Kernel::CompareAngle_3 Concept Reference

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.