CGAL 5.5.1 - Weights
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#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.
Alternative Formulations
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. | |
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 \(2\textbf{cot}\).
FT | a model of FieldNumberType |
cot | the cotangent value |
cotangent_weight()