CGAL 4.4 - 2D and 3D Linear Geometry Kernel
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#include <CGAL/Tetrahedron_3.h>
An object t
of the class Tetrahedron_3
is an oriented tetrahedron in the three-dimensional Euclidean space E3.
It is defined by four vertices p0, p1, p2 and p3. The orientation of a tetrahedron is the orientation of its four vertices. That means it is positive when p3 is on the positive side of the plane defined by p0, p1 and p2.
The tetrahedron itself splits the space E3 in a positive and a negative side.
The boundary of a tetrahedron splits the space in two open regions, a bounded one and an unbounded one.
Kernel::Tetrahedron_3
Creation | |
Tetrahedron_3 (const Point_3< Kernel > &p0, const Point_3< Kernel > &p1, const Point_3< Kernel > &p2, const Point_3< Kernel > &p3) | |
introduces a tetrahedron t with vertices p_0 , p_1 , p_2 and p_3 . | |
Operations | |
bool | operator== (const Tetrahedron_3< Kernel > &t2) const |
Test for equality: two tetrahedra t and t2 are equal, iff t and t2 have the same orientation and their sets (not sequences) of vertices are equal. | |
bool | operator!= (const Tetrahedron_3< Kernel > &t2) const |
Test for inequality. | |
Point_3< Kernel > | vertex (int i) const |
returns the i'th vertex modulo 4 of t . | |
Point_3< Kernel > | operator[] (int i) const |
returns vertex(int i) . | |
Predicates | |
bool | is_degenerate () const |
Tetrahedron t is degenerate, if the vertices are coplanar. | |
Orientation | orientation () const |
Oriented_side | oriented_side (const Point_3< Kernel > &p) const |
Bounded_side | bounded_side (const Point_3< Kernel > &p) const |
Convencience Boolean Functions | |
bool | has_on_positive_side (const Point_3< Kernel > &p) const |
bool | has_on_negative_side (const Point_3< Kernel > &p) const |
bool | has_on_boundary (const Point_3< Kernel > &p) const |
bool | has_on_bounded_side (const Point_3< Kernel > &p) const |
bool | has_on_unbounded_side (const Point_3< Kernel > &p) const |
Miscellaneous | |
Kernel::FT | volume () const |
returns the signed volume of t . | |
Bbox_3 | bbox () const |
returns a bounding box containing t . | |
Tetrahedron_3< Kernel > | transform (const Aff_transformation_3< Kernel > &at) const |
returns the tetrahedron obtained by applying at on the three vertices of t . | |
Bounded_side CGAL::Tetrahedron_3< Kernel >::bounded_side | ( | const Point_3< Kernel > & | p) | const |
t
is not degenerate. Oriented_side CGAL::Tetrahedron_3< Kernel >::oriented_side | ( | const Point_3< Kernel > & | p) | const |
t
is not degenerate.