2D Generalized Barycentric Coordinates Reference

Dmitry Anisimov, David Bommes, Kai Hormann, and Pierre Alliez

The package 2D Generalized Barycentric Coordinates offers an efficient and robust implementation of two-dimensional closed-form generalized barycentric coordinates defined for simple two-dimensional polygons. If coordinates with respect to multivariate scattered points instead of a polygon are required, please refer to natural neighbor coordinates from the Package 2D and Surface Function Interpolation.

Introduced in: CGAL 4.6
BibTeX: cgal:abha-gbc-17b
License: GPL

Classified Reference Pages

Concepts

• BarycentricTraits_2
• BarycentricCoordinates_2

Namespaces

• CGAL::Barycentric_coordinates

Classes

• CGAL::Barycentric_coordinates::Segment_coordinates_2<Traits>
• CGAL::Barycentric_coordinates::Triangle_coordinates_2<Traits>
• CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2<Coordinate_2, Traits>

• CGAL::Barycentric_coordinates::Wachspress_2<Traits>
• CGAL::Barycentric_coordinates::Mean_value_2<Traits>
• CGAL::Barycentric_coordinates::Discrete_harmonic_2<Traits>

Enumerations

• CGAL::Barycentric_coordinates::Query_point_location
• CGAL::Barycentric_coordinates::Type_of_algorithm

Todo:

To make the code parallel. Get iteration number from the thread. Add parallel class to each type of the coordinate functions. Use begin() + offset. Resize vector. Parallel class takes as parameters list of points and polygon. Use random access iterator. - Done but we have problems with it.

Todo:

Add hard tests with epsilon distance away from the polygon’s boundary, which we have discussed during our first group meeting, to current test suit.

Modules
	Concepts

Namespaces
	CGAL::Barycentric_coordinates
	The namespace Barycentric_coordinates contains implementations of all generalized barycentric coordinates: 2D, 3D, related enumerations, and so on.

Classes
class	CGAL::Barycentric_coordinates::Mean_value_2< Traits >
	The class Mean_value_2 implements 2D mean value coordinates (. More...
class	CGAL::Barycentric_coordinates::Triangle_coordinates_2< Traits >
	The class Triangle_coordinates_2 implements barycentric coordinates ( [1], [2] ) with respect to an arbitrary non-degenerate triangle in the plane. More...
class	CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2< Coordinate_2, Traits >
	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	CGAL::Barycentric_coordinates::Segment_coordinates_2< Traits >
	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	CGAL::Barycentric_coordinates::Wachspress_2< Traits >
	The class Wachspress_2 implements 2D Wachspress coordinates (. More...
class	CGAL::Barycentric_coordinates::Discrete_harmonic_2< Traits >
	The class Discrete_harmonic_2 implements 2D discrete harmonic coordinates (. More...