CGAL 5.6.1 - 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].

mixed_voronoi_cell.svg
Figure 106.1 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.

mixed_voronoi_cell_obtuse.svg
Figure 106.2 The case with the obtuse angle.

Template Parameters
GeomTraitsa model of AnalyticWeightTraits_2 for 2D points; a model of AnalyticWeightTraits_3 for 3D points
See also
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...
 

Function Documentation

◆ 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
GeomTraitsa 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
Kernela 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
GeomTraitsa 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
Kernela model of Kernel