CGAL 5.1.5 - 2D and 3D Linear Geometry Kernel
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Operations | |
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 \( cos(\theta_2) = cosine\). More... | |
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) . More... | |
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 \( cos(\theta_2) = cosine\). More... | |
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) . More... | |
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)
.
a_1
, b_1
, c_1
are not collinear, and a_1
, b_1
, d_1
are not collinear. 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)
.
a_i
, b_i
, c_i
are not collinear, and a_i
, b_i
, d_i
are not collinear. 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 \( cos(\theta_2) = cosine\).
u_1
and v_1
are not collinear, and u_1
and w_1
are not collinear. 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 \( [0, \pi]\).
u_i
and v_i
are not collinear, and u_i
and w_i
are not collinear.