#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 105.1 Notation used for the Shepard weight.

Specializations

For \(a = 1\), this weight is equal to the Inverse Distance 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::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.

Functions