CGAL::Barycentric_coordinates Namespace Reference

Classes
class	BarycentricTraits_3
	A concept that describes the set of requirements of the template parameter GeomTraits used to parameterize all classes and functions with 3D barycentric coordinates from the namespace CGAL::Barycentric_coordinates. The concept BarycentricTraits_3 extends the concept BarycentricTraits_2 and adds the requirements for 3D objects. More...
class	Discrete_harmonic_2
class	Discrete_harmonic_coordinates_3
	3D discrete harmonic coordinates. More...
class	Generalized_barycentric_coordinates_2
class	Mean_value_2
class	Mean_value_coordinates_3
	3D mean value coordinates. More...
class	Segment_coordinates_2
class	Triangle_coordinates_2
class	Wachspress_2
class	Wachspress_coordinates_3
	3D Wachspress coordinates. More...

Functions
template<typename TriangleMesh , typename OutIterator , typename GeomTraits , typename VertexToPointMap >
std::pair< OutIterator, bool >	boundary_coordinates_3 (const TriangleMesh &triangle_mesh, const typename GeomTraits::Point_3 &query, OutIterator c_begin, const GeomTraits &traits, const VertexToPointMap vertex_to_point_map)
	computes boundary barycentric coordinates. More...
template<typename TriangleMesh , typename Point_3 , typename OutIterator , typename VertexToPointMap = typename property_map_selector<TriangleMesh, CGAL::vertex_point_t>::const_type>
std::pair< OutIterator, bool >	boundary_coordinates_3 (const TriangleMesh &triangle_mesh, const Point_3 &query, OutIterator c_begin, const VertexToPointMap vertex_to_point_map)
	computes boundary barycentric coordinates. More...
template<typename Point_3 , typename TriangleMesh , typename OutIterator >
OutIterator	discrete_harmonic_coordinates_3 (const TriangleMesh &triangle_mesh, const Point_3 &query, OutIterator c_begin, const Computation_policy_3 policy=Computation_policy_3::FAST)
	computes 3D discrete harmonic coordinates. More...
template<typename Point_3 , typename TriangleMesh , typename OutIterator >
OutIterator	mean_value_coordinates_3 (const TriangleMesh &triangle_mesh, const Point_3 &query, OutIterator c_begin, const Computation_policy_3 policy=Computation_policy_3::FAST_WITH_EDGE_CASES)
	computes 3D mean value coordinates. More...
template<typename OutIterator , typename GeomTraits >
OutIterator	tetrahedron_coordinates (const typename GeomTraits::Point_3 &p0, const typename GeomTraits::Point_3 &p1, const typename GeomTraits::Point_3 &p2, const typename GeomTraits::Point_3 &p3, const typename GeomTraits::Point_3 &query, OutIterator c_begin, const GeomTraits &traits)
	computes tetrahedron coordinates. More...
template<typename GeomTraits >
std::array< typename GeomTraits::FT, 4 >	tetrahedron_coordinates_in_array (const typename GeomTraits::Point_3 &p0, const typename GeomTraits::Point_3 &p1, const typename GeomTraits::Point_3 &p2, const typename GeomTraits::Point_3 &p3, const typename GeomTraits::Point_3 &query, const GeomTraits &traits)
	computes tetrahedron coordinates. More...
template<typename Point_3 , typename PolygonMesh , typename OutIterator >
OutIterator	wachspress_coordinates_3 (const PolygonMesh &polygon_mesh, const Point_3 &query, OutIterator c_begin, const Computation_policy_3 policy=Computation_policy_3::FAST)
	computes 3D Wachspress coordinates. More...

Computation Policies
enum	Computation_policy_3 { Computation_policy_3::FAST = 0, Computation_policy_3::FAST_WITH_EDGE_CASES = 1 }
	Computation_policy_3 provides a way to choose an asymptotic time complexity of the algorithm and its precision for computing 3D barycentric weights and coordinates. More...

Definition

The namespace Barycentric_coordinates contains implementations of all generalized barycentric coordinates: 2D, 3D, related enumerations, etc.

Enumeration Type Documentation

Computation_policy_3

enum CGAL::Barycentric_coordinates::Computation_policy_3

strong

Computation_policy_3 provides a way to choose an asymptotic time complexity of the algorithm and its precision for computing 3D barycentric weights and coordinates.

Enumerator
FAST	Computation has a linear time complexity with respect to the number of polygon vertices, but may suffer imprecisions near the polygon boundary. No extra checks are carried out.
FAST_WITH_EDGE_CASES	Computation has a linear time complexity with respect to the number of polygon vertices, but may suffer imprecisions near the polygon boundary. In addition, we check a position of the query point with respect to the polygon and use different computation strategies for different positions.

Examples

Barycentric_coordinates_3/discrete_harmonic_coordinates.cpp, Barycentric_coordinates_3/mean_value_coordinates.cpp, and Barycentric_coordinates_3/wachspress_coordinates.cpp.