Inverse Distance Weight

#include <CGAL/Weights/inverse_distance_weights.h>

This weight is computed as \(w = \frac{1}{d}\) with notations shown in the figure below.

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

Alternative formulations are explained in Implementation.

Figure 106.1 Notation used for the inverse distance weight.

Alternative Formulations
This weight is a special case of the Shepard 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::inverse_distance_weight (const typename GeomTraits::Point_2 &, const typename GeomTraits::Point_2 &p, const typename GeomTraits::Point_2 &, const typename GeomTraits::Point_2 &q, const GeomTraits &traits)
	computes the inverse distance weight in 2D using the points p and q.
template<typename Kernel >
Kernel::FT	CGAL::Weights::inverse_distance_weight (const CGAL::Point_2< Kernel > &, const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &, const CGAL::Point_2< Kernel > &q)
	computes the inverse distance weight in 2D using the points p and q.
template<typename GeomTraits >
GeomTraits::FT	CGAL::Weights::inverse_distance_weight (const typename GeomTraits::Point_2 &p, const typename GeomTraits::Point_2 &q, const GeomTraits &traits)
	computes the inverse distance weight in 2D using the points p and q.
template<typename Kernel >
Kernel::FT	CGAL::Weights::inverse_distance_weight (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	computes the inverse distance weight in 2D using the points p and q.
template<typename GeomTraits >
GeomTraits::FT	CGAL::Weights::inverse_distance_weight (const typename GeomTraits::Point_3 &, const typename GeomTraits::Point_3 &p, const typename GeomTraits::Point_3 &, const typename GeomTraits::Point_3 &q, const GeomTraits &traits)
	computes the inverse distance weight in 3D using the points p and q.
template<typename Kernel >
Kernel::FT	CGAL::Weights::inverse_distance_weight (const CGAL::Point_3< Kernel > &, const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &, const CGAL::Point_3< Kernel > &q)
	computes the inverse distance weight in 3D using the points p and q.
template<typename GeomTraits >
GeomTraits::FT	CGAL::Weights::inverse_distance_weight (const typename GeomTraits::Point_3 &p, const typename GeomTraits::Point_3 &q, const GeomTraits &traits)
	computes the inverse distance weight in 3D using the points p and q.
template<typename Kernel >
Kernel::FT	CGAL::Weights::inverse_distance_weight (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	computes the inverse distance weight in 3D using the points p and q.

Function Documentation

inverse_distance_weight() [1/8]

template<typename Kernel >

Kernel::FT CGAL::Weights::inverse_distance_weight	(	const CGAL::Point_2< Kernel > &	,
		const CGAL::Point_2< Kernel > &	p,
		const CGAL::Point_2< Kernel > &	,
		const CGAL::Point_2< Kernel > &	q
	)

#include <CGAL/Weights/inverse_distance_weights.h>

computes the inverse distance weight in 2D using the points p and q.

Template Parameters

Kernel

a model of Kernel

inverse_distance_weight() [2/8]

template<typename Kernel >

Kernel::FT CGAL::Weights::inverse_distance_weight	(	const CGAL::Point_2< Kernel > &	p,
		const CGAL::Point_2< Kernel > &	q
	)

#include <CGAL/Weights/inverse_distance_weights.h>

computes the inverse distance weight in 2D using the points p and q.

Template Parameters

Kernel

a model of Kernel

inverse_distance_weight() [3/8]

template<typename Kernel >

Kernel::FT CGAL::Weights::inverse_distance_weight	(	const CGAL::Point_3< Kernel > &	,
		const CGAL::Point_3< Kernel > &	p,
		const CGAL::Point_3< Kernel > &	,
		const CGAL::Point_3< Kernel > &	q
	)

#include <CGAL/Weights/inverse_distance_weights.h>

computes the inverse distance weight in 3D using the points p and q.

Template Parameters

Kernel

a model of Kernel

inverse_distance_weight() [4/8]

template<typename Kernel >

Kernel::FT CGAL::Weights::inverse_distance_weight	(	const CGAL::Point_3< Kernel > &	p,
		const CGAL::Point_3< Kernel > &	q
	)

#include <CGAL/Weights/inverse_distance_weights.h>

computes the inverse distance weight in 3D using the points p and q.

Template Parameters

Kernel

a model of Kernel

inverse_distance_weight() [5/8]

template<typename GeomTraits >

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

#include <CGAL/Weights/inverse_distance_weights.h>

computes the inverse distance weight in 2D using the points p and q.

Template Parameters

GeomTraits

a model of AnalyticWeightTraits_2

Examples

Weights/custom_traits.cpp.

inverse_distance_weight() [6/8]

template<typename GeomTraits >

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

#include <CGAL/Weights/inverse_distance_weights.h>

computes the inverse distance weight in 2D using the points p and q.

Template Parameters

GeomTraits

a model of AnalyticWeightTraits_2

inverse_distance_weight() [7/8]

template<typename GeomTraits >

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

#include <CGAL/Weights/inverse_distance_weights.h>

computes the inverse distance weight in 3D using the points p and q.

Template Parameters

GeomTraits

a model of AnalyticWeightTraits_3

inverse_distance_weight() [8/8]

template<typename GeomTraits >

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

#include <CGAL/Weights/inverse_distance_weights.h>

computes the inverse distance weight in 3D using the points p and q.

Template Parameters

GeomTraits

a model of AnalyticWeightTraits_3