CGAL 5.0 - 2D and 3D Linear Geometry Kernel
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...

## ◆ 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.