CGAL 6.2 - 3D Generalized Barycentric Coordinates: CGAL::Barycentric_coordinates Namespace Reference

CGAL 6.2 - 3D Generalized Barycentric Coordinates

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Classes | Functions
CGAL::Barycentric_coordinates Namespace Reference
3D Generalized Barycentric Coordinates Reference

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

## Classes
class | BarycentricCoordinates_2
class | BarycentricTraits_2
class | Delaunay_domain_2
class | Discrete_harmonic_2
class | Discrete_harmonic_coordinates_2
class | Discrete_harmonic_coordinates_3
| computes 3D discrete harmonic coordinates with respect to a closed convex triangle mesh. More...
class | DiscretizedDomain_2
class | Generalized_barycentric_coordinates_2
class | Harmonic_coordinates_2
class | Mean_value_2
class | Mean_value_coordinates_2
class | Mean_value_coordinates_3
| computes 3D mean value barycentric coordinates with respect to a closed triangle mesh. More...
class | Segment_coordinates_2
class | Triangle_coordinates_2
class | Wachspress_2
class | Wachspress_coordinates_2
class | Wachspress_coordinates_3
| computes 3D Wachspress coordinates with respect to a closed convex triangle mesh. More...

## Functions
template<typename TriangleMesh , typename CoordinateRange , typename VertexPointMap , typename GeomTraits = typename CGAL::Kernel_traits<typename boost::property_traits<VertexPointMap>::value_type>::type>
boost::property_traits< VertexPointMap >::value_type | apply_barycentric_coordinates_3 (const TriangleMesh &tmesh, const CoordinateRange &coordinates, VertexPointMap vpm, GeomTraits geom_traits=GeomTraits())
| computes a point location from barycentric coordinates with respect to a triangle mesh.
template<typename PointRange , typename CoordinateRange , typename GeomTraits = typename Kernel_traits<typename boost::range_value<PointRange>::type>::Kernel>
boost::range_value< PointRange >::type | apply_barycentric_coordinates_3 (const PointRange &points, const CoordinateRange &coordinates, GeomTraits geom_traits=GeomTraits())
| computes a point location from barycentric coordinates with respect to a set of points.
template<typename TriangleMesh , typename Point , typename OutputIterator , typename NamedParameters = parameters::Default_named_parameters>
OutputIterator | discrete_harmonic_coordinates_3 (const TriangleMesh &tmesh, const Point &query, OutputIterator oi, const NamedParameters &np=parameters::default_values())
| computes 3D discrete harmonic coordinates with respect to a closed convex triangle mesh.
template<typename TriangleMesh , typename Point , typename OutputIterator , typename NamedParameters = parameters::Default_named_parameters>
OutputIterator | mean_value_coordinates_3 (const TriangleMesh &tmesh, const Point &query, OutputIterator oi, const NamedParameters &np=parameters::default_values())
| computes 3D mean value barycentric coordinates with respect to a closed triangle mesh.
template<typename TriangleMesh , typename Point , typename OutputIterator , typename NamedParameters = parameters::Default_named_parameters>
OutputIterator | wachspress_coordinates_3 (const TriangleMesh &tmesh, const Point query, OutputIterator oi, const NamedParameters &np=parameters::default_values())
| computes 3D Wachspress coordinates with respect to a closed convex triangle mesh.
template<typename TriangleMesh , typename Point , typename OutputIterator , typename NamedParameters = parameters::Default_named_parameters>
std::pair< OutputIterator, bool > | boundary_coordinates_3 (const TriangleMesh &tmesh, const Point &query, OutputIterator oi, const NamedParameters &np=parameters::default_values())
| computes boundary barycentric coordinates with respect to a closed convex triangle mesh.
template<typename OutputIterator , typename GeomTraits >
OutputIterator | tetrahedron_coordinates_3 (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, OutputIterator oi, const GeomTraits &traits)
| computes barycentric coordinates with respect to a tetrahedron.
template<typename GeomTraits >
std::array< typename GeomTraits::FT, 4 > | tetrahedron_coordinates_3 (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 barycentric coordinates with respect to a tetrahedron.

## Computation Policies
enum class | Computation_policy_3 { FAST = 0 , 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 class 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 face vertices, but may suffer imprecisions near the face boundary. No extra checks are carried out.
FAST_WITH_EDGE_CASES | Computation has a linear time complexity with respect to the number of face vertices, but may suffer imprecisions near the face boundary. In addition, we check a position of the query point with respect to the face and use different computation strategies for different positions.

Examples
  Barycentric_coordinates_3/discrete_harmonic_coordinates_3.cpp, Barycentric_coordinates_3/mean_value_coordinates_3.cpp, and Barycentric_coordinates_3/wachspress_coordinates_3.cpp.