CGAL 5.4.4 - Weights
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 104.1 Notation used for the Shepard weight.

Specializations

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. More...

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 More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

## ◆ shepard_weight() [1/8]

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() [2/8]

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() [3/8]

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() [4/8]

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() [5/8]

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() [6/8]

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() [7/8]

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

## ◆ shepard_weight() [8/8]

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