CGAL 5.4.4 - Weights
Mixed Voronoi Region Weight
#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].

Figure 104.1 Notation used for the mixed Voronoi cell.

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.

Figure 104.2 The case with the obtuse angle.

Template Parameters
 GeomTraits a model of AnalyticWeightTraits_2 for 2D points; a model of AnalyticWeightTraits_3 for 3D points
Voronoi Region Weight

## 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. More...

template<typename GeomTraits >
GeomTraits::FT CGAL::Weights::mixed_voronoi_area (const CGAL::Point_2< GeomTraits > &p, const CGAL::Point_2< GeomTraits > &q, const CGAL::Point_2< GeomTraits > &r)
computes the area of the mixed Voronoi cell in 2D using the points p, q, and r. More...

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. More...

template<typename Kernel >
Kernel::FT CGAL::Weights::mixed_voronoi_area (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
computes the area of the mixed Voronoi cell in 3D using the points p, q, and r. More...

## ◆ mixed_voronoi_area() [1/4]

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 )

#include <CGAL/Weights/mixed_voronoi_region_weights.h>

computes the area of the mixed Voronoi cell in 2D using the points p, q, and r.

Template Parameters
 GeomTraits a model of AnalyticWeightTraits_2
Examples:
Weights/weighted_laplacian.cpp.

## ◆ mixed_voronoi_area() [2/4]

template<typename GeomTraits >
 GeomTraits::FT CGAL::Weights::mixed_voronoi_area ( const CGAL::Point_2< GeomTraits > & p, const CGAL::Point_2< GeomTraits > & q, const CGAL::Point_2< GeomTraits > & r )

#include <CGAL/Weights/mixed_voronoi_region_weights.h>

computes the area of the mixed Voronoi cell in 2D using the points p, q, and r.

Template Parameters
 Kernel a model of Kernel

## ◆ mixed_voronoi_area() [3/4]

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 )

#include <CGAL/Weights/mixed_voronoi_region_weights.h>

computes the area of the mixed Voronoi cell in 3D using the points p, q, and r.

Template Parameters
 GeomTraits a model of AnalyticWeightTraits_3

## ◆ mixed_voronoi_area() [4/4]

template<typename Kernel >
 Kernel::FT CGAL::Weights::mixed_voronoi_area ( const CGAL::Point_3< Kernel > & p, const CGAL::Point_3< Kernel > & q, const CGAL::Point_3< Kernel > & r )

#include <CGAL/Weights/mixed_voronoi_region_weights.h>

computes the area of the mixed Voronoi cell in 3D using the points p, q, and r.

Template Parameters
 Kernel a model of Kernel