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 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.

Figure 106.2 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

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.
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.

Function Documentation

mixed_voronoi_area() [1/4]

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() [2/4]

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

mixed_voronoi_area() [3/4]

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() [4/4]

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