CGAL::Barycentric_coordinates::Wachspress_coordinates_3< TriangleMesh, VertexPointMap, GeomTraits > Class Template Reference

#include <CGAL/Barycentric_coordinates_3/Wachspress_coordinates_3.h>

Definition

template<typename TriangleMesh, typename VertexPointMap = typename boost::property_map<TriangleMesh, CGAL::vertex_point_t>::const_type, typename GeomTraits = typename Kernel_traits<typename boost::property_traits<VertexPointMap>::value_type>::Kernel>
class CGAL::Barycentric_coordinates::Wachspress_coordinates_3< TriangleMesh, VertexPointMap, GeomTraits >

computes 3D Wachspress coordinates with respect to a closed convex triangle mesh.

This class implements 3D Wachspress coordinates ( [1], [2] ), which can be computed at any point inside a convex polyhedron with triangular faces.

Wachspress coordinates are well-defined and non-negative in the closure of a convex polyhedron with triangular faces. The coordinates are computed analytically.

Template Parameters

TriangleMesh	must be a model of the concept FaceListGraph.
VertexPointMap	a property map with boost::graph_traits<TriangleMesh>::vertex_descriptor as key type and GeomTraits::Point_3 as value type.
GeomTraits	a model of BarycentricTraits_3.

Examples

Barycentric_coordinates_3/wachspress_coordinates_3.cpp.

Types
using	FT = typename GeomTraits::FT
	Number type.
using	Point_3 = typename GeomTraits::Point_3
	Point type.
using	Vector_3 = typename GeomTraits::Vector_3
	Vector type.

Initialization
	Wachspress_coordinates_3 (const TriangleMesh &tmesh, const Computation_policy_3 policy, const VertexPointMap vertex_point_map, const GeomTraits traits=GeomTraits())
	initializes all internal data structures.

Access
template<typename OutputIterator >
OutputIterator	operator() (const Point_3 &query, OutputIterator oi)
	computes 3D Wachspress coordinates with respect to a closed convex triangle mesh.

Constructor & Destructor Documentation

Wachspress_coordinates_3()

template<typename TriangleMesh , typename VertexPointMap = typename boost::property_map<TriangleMesh, CGAL::vertex_point_t>::const_type, typename GeomTraits = typename Kernel_traits<typename boost::property_traits<VertexPointMap>::value_type>::Kernel>

CGAL::Barycentric_coordinates::Wachspress_coordinates_3< TriangleMesh, VertexPointMap, GeomTraits >::Wachspress_coordinates_3	(	const TriangleMesh &	tmesh,
		const Computation_policy_3	policy,
		const VertexPointMap	vertex_point_map,
		const GeomTraits	traits = GeomTraits()
	)

initializes all internal data structures.

This class implements the behavior of Wachspress coordinates for 3D query points.

Parameters

tmesh	an instance of TriangleMesh
policy	one of the CGAL::Barycentric_coordinates::Computation_policy_3; the default is Computation_policy_3::FAST_WITH_EDGE_CASES
traits	a traits class with geometric objects, predicates, and constructions; the default initialization is provided
vertex_point_map	an instance of VertexPointMap that maps a vertex from tmesh to Point_3; the default initialization is provided

Precondition

num_vertices(tmesh) >= 4.

CGAL::is_triangle_mesh(tmesh).

CGAL::is_closed(tmesh).

CGAL::is_strongly_convex_3(tmesh).

Member Function Documentation

operator()()

template<typename TriangleMesh , typename VertexPointMap = typename boost::property_map<TriangleMesh, CGAL::vertex_point_t>::const_type, typename GeomTraits = typename Kernel_traits<typename boost::property_traits<VertexPointMap>::value_type>::Kernel>

template<typename OutputIterator >

OutputIterator CGAL::Barycentric_coordinates::Wachspress_coordinates_3< TriangleMesh, VertexPointMap, GeomTraits >::operator()	(	const Point_3 &	query,
		OutputIterator	oi
	)

computes 3D Wachspress coordinates with respect to a closed convex triangle mesh.

This function fills oi with 3D Wachspress coordinates computed at the query point with respect to the vertices of the input polyhedron.

The number of returned coordinates equals the number of vertices of tmesh.

After the coordinates \(b_i\) with \(i = 0\dots n-1\) are computed, where \(n\) is the number of vertices, the query point \(q\) can be obtained as \(q = \sum_{i = 0}^{n-1}b_ip_i\), where \(p_i\) are the polyhedron vertices.

Template Parameters

OutputIterator

a model of OutputIterator that accepts values of type FT

Parameters

query	a query point
oi	the beginning of the destination range with the computed coordinates

Returns

an output iterator to the element in the destination range, one past the last coordinate stored