CGAL 5.4.4 - Weights
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 104.1 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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

## ◆ inverse_distance_weight() [1/8]

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() [2/8]

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() [3/8]

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() [4/8]

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() [5/8]

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() [6/8]

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() [7/8]

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

## ◆ inverse_distance_weight() [8/8]

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