#include <CGAL/Weights/wachspress_weights.h>

This weight is computed as \(w = \frac{C}{A_0 A_2}\) with notations shown in the figure below.

Here, q is a query point and the points p0, p1, and p2 are its neighbors.

This weight supports only planar configurations (see more in section about Coplanarity) while alternative formulations are explained in Implementation.

Figure 105.1 Notation used for the Wachspress weight.

Alternative Formulations

This weight is equal to the Authalic Weight.
This weight is a special case of the Three Point Family Weight.

Template Parameters

GeomTraits a model of AnalyticWeightTraits_2 for 2D points; a model of AnalyticWeightTraits_3 for 3D points

Precondition: A1 != 0 && A2 != 0

Functions
template<typename GeomTraits >
GeomTraits::FT	CGAL::Weights::wachspress_weight (const typename GeomTraits::Point_2 &p0, const typename GeomTraits::Point_2 &p1, const typename GeomTraits::Point_2 &p2, const typename GeomTraits::Point_2 &q, const GeomTraits &traits)
	computes the Wachspress weight in 2D at `q` using the points `p0`, `p1`, and `p2`. More...

template<typename Kernel >
Kernel::FT	CGAL::Weights::wachspress_weight (const CGAL::Point_2< Kernel > &p0, const CGAL::Point_2< Kernel > &p1, const CGAL::Point_2< Kernel > &p2, const CGAL::Point_2< Kernel > &q)
	computes the Wachspress weight in 2D at `q` using the points `p0`, `p1`, and `p2`. More...

Function Documentation

◆ wachspress_weight() [1/2]

template<typename GeomTraits >

GeomTraits::FT CGAL::Weights::wachspress_weight	(	const typename GeomTraits::Point_2 &	p0,
		const typename GeomTraits::Point_2 &	p1,
		const typename GeomTraits::Point_2 &	p2,
		const typename GeomTraits::Point_2 &	q,
		const GeomTraits &	traits
	)

#include <CGAL/Weights/wachspress_weights.h>

computes the Wachspress weight in 2D at q using the points p0, p1, and p2.

Template Parameters

GeomTraits a model of AnalyticWeightTraits_2

◆ wachspress_weight() [2/2]

template<typename Kernel >

Kernel::FT CGAL::Weights::wachspress_weight	(	const CGAL::Point_2< Kernel > &	p0,
		const CGAL::Point_2< Kernel > &	p1,
		const CGAL::Point_2< Kernel > &	p2,
		const CGAL::Point_2< Kernel > &	q
	)

#include <CGAL/Weights/wachspress_weights.h>

computes the Wachspress weight in 2D at q using the points p0, p1, and p2.

Template Parameters

Kernel a model of Kernel

Functions

Function Documentation

◆ wachspress_weight() [1/2]

◆ wachspress_weight() [2/2]