CGAL 5.4.4  Weights

#include <CGAL/Weights/three_point_family_weights.h>
This weight is computed as \(w = \frac{d_2^a A_0  d^a B + d_0^a A_2}{A_0 A_2}\) 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 . More...  
template<typename Kernel >  
Kernel::FT  CGAL::Weights::three_point_family_weight (const CGAL::Point_2< Kernel > &p0, const CGAL::Point_2< Kernel > &p1, const CGAL::Point_2< Kernel > &p2, const CGAL::Point_2< Kernel > &q, const typename Kernel::FT a={1}) 
computes the threepoint family weight in 2D at q using the points p0 , p1 and p2 , and the power parameter a . More...  
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  
) 
#include <CGAL/Weights/three_point_family_weights.h>
computes the threepoint family weight in 2D at q
using the points p0
, p1
and p2
, and the power parameter a
.
GeomTraits  a model of AnalyticWeightTraits_2 
Kernel::FT CGAL::Weights::three_point_family_weight  (  const CGAL::Point_2< Kernel > &  p0, 
const CGAL::Point_2< Kernel > &  p1,  
const CGAL::Point_2< Kernel > &  p2,  
const CGAL::Point_2< Kernel > &  q,  
const typename Kernel::FT  a = {1} 

) 