CGAL 5.4 - 2D Generalized Barycentric Coordinates
CGAL::Barycentric_coordinates::Generalized_barycentric_coordinates_2< Coordinate_2, Traits > Class Template Reference

#include <CGAL/Barycentric_coordinates_2/Generalized_barycentric_coordinates_2.h>

## Definition

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. More...

## 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). More...

## Computation

template<class OutputIterator >
boost::optional< OutputIteratoroperator() (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. More...

template<class OutputIterator >
boost::optional< OutputIteratorcompute_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. More...

template<class OutputIterator >
boost::optional< OutputIteratorcompute_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. More...

template<class OutputIterator >
boost::optional< OutputIteratorcompute_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. More...

## Endpoint Accessors

const Vertex_rangevertices () const
Returns all the vertices of the polygon.

const Point_2first_vertex () const
Returns the first vertex of the polygon.

const Point_2last_vertex () const
Returns the last vertex of the polygon.

## ◆ 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.

## ◆ 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.

## ◆ compute_on_edge()

template<class Coordinate_2 , class Traits >
template<class OutputIterator >
 boost::optional 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 >
 boost::optional 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 >
 boost::optional 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 >
 boost::optional 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.