#include <CGAL/Weights/cotangent_weights.h>

This weight is computed as \(w = 2 (\cot\beta + \cot\gamma)\) with notations shown in the figure below.

Here, q is a query point and the points p0, p1, and p2 are its neighbors.

Alternative formulations are explained in Implementation.

Figure 105.1 Notation used for the cotangent weight.

Alternative Formulations

This weight is equal to the Discrete Harmonic Weight.
This weight is a special case of the Three Point Family Weight.

Template Parameters

GeomTraits a model of AnalyticWeightTraits_2 for 2D points; a model of AnalyticWeightTraits_3 for 3D points

Functions
template<typename FT >
FT	CGAL::Weights::half_cotangent_weight (const FT cot)
	computes the half value of the cotangent weight. More...

template<typename GeomTraits >
GeomTraits::FT	CGAL::Weights::cotangent_weight (const typename GeomTraits::Point_2 &p0, const typename GeomTraits::Point_2 &p1, const typename GeomTraits::Point_2 &p2, const typename GeomTraits::Point_2 &q, const GeomTraits &traits)
	computes the cotangent weight in 2D at `q` using the points `p0`, `p1`, and `p2`, given a traits class `traits` with geometric objects, predicates, and constructions.

template<typename GeomTraits >
GeomTraits::FT	CGAL::Weights::cotangent_weight (const typename GeomTraits::Point_3 &p0, const typename GeomTraits::Point_3 &p1, const typename GeomTraits::Point_3 &p2, const typename GeomTraits::Point_3 &q, const GeomTraits &traits)
	computes the cotangent weight in 3D at `q` using the points `p0`, `p1`, and `p2`, given a traits class `traits` with geometric objects, predicates, and constructions.

template<typename K >
K::FT	CGAL::Weights::cotangent_weight (const CGAL::Point_2< K > &p0, const CGAL::Point_2< K > &p1, const CGAL::Point_2< K > &p2, const CGAL::Point_2< K > &q)
	computes the cotangent weight in 2D at `q` using the points `p0`, `p1`, and `p2` which are parameterized by a `Kernel` K.

template<typename K >
K::FT	CGAL::Weights::cotangent_weight (const CGAL::Point_3< K > &p0, const CGAL::Point_3< K > &p1, const CGAL::Point_3< K > &p2, const CGAL::Point_3< K > &q)
	computes the cotangent weight in 3D at `q` using the points `p0`, `p1`, and `p2` which are parameterized by a `Kernel` K.

Function Documentation

◆ half_cotangent_weight()

template<typename FT >

FT CGAL::Weights::half_cotangent_weight ( const FT cot )

#include <CGAL/Weights/cotangent_weights.h>

computes the half value of the cotangent weight.

This function constructs the half of the cotangent weight using the precomputed cotangent value. The returned value is \(2\textbf{cot}\).

Template Parameters

FT	a model of `FieldNumberType`

Parameters

cot	the cotangent value

See also: cotangent_weight()

Functions

Function Documentation

◆ half_cotangent_weight()