CGAL::Barycentric_coordinates Namespace Reference

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

Classes
class	BarycentricCoordinates_2
	A concept that describes the set of methods that should be defined for all coordinate models used to parameterize the class Generalized_barycentric_coordinates_2. More...
class	BarycentricTraits_2
	A concept that describes the set of requirements of the template parameter GeomTraits used to parameterize all classes and functions with 2D barycentric coordinates from the namespace CGAL::Barycentric_coordinates. More...
class	Delaunay_domain_2
	2D Delaunay domain restricted to a simple polygon. More...
class	Discrete_harmonic_2
	The class Discrete_harmonic_2 implements 2D discrete harmonic coordinates ( [2], [9], [1] ). More...
class	Discrete_harmonic_coordinates_2
	2D discrete harmonic coordinates. More...
class	DiscretizedDomain_2
	A concept that describes the set of methods that should be defined for all discretized domains obtained by meshing the interior part of a simple polygon. More...
class	Generalized_barycentric_coordinates_2
	The class Generalized_barycentric_coordinates_2 implements generalized barycentric coordinates along the polygon's boundary and provides a common interface for all coordinate classes. More...
class	Harmonic_coordinates_2
	2D harmonic coordinates. More...
class	Mean_value_2
	The class Mean_value_2 implements 2D mean value coordinates ( [5], [2], [3] ). More...
class	Mean_value_coordinates_2
	2D mean value coordinates. More...
class	Segment_coordinates_2
	The class Segment_coordinates_2 implements barycentric coordinates with respect to an arbitrary non-degenerate segment along an arbitrary line in the plane. More...
class	Triangle_coordinates_2
	The class Triangle_coordinates_2 implements barycentric coordinates ( [1], [2] ) with respect to an arbitrary non-degenerate triangle in the plane. More...
class	Wachspress_2
	The class Wachspress_2 implements 2D Wachspress coordinates ( [2], [8], [10] ). More...
class	Wachspress_coordinates_2
	2D Wachspress coordinates. More...

Functions
template<typename VertexRange , typename OutIterator , typename GeomTraits , typename PointMap >
std::pair< OutIterator, bool >	boundary_coordinates_2 (const VertexRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits, const PointMap point_map)
	computes 2D boundary coordinates.
template<typename VertexRange , typename Query_2 , typename OutIterator , typename PointMap = CGAL::Identity_property_map<Query_2>>
std::pair< OutIterator, bool >	boundary_coordinates_2 (const VertexRange &polygon, const Query_2 &query, OutIterator c_begin, const PointMap point_map=PointMap())
	computes 2D boundary coordinates.
template<typename PointRange , typename OutIterator , typename GeomTraits >
OutIterator	discrete_harmonic_weights_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator w_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::FAST_WITH_EDGE_CASES)
	computes 2D discrete harmonic weights.
template<typename PointRange , typename OutIterator , typename GeomTraits >
OutIterator	discrete_harmonic_coordinates_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::PRECISE_WITH_EDGE_CASES)
	computes 2D discrete harmonic coordinates.
template<typename PointRange , typename OutIterator , typename GeomTraits >
OutIterator	mean_value_weights_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator w_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::FAST_WITH_EDGE_CASES)
	computes 2D mean value weights.
template<typename PointRange , typename OutIterator , typename GeomTraits >
OutIterator	mean_value_coordinates_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::PRECISE_WITH_EDGE_CASES)
	computes 2D mean value coordinates.
template<typename OutIterator , typename GeomTraits >
OutIterator	segment_coordinates_2 (const typename GeomTraits::Point_2 &p0, const typename GeomTraits::Point_2 &p1, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits)
	computes segment coordinates.
template<typename OutIterator , typename GeomTraits >
OutIterator	triangle_coordinates_2 (const typename GeomTraits::Point_2 &p0, const typename GeomTraits::Point_2 &p1, const typename GeomTraits::Point_2 &p2, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits)
	computes triangle coordinates.
template<typename PointRange , typename OutIterator , typename GeomTraits >
OutIterator	wachspress_weights_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator w_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::FAST_WITH_EDGE_CASES)
	computes 2D Wachspress weights.
template<typename PointRange , typename OutIterator , typename GeomTraits >
OutIterator	wachspress_coordinates_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::PRECISE_WITH_EDGE_CASES)
	computes 2D Wachspress coordinates.

Computation Policies
enum class	Computation_policy_2 { PRECISE_WITH_EDGE_CASES = 0 , PRECISE = 1 , FAST_WITH_EDGE_CASES = 2 , FAST = 3 }
	Computation_policy_2 provides a way to choose an asymptotic time complexity of the algorithm and its precision for computing 2D barycentric weights and coordinates. More...

Locations of a Query Point
enum	Query_point_location {   UNSPECIFIED_LOCATION , ON_VERTEX , ON_BOUNDARY , ON_BOUNDED_SIDE ,   ON_UNBOUNDED_SIDE }
	Query_point_location is enumeration with possible locations of a query point provided by the user. More...

Types of an Algorithm
enum	Type_of_algorithm { PRECISE , FAST }
	Type_of_algorithm is enumeration with possible algorithms to compute coordinates. More...

Definition

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

Enumeration Type Documentation

Computation_policy_2

enum class CGAL::Barycentric_coordinates::Computation_policy_2

strong

Computation_policy_2 provides a way to choose an asymptotic time complexity of the algorithm and its precision for computing 2D barycentric weights and coordinates.

Enumerator
PRECISE_WITH_EDGE_CASES	Computation is very precise but has a quadratic time complexity with respect to the number of polygon vertices. In addition, we check a position of the query point with respect to the polygon and use different computation strategies for different positions. This is the default policy.
PRECISE	Computation is very precise but has a quadratic time complexity with respect to the number of polygon vertices. 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.
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.

Examples

Barycentric_coordinates_2/discrete_harmonic_coordinates.cpp, and Barycentric_coordinates_2/mean_value_coordinates.cpp.

Query_point_location

enum CGAL::Barycentric_coordinates::Query_point_location

Query_point_location is enumeration with possible locations of a query point provided by the user.

Deprecated:

This part of the package is deprecated since the version 5.4 of CGAL.

Enumerator
UNSPECIFIED_LOCATION	Location is not known apriori and is defined automatically by the algorithm.
ON_VERTEX	Query point is located at one of the polygon's vertices.
ON_BOUNDARY	Query point is located on the boundary of the polygon.
ON_BOUNDED_SIDE	Query point is located inside the polygon, excluding the boundary.
ON_UNBOUNDED_SIDE	Query point is located outside the polygon, excluding the boundary.

Type_of_algorithm

enum CGAL::Barycentric_coordinates::Type_of_algorithm

Type_of_algorithm is enumeration with possible algorithms to compute coordinates.

Deprecated:

This part of the package is deprecated since the version 5.4 of CGAL.

Enumerator
PRECISE	A default slow algorithm, which is as precise as possible.
FAST	A fast algorithm, which is less precise but much faster.