Functions to compute lengths of edges and borders, areas of faces and patches, as well as volumes of closed meshes.

Functions
template<typename PolygonMesh , typename NamedParameters >
FT	CGAL::Polygon_mesh_processing::edge_length (typename boost::graph_traits< PolygonMesh >::halfedge_descriptor h, const PolygonMesh &pmesh, const NamedParameters &np)
	computes the length of an edge of a given polygon mesh. More...

template<typename PolygonMesh , typename NamedParameters >
FT	CGAL::Polygon_mesh_processing::face_border_length (typename boost::graph_traits< PolygonMesh >::halfedge_descriptor h, const PolygonMesh &pmesh, const NamedParameters &np)
	computes the length of the border polyline that contains a given halfedge. More...

template<typename PolygonMesh , typename NamedParameters >
std::pair< halfedge_descriptor, FT >	CGAL::Polygon_mesh_processing::longest_border (const PolygonMesh &pmesh, const NamedParameters &np)
	finds the longest border of a given triangulated surface and returns a halfedge that is part of this border and the length of this border. More...

template<typename TriangleMesh , typename NamedParameters >
FT	CGAL::Polygon_mesh_processing::face_area (typename boost::graph_traits< TriangleMesh >::face_descriptor f, const TriangleMesh &tmesh, const NamedParameters &np)
	computes the area of a face of a given triangulated surface mesh. More...

template<typename FaceRange , typename TriangleMesh , typename NamedParameters >
FT	CGAL::Polygon_mesh_processing::area (FaceRange face_range, const TriangleMesh &tmesh, const NamedParameters &np)
	computes the area of a range of faces of a given triangulated surface mesh. More...

template<typename TriangleMesh , typename NamedParameters >
FT	CGAL::Polygon_mesh_processing::area (const TriangleMesh &tmesh, const NamedParameters &np)
	computes the surface area of a triangulated surface mesh. More...

template<typename TriangleMesh , typename NamedParameters >
FT	CGAL::Polygon_mesh_processing::volume (const TriangleMesh &tmesh, const NamedParameters &np)
	computes the volume of the domain bounded by a closed triangulated surface mesh. More...

Function Documentation

template<typename FaceRange , typename TriangleMesh , typename NamedParameters >

FT CGAL::Polygon_mesh_processing::area	(	FaceRange	face_range,
		const TriangleMesh &	tmesh,
		const NamedParameters &	np
	)

computes the area of a range of faces of a given triangulated surface mesh.

Template Parameters

FaceRange	range of `boost::graph_traits<PolygonMesh>::face_descriptor`, model of `Range`. Its iterator type is `InputIterator`.
TriangleMesh	a model of `HalfedgeGraph`
NamedParameters	a sequence of Named Parameters

Parameters

face_range	the range of faces of which the area is computed
tmesh	the triangulated surface mesh to which the faces of `face_range` belong
np	optional sequence of Named Parameters among the ones listed below

Named Parameters

vertex_point_map	the property map with the points associated to the vertices of `pmesh`. If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available in `TriangleMesh`
geom_traits	an instance of a geometric traits class, model of `Kernel`

Returns: sum of face areas of faces. The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of tmesh.

Warning: This function involves a square root computation. If Kernel::FT does not have a sqrt() operation, the square root computation will be done approximately.

See Also: face_area()

#include <CGAL/Polygon_mesh_processing/measure.h>

template<typename TriangleMesh , typename NamedParameters >

FT CGAL::Polygon_mesh_processing::area	(	const TriangleMesh &	tmesh,
		const NamedParameters &	np
	)

computes the surface area of a triangulated surface mesh.

Template Parameters

TriangleMesh	a model of `HalfedgeGraph`
NamedParameters	a sequence of Named Parameters

Parameters

tmesh	the triangulated surface mesh
np	optional sequence of Named Parameters among the ones listed below

Named Parameters

vertex_point_map	the property map with the points associated to the vertices of `pmesh`. If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available in `TriangleMesh`
geom_traits	an instance of a geometric traits class, model of `Kernel`

Returns: the surface area of tmesh. The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of tmesh.

Warning: This function involves a square root computation. If Kernel::FT does not have a sqrt() operation, the square root computation will be done approximately.

See Also: face_area()

#include <CGAL/Polygon_mesh_processing/measure.h>

template<typename PolygonMesh , typename NamedParameters >

FT CGAL::Polygon_mesh_processing::edge_length	(	typename boost::graph_traits< PolygonMesh >::halfedge_descriptor	h,
		const PolygonMesh &	pmesh,
		const NamedParameters &	np
	)

computes the length of an edge of a given polygon mesh.

The edge is given by one of its halfedges, or the edge itself.

Template Parameters

PolygonMesh	a model of `HalfedgeGraph`
NamedParameters	a sequence of Named Parameters

Parameters

h	one halfedge of the edge to compute the length
pmesh	the polygon mesh to which `h` belongs
np	optional sequence of Named Parameters among the ones listed below

Named Parameters

vertex_point_map	the property map with the points associated to the vertices of `pmesh`. If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available in `PolygonMesh`
geom_traits	an instance of a geometric traits class, model of `Kernel`

Returns: the length of h. The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of pmesh.

Warning: This function involves a square root computation. If FT does not have a sqrt() operation, the square root computation will be done approximately.

See Also: face_border_length()

#include <CGAL/Polygon_mesh_processing/measure.h>

template<typename TriangleMesh , typename NamedParameters >

FT CGAL::Polygon_mesh_processing::face_area	(	typename boost::graph_traits< TriangleMesh >::face_descriptor	f,
		const TriangleMesh &	tmesh,
		const NamedParameters &	np
	)

computes the area of a face of a given triangulated surface mesh.

Template Parameters

TriangleMesh	a model of `HalfedgeGraph`
NamedParameters	a sequence of Named Parameters

Parameters

f	the face of which the area is computed
tmesh	the triangulated surface mesh to which `f` belongs
np	optional sequence of Named Parameters among the ones listed below

Named Parameters

vertex_point_map	the property map with the points associated to the vertices of `pmesh`. If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available in `TriangleMesh`
geom_traits	an instance of a geometric traits class, model of `Kernel`

Precondition: f != boost::graph_traits<TriangleMesh>::null_face()

Returns: the area of f. The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of tmesh.

See Also: area()

#include <CGAL/Polygon_mesh_processing/measure.h>

template<typename PolygonMesh , typename NamedParameters >

FT CGAL::Polygon_mesh_processing::face_border_length	(	typename boost::graph_traits< PolygonMesh >::halfedge_descriptor	h,
		const PolygonMesh &	pmesh,
		const NamedParameters &	np
	)

computes the length of the border polyline that contains a given halfedge.

Template Parameters

PolygonMesh	a model of `HalfedgeGraph`
NamedParameters	a sequence of Named Parameters

Parameters

h	a halfedge of the border polyline of which the length is computed
pmesh	the polygon mesh to which `h` belongs
np	optional sequence of Named Parameters among the ones listed below

Named Parameters

vertex_point_map	the property map with the points associated to the vertices of `pmesh`. If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available in `PolygonMesh`
geom_traits	an instance of a geometric traits class, model of `Kernel`

Returns: the length of the sequence of border edges of face(h, pmesh). The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of pmesh.

Warning: This function involves a square root computation. If Kernel::FT does not have a sqrt() operation, the square root computation will be done approximately.

See Also: edge_length()

#include <CGAL/Polygon_mesh_processing/measure.h>

template<typename PolygonMesh , typename NamedParameters >

std::pair<halfedge_descriptor, FT> CGAL::Polygon_mesh_processing::longest_border	(	const PolygonMesh &	pmesh,
		const NamedParameters &	np
	)

finds the longest border of a given triangulated surface and returns a halfedge that is part of this border and the length of this border.

Template Parameters

PolygonMesh	a model of `HalfedgeGraph`
NamedParameters	a sequence of Named Parameters

Parameters

pmesh	the polygon mesh
np	optional sequence of Named Parameters among the ones listed below

Named Parameters

vertex_point_map	the property map with the points associated to the vertices of `pmesh`. If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available in `PolygonMesh`
geom_traits	an instance of a geometric traits class, model of `Kernel`

Returns

a pair composed of two members:

first: a halfedge on the longest border. The return type halfedge_descriptor is a halfedge descriptor. It is deduced from the graph traits corresponding to the type PolygonMesh.
second: the length of the longest border The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of pmesh

#include <CGAL/Polygon_mesh_processing/measure.h>

template<typename TriangleMesh , typename NamedParameters >

FT CGAL::Polygon_mesh_processing::volume	(	const TriangleMesh &	tmesh,
		const NamedParameters &	np
	)

computes the volume of the domain bounded by a closed triangulated surface mesh.

Template Parameters

TriangleMesh	a model of `HalfedgeGraph`
NamedParameters	a sequence of Named Parameters

Parameters

tmesh	the closed triangulated surface mesh bounding the volume
np	optional sequence of Named Parameters among the ones listed below

Precondition: tmesh is closed

Named Parameters

vertex_point_map	the property map with the points associated to the vertices of `pmesh`. If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available in `TriangleMesh`
geom_traits	an instance of a geometric traits class, model of `Kernel`

Returns: the volume bounded by tmesh. The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of tmesh.

#include <CGAL/Polygon_mesh_processing/measure.h>