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 $cos(\theta_2) = cosine$. More...
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). More...
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 $cos(\theta_2) = cosine$. More...
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). More...

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 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() [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 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() [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 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.

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 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.