid_face_graph	(	const Graph &	g,
		bool	verb = `false`
	)

#include <CGAL/boost/graph/helpers.h>

checks the integrity of g.

g is valid if it is a valid HalfedgeListGraph, if it follows the rules of the FaceListGraph concept, and all of its associations are reciprocal. For example, face(halfedge(f,g),g) must be f. calls is_valid_halfedge_graph()

Parameters

g	the `Graph` to test.
verb	: if `true`, the details of the check will be written in the standard output.

Template Parameters

<tt>Graph</tt> a model of FaceListGraph

Returns: true if g is valid, false otherwise.

See also: is_valid_halfedge_graph()

◆ is_valid_halfedge_graph()

template<typename Graph >

bool CGAL::is_valid_halfedge_graph	(	const Graph &	g,
		bool	verb = `false`
	)

#include <CGAL/boost/graph/helpers.h>

checks the integrity of g.

g is valid if it follows the rules of the HalfedgeListGraph concept, and all of its associations are reciprocal. For example, prev(next(h, g), g) must be h, and next(prev(h, g), g) must be h.

Parameters

g	the `Graph` to test.
verb	: if `true`, the details of the check will be written in the standard output.

Template Parameters

<tt>Graph</tt> a model of HalfedgeListGraph

Returns: true if g is valid, false otherwise.

◆ is_valid_polygon_mesh()

template<typename Mesh >

bool CGAL::is_valid_polygon_mesh	(	const Mesh &	g,
		bool	verb = `false`
	)

#include <CGAL/boost/graph/helpers.h>

checks the integrity of g.

g is valid if it is a valid FaceListGraph and it has distinct faces on each side of an edge. calls is_valid_face_graph().

Parameters

g	the `Mesh` to test.
verb	: if `true`, the details of the check will be written in the standard output.

Template Parameters

Mesh	a model of `FaceListGraph` and `HalfedgeListGraph`, and follows the definition of a PolygonMesh

Returns: true if g is valid, false otherwise.

See also: is_valid_face_graph(); is_valid_halfedge_graph()

Examples:: BGL_polyhedron_3/copy_polyhedron.cpp.

◆ make_grid()

template<class Graph , class CoordinateFunctor >

boost::graph_traits<Graph>::halfedge_descriptor CGAL::make_grid	(	typename boost::graph_traits< Graph >::vertices_size_type	i,
		typename boost::graph_traits< Graph >::vertices_size_type	j,
		Graph &	g,
		const CoordinateFunctor &	calculator,
		bool	triangulated = `false`
	)

#include <CGAL/boost/graph/generators.h>

Creates a row major ordered grid with i cells along the width and j cells along the height and adds it to the graph g.

An internal property map for CGAL::vertex_point_t must be available in Graph.

Parameters

i	the number of cells along the width.
j	the number of cells along the height.
g	the graph in which the grid will be created.
calculator	the functor that will assign coordinates to the grid vertices.
triangulated	decides if a cell is composed of one quad or two triangles. If `triangulated` is `true`, the diagonal of each cell is oriented from (0,0) to (1,1) in the cell coordinates.

Template Parameters

CoordinateFunctor a function object providing: Point_3 operator()(size_type I, size_type J), with Point_3 being the value_type of the internal property_map for CGAL::vertex_point_t and outputs an object of type boost::property_traits<boost::property_map<Graph,CGAL::vertex_point_t>::type>::value_type. It will be called with arguments (w, h), with w in [0..i] and h in [0..j].
Default: a point with positive integer coordinates (w, h, 0), with w in [0..i] and h in [0..j]

Returns: the non-border non-diagonal halfedge that has the target vertex associated with the first point of the grid (default is (0,0,0) ).

◆ make_hexahedron()

template<typename Graph , typename P >

boost::graph_traits<Graph>::halfedge_descriptor CGAL::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
	)

#include <CGAL/boost/graph/generators.h>

Creates an isolated hexahedron with its vertices initialized to p0, p1, ... , and p7, and adds it to the graph g.

Returns: the halfedge that has the target vertex associated with p0, in the face with the vertices with the points p0, p1, p2, and p3.

Examples:: BGL_surface_mesh/gwdwg.cpp.

◆ make_icosahedron()

template<class Graph , class P >

boost::graph_traits<Graph>::halfedge_descriptor CGAL::make_icosahedron	(	Graph &	g,
		const P &	center = `P(0,0,0)`,
		typename CGAL::Kernel_traits< P >::Kernel::FT	radius = `1.0`
	)

#include <CGAL/boost/graph/generators.h>

Creates an icosahedron, outward oriented, centered in center and adds it to the graph g.

Parameters

g	the graph in which the icosahedron will be created.
center	the center of the sphere in which the icosahedron is inscribed.
radius	the radius of the sphere in which the icosahedron is inscribed.

Returns: the halfedge that has the target vertex associated with the first point in the first face.

◆ make_pyramid()

template<class Graph , class P >

boost::graph_traits<Graph>::halfedge_descriptor CGAL::make_pyramid	(	typename boost::graph_traits< Graph >::vertices_size_type	nb_vertices,
		Graph &	g,
		const P &	base_center = `P(0,0,0)`,
		typename CGAL::Kernel_traits< P >::Kernel::FT	height = `1.0`,
		typename CGAL::Kernel_traits< P >::Kernel::FT	radius = `1.0`,
		bool	is_closed = `true`
	)

#include <CGAL/boost/graph/generators.h>

Creates a pyramid, outward oriented, having nb_vertices vertices in its base and adds it to the graph g.

If center is (0, 0, 0), then the first point of the base is (radius, 0, 0)

Parameters

nb_vertices	the number of vertices in the base. It must be greater than or equal to 3.
g	the graph in which the pyramid will be created
base_center	the center of the circle in which the base is inscribed.
height	the distance between the base and the apex.
radius	the radius of the circle in which the base is inscribed.
is_closed	determines if the base must be created or not. If `is_closed` is `true`, `center` is a vertex.

Returns: the halfedge that has the target vertex associated with the apex point in the first face.

◆ make_quad()

template<typename Graph , typename P >

boost::graph_traits<Graph>::halfedge_descriptor CGAL::make_quad	(	const P &	p0,
		const P &	p1,
		const P &	p2,
		const P &	p3,
		Graph &	g
	)

#include <CGAL/boost/graph/generators.h>

Creates an isolated quad with its vertices initialized to p0, p1, p2, and p3, and adds it to the graph g.

Returns: the non-border halfedge that has the target vertex associated with p0.

Examples:: BGL_surface_mesh/write_inp.cpp.

◆ make_regular_prism()

template<class Graph , class P >

boost::graph_traits<Graph>::halfedge_descriptor CGAL::make_regular_prism	(	typename boost::graph_traits< Graph >::vertices_size_type	nb_vertices,
		Graph &	g,
		const P &	base_center = `P(0,0,0)`,
		typename CGAL::Kernel_traits< P >::Kernel::FT	height = `1.0`,
		typename CGAL::Kernel_traits< P >::Kernel::FT	radius = `1.0`,
		bool	is_closed = `true`
	)

#include <CGAL/boost/graph/generators.h>

Creates a triangulated regular prism, outward oriented, having nb_vertices vertices in each of its bases and adds it to the graph g.

If center is (0, 0, 0), then the first point of the prism is (radius, height, 0)

Parameters

nb_vertices	the number of vertices per base. It must be greater than or equal to 3.
g	the graph in which the regular prism will be created.
base_center	the center of the circle in which the lower base is inscribed.
height	the distance between the two bases.
radius	the radius of the circles in which the bases are inscribed.
is_closed	determines if the bases must be created or not. If `is_closed` is `true`, `center` is a vertex.

Returns: the halfedge that has the target vertex associated with the first point in the first face.

◆ make_tetrahedron()

template<typename Graph , typename P >

boost::graph_traits<Graph>::halfedge_descriptor CGAL::make_tetrahedron	(	const P &	p0,
		const P &	p1,
		const P &	p2,
		const P &	p3,
		Graph &	g
	)

#include <CGAL/boost/graph/generators.h>

Creates an isolated tetrahedron with its vertices initialized to p0, p1, p2, and p3, and adds it to the graph g.

Returns: the halfedge that has the target vertex associated with p0, in the face with the vertices with the points p0, p1, and p2.

◆ make_triangle()

template<typename Graph , typename P >

boost::graph_traits<Graph>::halfedge_descriptor CGAL::make_triangle	(	const P &	p0,
		const P &	p1,
		const P &	p2,
		Graph &	g
	)

#include <CGAL/boost/graph/generators.h>

Creates an isolated triangle with its vertices initialized to p0, p1 and p2, and adds it to the graph g.

Returns: the non-border halfedge that has the target vertex associated with p0.

Examples:: Property_map/dynamic_properties.cpp.

◆ vertex_index_in_face()

template<typename Graph >

int CGAL::vertex_index_in_face	(	const typename boost::graph_traits< Graph >::vertex_descriptor	vd,
		const typename boost::graph_traits< Graph >::face_descriptor	fd,
		const Graph &	g
	)

#include <CGAL/boost/graph/helpers.h>

returns the number of calls to next() one has to apply to the halfedge hd for source(hd, mesh) == vd to be true, starting from hd = halfedge(fd, tm).

Template Parameters

Graph a model of FaceGraph

Parameters

vd	a vertex of `g` whose index is sought
fd	a face of `g` in which the index of `vd` is sought
g	a mesh of type `Graph`

Precondition: vd is a vertex of fd.

Functions

Function Documentation

◆ clear()

◆ copy_face_graph()

◆ halfedge_index_in_face()

◆ is_empty()

◆ is_isolated_triangle()

◆ is_valid_face_graph()

◆ is_valid_halfedge_graph()

◆ is_valid_polygon_mesh()

◆ make_grid()

◆ make_hexahedron()

◆ make_icosahedron()

◆ make_pyramid()

◆ make_quad()

◆ make_regular_prism()

◆ make_tetrahedron()

◆ make_triangle()

◆ vertex_index_in_face()