#include <CGAL/Weights/three_point_family_weights.h>

This weight is computed as \(w = \frac{d_2^a A_1 - d^a B + d_1^a A_2}{A_1 A_2}\) with notations shown in the figure below and \(a\) any real number being the power parameter.

Here, q is a query point and the points p0, p1, and p2 are its neighbors.

This weight supports only planar configurations (see more in section about Coplanarity) while alternative formulations are explained in Implementation.

Figure 105.1 Notation used for the three point family weight.

Specializations

For \(a = 0\), this weight is equal to the Wachspress Weight and Authalic Weight.
For \(a = 1\), this weight is equal to the Mean Value Weight and Tangent Weight.
For \(a = 2\), this weight is equal to the Discrete Harmonic Weight and Cotangent Weight.

Template Parameters

GeomTraits a model of AnalyticWeightTraits_2 for 2D points; a model of AnalyticWeightTraits_3 for 3D points

Precondition: A1 != 0 && A2 != 0

Functions
template<typename GeomTraits >
GeomTraits::FT	CGAL::Weights::three_point_family_weight (const typename GeomTraits::Point_2 &p0, const typename GeomTraits::Point_2 &p1, const typename GeomTraits::Point_2 &p2, const typename GeomTraits::Point_2 &q, const typename GeomTraits::FT a, const GeomTraits &traits)
	computes the three-point family weight in 2D at `q` using the points `p0`, `p1`, and `p2` and the power parameter `a`, given a traits class `traits` with geometric objects, predicates, and constructions.

template<typename K >
K::FT	CGAL::Weights::three_point_family_weight (const CGAL::Point_2< K > &p0, const CGAL::Point_2< K > &p1, const CGAL::Point_2< K > &p2, const CGAL::Point_2< K > &q, const typename K::FT a=typename K::FT(1))
	computes the three-point family weight in 2D at `q` using the points `p0`, `p1`, and `p2` which are parameterized by a `Kernel` K, and the power parameter `a` which can be omitted.

Functions