Wachspress Weights

#include<CGAL/Weights/wachspress_weights.h>

Wachspress weights which can be computed for a query point with respect to the vertices of a strictly convex polygon.

Classes
class	CGAL::Weights::Wachspress_weights_2< VertexRange, GeomTraits, PointMap >
	2D Wachspress weights for polygons. More...

Functions
template<typename PointRange , typename OutIterator , typename GeomTraits >
OutIterator	CGAL::Weights::wachspress_weights_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator w_begin, const GeomTraits &traits)
	computes 2D Wachspress weights for polygons.

Function Documentation

wachspress_weights_2()

template<typename PointRange , typename OutIterator , typename GeomTraits >

OutIterator CGAL::Weights::wachspress_weights_2	(	const PointRange &	polygon,
		const typename GeomTraits::Point_2 &	query,
		OutIterator	w_begin,
		const GeomTraits &	traits
	)

#include <CGAL/Weights/wachspress_weights.h>

computes 2D Wachspress weights for polygons.

This function computes 2D Wachspress weights at a given query point with respect to the vertices of a strictly convex polygon, that is one weight per vertex. The weights are stored in a destination range beginning at w_begin.

Internally, the class Wachspress_weights_2 is used. If one wants to process multiple query points, it is better to use that class. When using the free function, internal memory is allocated for each query point, while when using the class, it is allocated only once which is much more efficient. However, for a few query points, it is easier to use this function. It can also be used when the processing time is not a concern.

Template Parameters

PointRange	a model of ConstRange whose iterator type is RandomAccessIterator and value type is GeomTraits::Point_2
OutIterator	a model of OutputIterator whose value type is GeomTraits::FT
GeomTraits	a model of AnalyticWeightTraits_2

Parameters

polygon	an instance of PointRange with 2D points which form a strictly convex polygon
query	a query point
w_begin	the beginning of the destination range with the computed weights
traits	a traits class with geometric objects, predicates, and constructions; this parameter can be omitted if the traits class can be deduced from the point type

Returns

an output iterator to the element in the destination range, one past the last weight stored

Precondition

polygon.size() >= 3

polygon is simple

polygon is strictly convex