CGAL 6.0 - Weights
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#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 . | |
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 . | |
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 . | |
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 . | |
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 | ||
) |
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 | ||
) |
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
.
GeomTraits | a model of AnalyticWeightTraits_2 |
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
.
GeomTraits | a model of AnalyticWeightTraits_3 |