Definition

Operations
A model of this concept must provide:
Comparison_result	operator() (const K::Point_3 &a1, const K::Point_3 &b1, const K::Point_3 &c1, const K::Point_3 &d1, const K::FT &cosine)
	compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the dihedral angle, in \( [0, \pi]\), of the tetrahedron \( (a_1, b_1, c_1, d_1)\) at the edge `(a_1, b_1)`, 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 &d1, const K::Point_3 &a2, const K::Point_3 &b2, const K::Point_3 &c2, const K::Point_3 &d2)
	compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_i\) is the dihedral angle in the tetrahedron `(a_i, b_i, c_i, d_i)` at the edge `(a_i, b_i)`.

Comparison_result	operator() (const K::Vector_3 &u1, const K::Vector_3 &v1, const K::Vector_3 &w1, const K::FT &cosine)
	compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the dihedral angle, in \( [0, \pi]\), between the vectorial planes defined by `(u_1, v_1)` and `(u_1, w_1)`, and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) = cosine\).

Comparison_result	operator() (const K::Vector_3 &u1, const K::Vector_3 &v1, const K::Vector_3 &w1, const K::Vector_3 &u2, const K::Vector_3 &v2, const K::Vector_3 &w2)
	compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_i\) is the dihedral angle between the vectorial planes defined by `(u_i, v_i)` and `(u_i, w_i)`.

Member Function Documentation

◆ operator()() [1/4]

Comparison_result Kernel::CompareDihedralAngle_3::operator()	(	const K::Point_3 &	a1,
		const K::Point_3 &	b1,
		const K::Point_3 &	c1,
		const K::Point_3 &	d1,
		const K::FT &	cosine
	)

compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the dihedral angle, in \( [0, \pi]\), of the tetrahedron \( (a_1, b_1, c_1, d_1)\) at the edge (a_1, b_1), and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) = cosine\).

The result is the same as operator()(b1-a1, c1-a1, d1-a1, cosine).

Precondition: a_1, b_1, c_1 are not collinear, and a_1, b_1, d_1 are not collinear.

◆ operator()() [2/4]

Comparison_result Kernel::CompareDihedralAngle_3::operator()	(	const K::Point_3 &	a1,
		const K::Point_3 &	b1,
		const K::Point_3 &	c1,
		const K::Point_3 &	d1,
		const K::Point_3 &	a2,
		const K::Point_3 &	b2,
		const K::Point_3 &	c2,
		const K::Point_3 &	d2
	)

compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_i\) is the dihedral angle in the tetrahedron (a_i, b_i, c_i, d_i) at the edge (a_i, b_i).

These two angles are computed in \( [0, \pi]\). The result is the same as operator()(b1-a1, c1-a1, d1-a1, b2-a2, c2-a2, d2-a2).

Precondition: For \( i \in\{1,2\}\), a_i, b_i, c_i are not collinear, and a_i, b_i, d_i are not collinear.

◆ operator()() [3/4]

Comparison_result Kernel::CompareDihedralAngle_3::operator()	(	const K::Vector_3 &	u1,
		const K::Vector_3 &	v1,
		const K::Vector_3 &	w1,
		const K::FT &	cosine
	)

compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the dihedral angle, in \( [0, \pi]\), between the vectorial planes defined by (u_1, v_1) and (u_1, w_1), and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) = cosine\).

Precondition: u_1 and v_1 are not collinear, and u_1 and w_1 are not collinear.

◆ operator()() [4/4]

Comparison_result Kernel::CompareDihedralAngle_3::operator()	(	const K::Vector_3 &	u1,
		const K::Vector_3 &	v1,
		const K::Vector_3 &	w1,
		const K::Vector_3 &	u2,
		const K::Vector_3 &	v2,
		const K::Vector_3 &	w2
	)

compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_i\) is the dihedral angle between the vectorial planes defined by (u_i, v_i) and (u_i, w_i).

These two angles are computed in \( [0, \pi]\).