CGAL 6.0 - 2D and 3D Linear Geometry Kernel
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Definition

Operations

A model of this concept must provide:

Comparison_result operator() (const K::Point_3 &a, const K::Point_3 &b, const K::Point_3 &c, const K::FT &cosine)
 compares the angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the angle in \( [0, \pi]\) of the triangle \( (a, b, c)\) at the vertex b, and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) = cosine\).
 
Comparison_result operator() (const K::Point_3 &a1, const K::Point_3 &b1, const K::Point_3 &c1, const K::Point_3 &a2, const K::Point_3 &b2, const K::Point_3 &c2)
 compares the angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the angle in \( [0, \pi]\) of the triangle \( (a1, b1, c1)\) at the vertex b1, and \( \theta_2\) is the angle in \( [0, \pi]\) of the triangle \( (a2, b2, c2)\) at the vertex b2.
 
Comparison_result operator() (const K::Vector_3 &u1, const K::Vector_3 &v1, const K::Vector_3 &u2, const K::Vector_3 &v2)
 compares the angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the angle in \( [0, \pi]\) between the vectors \( u1\) and \( v1\), and \( \theta_2\) is the angle in \( [0, \pi]\) between the vectors \( u2\) and \( v2\).
 

Member Function Documentation

◆ operator()() [1/3]

Comparison_result Kernel::CompareAngle_3::operator() ( const K::Point_3 &  a,
const K::Point_3 &  b,
const K::Point_3 &  c,
const K::FT &  cosine 
)

compares the angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the angle in \( [0, \pi]\) of the triangle \( (a, b, c)\) at the vertex b, and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) = cosine\).

Precondition
a!=b && c!=b.

◆ operator()() [2/3]

Comparison_result Kernel::CompareAngle_3::operator() ( const K::Point_3 &  a1,
const K::Point_3 &  b1,
const K::Point_3 &  c1,
const K::Point_3 &  a2,
const K::Point_3 &  b2,
const K::Point_3 &  c2 
)

compares the angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the angle in \( [0, \pi]\) of the triangle \( (a1, b1, c1)\) at the vertex b1, and \( \theta_2\) is the angle in \( [0, \pi]\) of the triangle \( (a2, b2, c2)\) at the vertex b2.

Precondition
a1!=b1 && c1!=b1 && a2!=b2 && c2!=b2.

◆ operator()() [3/3]

Comparison_result Kernel::CompareAngle_3::operator() ( const K::Vector_3 &  u1,
const K::Vector_3 &  v1,
const K::Vector_3 &  u2,
const K::Vector_3 &  v2 
)

compares the angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the angle in \( [0, \pi]\) between the vectors \( u1\) and \( v1\), and \( \theta_2\) is the angle in \( [0, \pi]\) between the vectors \( u2\) and \( v2\).

Precondition
none of the vectors have zero length.