Shepard Weight

#include<CGAL/Weights/shepard_weights.h>

This weight is computed as \(w = \frac{1}{d^a}\) with notations shown in the figure below and \(a\) any real number being the power parameter.

Here, the distance is computed between the points p and q.

Figure 113.1 Notation used for the Shepard weight.

Specializations

• For \(a = 1\), this weight is equal to the Inverse Distance Weight.

Template Parameters

GeomTraits

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

Precondition

d != 0

Functions
template<typename GeomTraits>
GeomTraits::FT	CGAL::Weights::shepard_weight (const typename GeomTraits::Point_2 &, const typename GeomTraits::Point_2 &p, const typename GeomTraits::Point_2 &, const typename GeomTraits::Point_2 &q, const typename GeomTraits::FT a, const GeomTraits &traits)
	computes the Shepard weight in 2D using the points p and q and the power parameter a.
template<typename Kernel>
Kernel::FT	CGAL::Weights::shepard_weight (const CGAL::Point_2< Kernel > &, const CGAL::Point_2< Kernel > &p^, const CGAL::Point_2< Kernel > &, const CGAL::Point_2< Kernel > &q, const typename Kernel::FT a={1})
	computes the Shepard weight in 2D using the points p and q, and the power parameter a
template<typename GeomTraits>
GeomTraits::FT	CGAL::Weights::shepard_weight (const typename GeomTraits::Point_2 &p, const typename GeomTraits::Point_2 &q, const typename GeomTraits::FT a, const GeomTraits &traits)
	computes the Shepard weight in 2D using the points p and q and the power parameter a.
template<typename Kernel>
Kernel::FT	CGAL::Weights::shepard_weight (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const typename Kernel::FT a={1})
	computes the Shepard weight in 2D using the points p and q, and the power parameter a.
template<typename GeomTraits>
GeomTraits::FT	CGAL::Weights::shepard_weight (const typename GeomTraits::Point_3 &, const typename GeomTraits::Point_3 &p, const typename GeomTraits::Point_3 &, const typename GeomTraits::Point_3 &q, const typename GeomTraits::FT a, const GeomTraits &traits)
	computes the Shepard weight in 3D using the points p and q and the power parameter a.
template<typename Kernel>
Kernel::FT	CGAL::Weights::shepard_weight (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &, const typename Kernel::FT a={1})
	computes the Shepard weight in 3D using the points p and q, and the power parameter a.
template<typename GeomTraits>
GeomTraits::FT	CGAL::Weights::shepard_weight (const typename GeomTraits::Point_3 &p, const typename GeomTraits::Point_3 &q, const typename GeomTraits::FT a, const GeomTraits &traits)
	computes the Shepard weight in 3D using the points p and q and the power parameter a.
template<typename Kernel>
Kernel::FT	CGAL::Weights::shepard_weight (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const typename Kernel::FT a={1})
	computes the Shepard weight in 3D using the points p and q, and the power parameter a.

Function Documentation

shepard_weight() [1/8]

template<typename Kernel>

Kernel::FT CGAL::Weights::shepard_weight	(	const CGAL::Point_2< Kernel > &	,
		const CGAL::Point_2< Kernel > &p^	,
		const CGAL::Point_2< Kernel > &	,
		const CGAL::Point_2< Kernel > &	q,
		const typename Kernel::FT	a = {1} )

#include <CGAL/Weights/shepard_weights.h>

computes the Shepard weight in 2D using the points p and q, and the power parameter a

Template Parameters

Kernel

a model of Kernel

shepard_weight() [2/8]

template<typename Kernel>

Kernel::FT CGAL::Weights::shepard_weight	(	const CGAL::Point_2< Kernel > &	p,
		const CGAL::Point_2< Kernel > &	q,
		const typename Kernel::FT	a = {1} )

#include <CGAL/Weights/shepard_weights.h>

computes the Shepard weight in 2D using the points p and q, and the power parameter a.

Template Parameters

Kernel

a model of Kernel

shepard_weight() [3/8]

template<typename Kernel>

Kernel::FT CGAL::Weights::shepard_weight	(	const CGAL::Point_3< Kernel > &	p,
		const CGAL::Point_3< Kernel > &	,
		const CGAL::Point_3< Kernel > &	q,
		const CGAL::Point_3< Kernel > &	,
		const typename Kernel::FT	a = {1} )

#include <CGAL/Weights/shepard_weights.h>

computes the Shepard weight in 3D using the points p and q, and the power parameter a.

Template Parameters

Kernel

a model of Kernel

shepard_weight() [4/8]

template<typename Kernel>

Kernel::FT CGAL::Weights::shepard_weight	(	const CGAL::Point_3< Kernel > &	p,
		const CGAL::Point_3< Kernel > &	q,
		const typename Kernel::FT	a = {1} )

#include <CGAL/Weights/shepard_weights.h>

computes the Shepard weight in 3D using the points p and q, and the power parameter a.

Template Parameters

Kernel

a model of Kernel

shepard_weight() [5/8]

template<typename GeomTraits>

GeomTraits::FT CGAL::Weights::shepard_weight	(	const typename GeomTraits::Point_2 &	,
		const typename GeomTraits::Point_2 &	p,
		const typename GeomTraits::Point_2 &	,
		const typename GeomTraits::Point_2 &	q,
		const typename GeomTraits::FT	a,
		const GeomTraits &	traits )

#include <CGAL/Weights/shepard_weights.h>

computes the Shepard weight in 2D using the points p and q and the power parameter a.

Template Parameters

GeomTraits

a model of AnalyticWeightTraits_2

Examples

Weights/weights.cpp.

shepard_weight() [6/8]

template<typename GeomTraits>

GeomTraits::FT CGAL::Weights::shepard_weight	(	const typename GeomTraits::Point_2 &	p,
		const typename GeomTraits::Point_2 &	q,
		const typename GeomTraits::FT	a,
		const GeomTraits &	traits )

#include <CGAL/Weights/shepard_weights.h>

computes the Shepard weight in 2D using the points p and q and the power parameter a.

Template Parameters

GeomTraits

a model of AnalyticWeightTraits_2

shepard_weight() [7/8]

template<typename GeomTraits>

GeomTraits::FT CGAL::Weights::shepard_weight	(	const typename GeomTraits::Point_3 &	,
		const typename GeomTraits::Point_3 &	p,
		const typename GeomTraits::Point_3 &	,
		const typename GeomTraits::Point_3 &	q,
		const typename GeomTraits::FT	a,
		const GeomTraits &	traits )

#include <CGAL/Weights/shepard_weights.h>

computes the Shepard weight in 3D using the points p and q and the power parameter a.

Template Parameters

GeomTraits

a model of AnalyticWeightTraits_3

shepard_weight() [8/8]

template<typename GeomTraits>

GeomTraits::FT CGAL::Weights::shepard_weight	(	const typename GeomTraits::Point_3 &	p,
		const typename GeomTraits::Point_3 &	q,
		const typename GeomTraits::FT	a,
		const GeomTraits &	traits )

#include <CGAL/Weights/shepard_weights.h>

computes the Shepard weight in 3D using the points p and q and the power parameter a.

Template Parameters

GeomTraits

a model of AnalyticWeightTraits_3