CGAL 5.4  Weights

#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.
Specializations
GeomTraits  a model of AnalyticWeightTraits_2 for 2D points; a model of AnalyticWeightTraits_3 for 3D points 
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 threepoint 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 threepoint 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.  