CGAL 5.5.2 - Weights

#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.

shepard.svg
Figure 105.1 Notation used for the Shepard weight.

Specializations

Template Parameters
GeomTraitsa 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...
 

Function Documentation

◆ 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
GeomTraitsa 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
Kernela 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
GeomTraitsa 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
Kernela 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
GeomTraitsa 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
Kernela 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
GeomTraitsa 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
Kernela model of Kernel