CGAL 5.4  Weights

#include <CGAL/Weights/mixed_voronoi_region_weights.h>
This weight is the area of the shaded region in the figure below. The region is formed by the two midpoints of the edges incident to q
and the circumcenter of the triangle [p, q, r]
.
However, unlike the original Voronoi Region Weight, if one of the angles in the triangle [p, q, r]
is obtuse and the circumcenter vertex of the region is outside this triangle, this vertex is moved to the midpoint of the edge [r, p]
as shown in the figure below.
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::mixed_voronoi_area (const typename GeomTraits::Point_2 &p, const typename GeomTraits::Point_2 &q, const typename GeomTraits::Point_2 &r, const GeomTraits &traits) 
computes the area of the mixed Voronoi cell in 2D using the points p , q and r , given a traits class traits with geometric objects, predicates, and constructions.  
template<typename GeomTraits >  
GeomTraits::FT  CGAL::Weights::mixed_voronoi_area (const typename GeomTraits::Point_3 &p, const typename GeomTraits::Point_3 &q, const typename GeomTraits::Point_3 &r, const GeomTraits &traits) 
computes the area of the mixed Voronoi cell in 3D using the points p , q and r , given a traits class traits with geometric objects, predicates, and constructions.  
template<typename K >  
K::FT  CGAL::Weights::mixed_voronoi_area (const CGAL::Point_2< K > &p, const CGAL::Point_2< K > &q, const CGAL::Point_2< K > &r) 
computes the area of the mixed Voronoi cell in 2D using the points p , q and r which are parameterized by a Kernel K.  
template<typename K >  
K::FT  CGAL::Weights::mixed_voronoi_area (const CGAL::Point_3< K > &p, const CGAL::Point_3< K > &q, const CGAL::Point_3< K > &r) 
computes the area of the mixed Voronoi cell in 3D using the points p , q and r which are parameterized by a Kernel K.  