CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2< Coordinate_2, Traits > Class Template Reference

#include <CGAL/Barycentric_coordinates_2/Generalized_barycentric_coordinates_2.h>

Definition

template<class Coordinate_2, class Traits>
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.

This class is parameterized by a coordinate class Coordinate_2, and a traits class Traits.

Deprecated:

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

Template Parameters

Coordinate_2	must be a model of the concept BarycentricCoordinates_2.
Traits	must be a model of the concepts BarycentricTraits_2 and PolygonTraits_2.

Examples

Barycentric_coordinates_2/deprecated_coordinates.cpp.

Types
typedef Traits::FT	FT
	Number type.
typedef Traits::Point_2	Point_2
	Point type.
typedef unspecified_type	Vertex_range
	Range of vertices in a polygon.

Creation
template<class InputIterator >
	Generalized_barycentric_coordinates_2 (const InputIterator &first_vertex, const InputIterator &last_vertex, const Traits &b_traits=Traits())
	Creates the class Generalized_barycentric_coordinates_2 that implements generalized barycentric coordinates along the polygon's boundary given by a range of vertices [first_vertex, last_vertex).

Computation
template<class OutputIterator >
std::optional< OutputIterator >	operator() (const Point_2 &query_point, OutputIterator output, Query_point_location query_point_location=UNSPECIFIED_LOCATION, Type_of_algorithm type_of_algorithm=PRECISE)
	Computes generalized barycentric coordinates for any query point in the plane with respect to all the vertices of the polygon.
template<class OutputIterator >
std::optional< OutputIterator >	compute_on_edge (const Point_2 &query_point, const int index, OutputIterator output) const
	Computes generalized barycentric coordinates for a query point on the polygon's boundary with known index of the edge to which this point belongs.
template<class OutputIterator >
std::optional< OutputIterator >	compute_on_vertex (const int index, OutputIterator output) const
	Computes generalized barycentric coordinates for a query point, which coincides with one of the polygon's vertices, with known index.
template<class OutputIterator >
std::optional< OutputIterator >	compute_weights (const Point_2 &query_point, OutputIterator output)
	Computes generalized barycentric weights (unnormalized coordinates) for any strictly interior query point with respect to all the vertices of the polygon.

Endpoint Accessors
const Vertex_range &	vertices () const
	Returns all the vertices of the polygon.
const Point_2 &	first_vertex () const
	Returns the first vertex of the polygon.
const Point_2 &	last_vertex () const
	Returns the last vertex of the polygon.

Member Typedef Documentation

Vertex_range

template<class Coordinate_2 , class Traits >

typedef unspecified_type CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2< Coordinate_2, Traits >::Vertex_range

Range of vertices in a polygon.

This type is a model of the concept Range. Its iterator type is RandomAccessIterator, and its value type is Traits::Point_2.

Constructor & Destructor Documentation

Generalized_barycentric_coordinates_2()

template<class Coordinate_2 , class Traits >

template<class InputIterator >

CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2< Coordinate_2, Traits >::Generalized_barycentric_coordinates_2	(	const InputIterator &	first_vertex,
		const InputIterator &	last_vertex,
		const Traits &	b_traits = Traits()
	)

Creates the class Generalized_barycentric_coordinates_2 that implements generalized barycentric coordinates along the polygon's boundary given by a range of vertices [first_vertex, last_vertex).

InputIterator must be an input iterator with a value type equivalent to Traits::Point_2.

Precondition

Number of the polygon's vertices > 2.

The provided polygon is simple.

Member Function Documentation

compute_on_edge()

template<class Coordinate_2 , class Traits >

template<class OutputIterator >

std::optional< OutputIterator > CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2< Coordinate_2, Traits >::compute_on_edge	(	const Point_2 &	query_point,
		const int	index,
		OutputIterator	output
	)		const

Computes generalized barycentric coordinates for a query point on the polygon's boundary with known index of the edge to which this point belongs.

Computed coordinates are stored in the output iterator output, and it is a set of zeros with two possibly non zero values.

Precondition

The provided query point belongs to the polygon's boundary.

(0 <= index) && (index < number of the polygon's vertices).

compute_on_vertex()

template<class Coordinate_2 , class Traits >

template<class OutputIterator >

std::optional< OutputIterator > CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2< Coordinate_2, Traits >::compute_on_vertex	(	const int	index,
		OutputIterator	output
	)		const

Computes generalized barycentric coordinates for a query point, which coincides with one of the polygon's vertices, with known index.

Computed coordinates are stored in the output iterator output, and it is a set of zeros with value of one at the vertex of interest.

Precondition

(0 <= index) && (index < number of the polygon's vertices).

compute_weights()

template<class Coordinate_2 , class Traits >

template<class OutputIterator >

std::optional< OutputIterator > CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2< Coordinate_2, Traits >::compute_weights	(	const Point_2 &	query_point,
		OutputIterator	output
	)

Computes generalized barycentric weights (unnormalized coordinates) for any strictly interior query point with respect to all the vertices of the polygon.

Computed weights are stored in the output iterator output.

Precondition

The provided query point belongs to the polygon's interior, excluding the boundary.

operator()()

template<class Coordinate_2 , class Traits >

template<class OutputIterator >

std::optional< OutputIterator > CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2< Coordinate_2, Traits >::operator()	(	const Point_2 &	query_point,
		OutputIterator	output,
		Query_point_location	query_point_location = UNSPECIFIED_LOCATION,
		Type_of_algorithm	type_of_algorithm = PRECISE
	)

Computes generalized barycentric coordinates for any query point in the plane with respect to all the vertices of the polygon.

Computed coordinates are stored in the output iterator output.

Different choices of the parameter query_point_location are possible: CGAL::Barycentric_coordinates::UNSPECIFIED_LOCATION - default constant with automatic check for a location, CGAL::Barycentric_coordinates::ON_BOUNDED_SIDE - for a strictly interior query point, CGAL::Barycentric_coordinates::ON_BOUNDARY - for a query point on the boundary of the polygon, CGAL::Barycentric_coordinates::ON_VERTEX - for a query point at one of the polygon's vertices, and CGAL::Barycentric_coordinates::ON_UNBOUNDED_SIDE - for a strictly exterior query point.

Another parameter is type_of_algorithm with the following possible constants: CGAL::Barycentric_coordinates::PRECISE - default slow algorithm, which is as precise as possible and CGAL::Barycentric_coordinates::FAST - fast algorithm, which is less precise but much faster.