CGAL 5.4 - 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, given a traits class traits with geometric objects, predicates, and constructions.

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, given a traits class traits with geometric objects, predicates, and constructions.

template<typename K >
K::FT CGAL::Weights::shepard_weight (const CGAL::Point_2< K > &, const CGAL::Point_2< K > &p, const CGAL::Point_2< K > &, const CGAL::Point_2< K > &q, const typename K::FT a=typename K::FT(1))
computes the Shepard weight in 2D using the points p and q, which are parameterized by a Kernel K, and the power parameter a which can be omitted.

template<typename K >
K::FT CGAL::Weights::shepard_weight (const CGAL::Point_3< K > &, const CGAL::Point_3< K > &p, const CGAL::Point_3< K > &, const CGAL::Point_3< K > &q, const typename K::FT a=typename K::FT(1))
computes the Shepard weight in 3D using the points p and q, which are parameterized by a Kernel K, and the power parameter a which can be omitted.

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, given a traits class traits with geometric objects, predicates, and constructions.

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, given a traits class traits with geometric objects, predicates, and constructions.

template<typename K >
K::FT CGAL::Weights::shepard_weight (const CGAL::Point_2< K > &p, const CGAL::Point_2< K > &q, const typename K::FT a=typename K::FT(1))
computes the Shepard weight in 2D using the points p and q, which are parameterized by a Kernel K, and the power parameter a which can be omitted.

template<typename K >
K::FT CGAL::Weights::shepard_weight (const CGAL::Point_3< K > &p, const CGAL::Point_3< K > &q, const typename K::FT a=typename K::FT(1))
computes the Shepard weight in 3D using the points p and q, which are parameterized by a Kernel K, and the power parameter a which can be omitted.