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CGAL 6.0 - 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 \( \E^3\).
It is defined by four vertices \( p_0\), \( p_1\), \( p_2\) and \( p_3\). The orientation of a tetrahedron is the orientation of its four vertices. That means it is positive when \( p_3\) is on the positive side of the plane defined by \( p_0\), \( p_1\) and \( p_2\).
The tetrahedron itself splits the space \( \E^3\) 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 p0, p1, p2 and p3. | |
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 |
Convenience 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. | |
| CGAL::Tetrahedron_3< Kernel >::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 p0, p1, p2 and p3.
Exact_predicates_inexact_constructions_kernel.| Bbox_3 CGAL::Tetrahedron_3< Kernel >::bbox | ( | ) | const |
returns a bounding box containing t.
Exact_predicates_inexact_constructions_kernel.| Bounded_side CGAL::Tetrahedron_3< Kernel >::bounded_side | ( | const Point_3< Kernel > & | p | ) | const |
t is not degenerate. | Point_3< Kernel > CGAL::Tetrahedron_3< Kernel >::operator[] | ( | int | i | ) | const |
returns vertex(int i).
Exact_predicates_inexact_constructions_kernel.| Oriented_side CGAL::Tetrahedron_3< Kernel >::oriented_side | ( | const Point_3< Kernel > & | p | ) | const |
t is not degenerate. | Point_3< Kernel > CGAL::Tetrahedron_3< Kernel >::vertex | ( | int | i | ) | const |
returns the i'th vertex modulo 4 of t.
Exact_predicates_inexact_constructions_kernel.