Predicates

Classes and functions that answer queries about a polygon mesh or its elements.

Classes
class	CGAL::Side_of_triangle_mesh< TriangleMesh, GeomTraits, VertexPointMap_ >
	This class provides an efficient point location functionality with respect to a domain bounded by one or several disjoint closed triangle meshes. More...

Functions
template<typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
bool	CGAL::Polygon_mesh_processing::is_degenerate_edge (typename boost::graph_traits< PolygonMesh >::edge_descriptor e, const PolygonMesh &pm, const NamedParameters &np=parameters::default_values())
	checks whether an edge is degenerate. More...
template<typename EdgeRange , typename TriangleMesh , typename OutputIterator , typename NamedParameters = CGAL::parameters::Default_named_parameters>
OutputIterator	CGAL::Polygon_mesh_processing::degenerate_edges (const EdgeRange &edges, const TriangleMesh &tm, OutputIterator out, const NamedParameters &np=parameters::default_values())
	collects the degenerate edges within a given range of edges. More...
template<typename TriangleMesh , typename OutputIterator , typename NamedParameters = CGAL::parameters::Default_named_parameters>
OutputIterator	CGAL::Polygon_mesh_processing::degenerate_edges (const TriangleMesh &tm, OutputIterator out, const NamedParameters &np=parameters::default_values())
	calls the function degenerate_edges() with the range: edges(tm). More...
template<typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>
bool	CGAL::Polygon_mesh_processing::is_degenerate_triangle_face (typename boost::graph_traits< TriangleMesh >::face_descriptor f, const TriangleMesh &tm, const NamedParameters &np=parameters::default_values())
	checks whether a triangle face is degenerate. More...
template<typename FaceRange , typename TriangleMesh , typename OutputIterator , typename NamedParameters = CGAL::parameters::Default_named_parameters>
OutputIterator	CGAL::Polygon_mesh_processing::degenerate_faces (const FaceRange &faces, const TriangleMesh &tm, OutputIterator out, const NamedParameters &np=parameters::default_values())
	collects the degenerate faces within a given range of faces. More...
template<typename TriangleMesh , typename OutputIterator , typename NamedParameters = CGAL::parameters::Default_named_parameters>
OutputIterator	CGAL::Polygon_mesh_processing::degenerate_faces (const TriangleMesh &tm, OutputIterator out, const NamedParameters &np=parameters::default_values())
	calls the function degenerate_faces() with the range: faces(tm). More...
template<typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>
boost::graph_traits< TriangleMesh >::halfedge_descriptor	CGAL::Polygon_mesh_processing::is_needle_triangle_face (typename boost::graph_traits< TriangleMesh >::face_descriptor f, const TriangleMesh &tm, const double threshold, const NamedParameters &np=parameters::default_values())
	checks whether a triangle face is needle. More...
template<typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>
boost::graph_traits< TriangleMesh >::halfedge_descriptor	CGAL::Polygon_mesh_processing::is_cap_triangle_face (typename boost::graph_traits< TriangleMesh >::face_descriptor f, const TriangleMesh &tm, const double threshold, const NamedParameters &np=parameters::default_values())
	checks whether a triangle face is a cap. More...

Function Documentation

degenerate_edges() [1/2]

template<typename EdgeRange , typename TriangleMesh , typename OutputIterator , typename NamedParameters = CGAL::parameters::Default_named_parameters>

OutputIterator CGAL::Polygon_mesh_processing::degenerate_edges	(	const EdgeRange &	edges,
		const TriangleMesh &	tm,
		OutputIterator	out,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/shape_predicates.h>

collects the degenerate edges within a given range of edges.

Template Parameters

EdgeRange	a model of Range with value type boost::graph_traits<TriangleMesh>::edge_descriptor
TriangleMesh	a model of HalfedgeGraph
NamedParameters	a sequence of Named Parameters

Parameters

edges	a subset of edges of tm
tm	a triangle mesh
out	an output iterator in which the degenerate edges are written
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

vertex_point_map a property map associating points to the vertices of tm Type: a class model of ReadablePropertyMap with boost::graph_traits<TriangleMesh>::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 TriangleMesh.
geom_traits an instance of a geometric traits class Type: The traits class must provide the nested type Point_3, and the nested functor Equal_3 to check whether two points are identical. Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the vertex point type.

See also

is_degenerate_edge()

degenerate_edges() [2/2]

template<typename TriangleMesh , typename OutputIterator , typename NamedParameters = CGAL::parameters::Default_named_parameters>

OutputIterator CGAL::Polygon_mesh_processing::degenerate_edges	(	const TriangleMesh &	tm,
		OutputIterator	out,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/shape_predicates.h>

calls the function degenerate_edges() with the range: edges(tm).

See the other overload for the comprehensive description of the parameters.

degenerate_faces() [1/2]

template<typename FaceRange , typename TriangleMesh , typename OutputIterator , typename NamedParameters = CGAL::parameters::Default_named_parameters>

OutputIterator CGAL::Polygon_mesh_processing::degenerate_faces	(	const FaceRange &	faces,
		const TriangleMesh &	tm,
		OutputIterator	out,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/shape_predicates.h>

collects the degenerate faces within a given range of faces.

Template Parameters

FaceRange	a model of Range with value type boost::graph_traits<TriangleMesh>::face_descriptor
TriangleMesh	a model of FaceGraph
NamedParameters	a sequence of Named Parameters

Parameters

faces	a subset of faces of tm
tm	a triangle mesh
out	an output iterator in which the degenerate faces are put
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

vertex_point_map a property map associating points to the vertices of tm Type: a class model of ReadablePropertyMap with boost::graph_traits<TriangleMesh>::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 TriangleMesh.
geom_traits an instance of a geometric traits class Type: The traits class must provide the nested type Point_3, and the nested functor Collinear_3 to check whether three points are collinear. Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the vertex point type.

See also

is_degenerate_triangle_face()

degenerate_faces() [2/2]

template<typename TriangleMesh , typename OutputIterator , typename NamedParameters = CGAL::parameters::Default_named_parameters>

OutputIterator CGAL::Polygon_mesh_processing::degenerate_faces	(	const TriangleMesh &	tm,
		OutputIterator	out,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/shape_predicates.h>

calls the function degenerate_faces() with the range: faces(tm).

See the other overload for the comprehensive description of the parameters.

is_cap_triangle_face()

template<typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>

boost::graph_traits<TriangleMesh>::halfedge_descriptor CGAL::Polygon_mesh_processing::is_cap_triangle_face	(	typename boost::graph_traits< TriangleMesh >::face_descriptor	f,
		const TriangleMesh &	tm,
		const double	threshold,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/shape_predicates.h>

checks whether a triangle face is a cap.

A triangle is said to be a cap if one of its angles is close to 180 degrees.

Template Parameters

TriangleMesh	a model of FaceGraph
NamedParameters	a sequence of Named Parameters

Parameters

f	a triangle face of tm
tm	triangle mesh containing f
threshold	the cosine of a minimum angle such that if f has an angle greater than this bound, it is a cap. The threshold is in range [-1 0] and corresponds to an angle between 90 and 180 degrees.
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

vertex_point_map a property map associating points to the vertices of tm Type: a class model of ReadablePropertyMap with boost::graph_traits<TriangleMesh>::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, tm)
geom_traits an instance of a geometric traits class Type: The traits class must provide the nested type Point_3, the nested functors Compute_squared_distance_3, Construct_vector_3, and Compute_scalar_product_3. Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the vertex point type.

Returns

the halfedge opposite of the largest angle if the face is a cap, and a null halfedge otherwise.

See also

is_needle_triangle_face()

remove_almost_degenerate_faces()

is_degenerate_edge()

template<typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>

bool CGAL::Polygon_mesh_processing::is_degenerate_edge	(	typename boost::graph_traits< PolygonMesh >::edge_descriptor	e,
		const PolygonMesh &	pm,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/shape_predicates.h>

checks whether an edge is degenerate.

An edge is considered degenerate if the geometric positions of its two extremities are identical.

Template Parameters

PolygonMesh	a model of HalfedgeGraph
NamedParameters	a sequence of Named Parameters

Parameters

e	an edge of pm
pm	polygon mesh containing e
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

vertex_point_map a property map associating points to the vertices of pm Type: a class model of ReadablePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, pm)
geom_traits an instance of a geometric traits class Type: The traits class must provide the nested type Point_3, and the nested functor Equal_3 to check whether two points are identical. Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the vertex point type.

Returns

true if the edge e is degenerate, false otherwise.

See also

degenerate_edges()

is_degenerate_triangle_face()

template<typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>

bool CGAL::Polygon_mesh_processing::is_degenerate_triangle_face	(	typename boost::graph_traits< TriangleMesh >::face_descriptor	f,
		const TriangleMesh &	tm,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/shape_predicates.h>

checks whether a triangle face is degenerate.

A triangle face is considered degenerate if the geometric positions of its vertices are collinear.

Template Parameters

TriangleMesh	a model of FaceGraph
NamedParameters	a sequence of Named Parameters

Parameters

f	a triangle face of tm
tm	a triangle mesh containing f
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

vertex_point_map a property map associating points to the vertices of tm Type: a class model of ReadablePropertyMap with boost::graph_traits<TriangleMesh>::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, tm)
geom_traits an instance of a geometric traits class Type: The traits class must provide the nested type Point_3, and the nested functor Collinear_3 to check whether three points are aligned. Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the vertex point type.

Returns

true if the face f is degenerate, false otherwise.

See also

degenerate_faces()

is_needle_triangle_face()

template<typename TriangleMesh , typename NamedParameters = parameters::Default_named_parameters>

boost::graph_traits<TriangleMesh>::halfedge_descriptor CGAL::Polygon_mesh_processing::is_needle_triangle_face	(	typename boost::graph_traits< TriangleMesh >::face_descriptor	f,
		const TriangleMesh &	tm,
		const double	threshold,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/shape_predicates.h>

checks whether a triangle face is needle.

A triangle is said to be a needle if its longest edge is much longer than its shortest edge.

Template Parameters

TriangleMesh	a model of FaceGraph
NamedParameters	a sequence of Named Parameters

Parameters

f	a triangle face of tm
tm	triangle mesh containing f
threshold	a bound on the ratio of the longest edge length and the shortest edge length
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

vertex_point_map a property map associating points to the vertices of tm Type: a class model of ReadablePropertyMap with boost::graph_traits<TriangleMesh>::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, tm)
geom_traits an instance of a geometric traits class Type: The traits class must provide the nested type FT, and the nested functor Compute_squared_distance_3. Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the vertex point type.

Returns

the shortest halfedge if the triangle face is a needle, and a null halfedge otherwise. If the face contains degenerate edges, a halfedge corresponding to one of these edges is returned.

See also

is_cap_triangle_face()

remove_almost_degenerate_faces()