CGAL::compare_dihedral_angle()

Functions
template<typename Kernel>
Comparison_result	CGAL::compare_dihedral_angle (const CGAL::Point_3< Kernel > &a1, const CGAL::Point_3< Kernel > &b1, const CGAL::Point_3< Kernel > &c1, const CGAL::Point_3< Kernel > &d1, const Kernel::FT &cosine)
	compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the dihedral angle, in \( [0, \pi]\), of the tetrahedron (a1, b1, c1, d1) at the edge (a1, b1), and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) = cosine\).
template<typename Kernel>
Comparison_result	CGAL::compare_dihedral_angle (const CGAL::Point_3< Kernel > &a1, const CGAL::Point_3< Kernel > &b1, const CGAL::Point_3< Kernel > &c1, const CGAL::Point_3< Kernel > &d1, const CGAL::Point_3< Kernel > &a2, const CGAL::Point_3< Kernel > &b2, const CGAL::Point_3< Kernel > &c2, const CGAL::Point_3< Kernel > &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).
template<typename Kernel>
Comparison_result	CGAL::compare_dihedral_angle (const CGAL::Vector_3< Kernel > &u1, const CGAL::Vector_3< Kernel > &v1, const CGAL::Vector_3< Kernel > &w1, const Kernel::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 \( cos(\theta_2) = cosine\).
template<typename Kernel>
Comparison_result	CGAL::compare_dihedral_angle (const CGAL::Vector_3< Kernel > &u1, const CGAL::Vector_3< Kernel > &v1, const CGAL::Vector_3< Kernel > &w1, const CGAL::Vector_3< Kernel > &u2, const CGAL::Vector_3< Kernel > &v2, const CGAL::Vector_3< Kernel > &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).

Function Documentation

compare_dihedral_angle() [1/4]

template<typename Kernel>

Comparison_result CGAL::compare_dihedral_angle	(	const CGAL::Point_3< Kernel > &	a1,
		const CGAL::Point_3< Kernel > &	b1,
		const CGAL::Point_3< Kernel > &	c1,
		const CGAL::Point_3< Kernel > &	d1,
		const CGAL::Point_3< Kernel > &	a2,
		const CGAL::Point_3< Kernel > &	b2,
		const CGAL::Point_3< Kernel > &	c2,
		const CGAL::Point_3< Kernel > &	d2 )

#include <CGAL/Kernel/global_functions.h>

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 compare_dihedral_angle(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.

compare_dihedral_angle() [2/4]

template<typename Kernel>

Comparison_result CGAL::compare_dihedral_angle	(	const CGAL::Point_3< Kernel > &	a1,
		const CGAL::Point_3< Kernel > &	b1,
		const CGAL::Point_3< Kernel > &	c1,
		const CGAL::Point_3< Kernel > &	d1,
		const Kernel::FT &	cosine )

#include <CGAL/Kernel/global_functions.h>

compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the dihedral angle, in \( [0, \pi]\), of the tetrahedron (a1, b1, c1, d1) at the edge (a1, b1), and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) = cosine\).

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

Precondition

a1, b1, c1 are not collinear, and a1, b1, d1 are not collinear.

compare_dihedral_angle() [3/4]

template<typename Kernel>

Comparison_result CGAL::compare_dihedral_angle	(	const CGAL::Vector_3< Kernel > &	u1,
		const CGAL::Vector_3< Kernel > &	v1,
		const CGAL::Vector_3< Kernel > &	w1,
		const CGAL::Vector_3< Kernel > &	u2,
		const CGAL::Vector_3< Kernel > &	v2,
		const CGAL::Vector_3< Kernel > &	w2 )

#include <CGAL/Kernel/global_functions.h>

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 \( [0, \pi]\).

Precondition

For \( i \in\{1,2\}\), u_i and v_i are not collinear, and u_i and w_i are not collinear.

compare_dihedral_angle() [4/4]

template<typename Kernel>

Comparison_result CGAL::compare_dihedral_angle	(	const CGAL::Vector_3< Kernel > &	u1,
		const CGAL::Vector_3< Kernel > &	v1,
		const CGAL::Vector_3< Kernel > &	w1,
		const Kernel::FT &	cosine )

#include <CGAL/Kernel/global_functions.h>

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.