mirror of https://github.com/CGAL/cgal
105 lines
3.3 KiB
TeX
105 lines
3.3 KiB
TeX
\begin{ccRefClass} {Tetrahedron_3<Kernel>}
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\ccDefinition An object $t$ of the class \ccRefName\ is an oriented
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tetrahedron in the three-dimensional Euclidean space $\E^3$.
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It is defined by four vertices $p_0$, $p_1$, $p_2$ and $p_3$.
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The orientation of a tetrahedron is the orientation of its four
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vertices. That means it is positive when $p_3$ is on the positive
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side of the plane defined by $p_0$, $p_1$ and $p_2$.
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The tetrahedron itself splits the space $\E_3$ in a {\em positive} and
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a {\em negative} side.
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The boundary of a tetrahedron splits the space in two open regions, a
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bounded one and an unbounded one.
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\ccCreation
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\ccCreationVariable{t}
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\ccHidden \ccConstructor{Tetrahedron_3();}
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{introduces an uninitialized variable \ccVar.}
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\ccHidden \ccConstructor{Tetrahedron_3(const Tetrahedron_3<Kernel> &u);}
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{copy constructor.}
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\ccConstructor{Tetrahedron_3(const Point_3<Kernel> &p0,
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const Point_3<Kernel> &p1,
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const Point_3<Kernel> &p2,
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const Point_3<Kernel> &p3);}
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{introduces a tetrahedron \ccVar\ with vertices $p_0$, $p_1$, $p_2$ and $p_3$.}
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\ccOperations
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\ccHidden \ccMethod{Tetrahedron_3<Kernel> & operator=(const Tetrahedron_3<Kernel> &t2);}
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{Assignment.}
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\ccMethod{bool operator==(const Tetrahedron_3<Kernel> &t2) const;}
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% {Test for equality: two tetrahedra are equal, iff there exists a
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% cyclic permutation of the vertices of $t2$, such that they are
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% equal to the vertices of~\ccVar.}
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{Test for equality: two tetrahedra \ccVar\ and \ccc{t2} are equal,
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iff \ccVar\ and \ccc{t2} have the same orientation and
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their sets (not sequences) of vertices are equal.}
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\ccMethod{bool operator!=(const Tetrahedron_3<Kernel> &t2) const;}
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{Test for inequality.}
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\ccMethod{Point_3<Kernel> vertex(int i) const;}
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{returns the i'th vertex modulo 4 of~\ccVar.}
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\ccMethod{Point_3<Kernel> operator[](int i) const;}
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{returns \ccStyle{vertex(int i)}.}
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\ccPredicates
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\ccMethod{bool is_degenerate() const;}
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{Tetrahedron \ccVar\ is degenerate, if the vertices are coplanar.}
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\ccMethod{Orientation orientation() const;}
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{ }
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\ccMethod{Oriented_side oriented_side(const Point_3<Kernel> &p) const;}
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{\ccPrecond: \ccVar\ is not degenerate.}
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\ccMethod{Bounded_side bounded_side(const Point_3<Kernel> &p) const;}
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{\ccPrecond: \ccVar\ is not degenerate.}
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For convenience we provide the following boolean functions:
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\ccMethod{bool has_on_positive_side(const Point_3<Kernel> &p) const;}
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{}
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\ccGlue
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\ccMethod{bool has_on_negative_side(const Point_3<Kernel> &p) const;}
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{}
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\ccGlue
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\ccMethod{bool has_on_boundary(const Point_3<Kernel> &p) const;}
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{}
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\ccGlue
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\ccMethod{bool has_on_bounded_side(const Point_3<Kernel> &p) const;}
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{}
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\ccGlue
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\ccMethod{bool has_on_unbounded_side(const Point_3<Kernel> &p) const;}
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{}
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\ccHeading{Miscellaneous}
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\ccMethod{Kernel::FT volume() const;}
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{returns the signed volume of \ccVar.}
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\ccMethod{Bbox_3 bbox() const;}
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{returns a bounding box containing \ccVar.}
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\ccMethod{Tetrahedron_3<Kernel> transform(const Aff_transformation_3<Kernel> &at) const;}
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{returns the tetrahedron obtained by applying $at$ on the three
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vertices of~\ccVar.}
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\ccSeeAlso
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\ccRefConceptPage{Kernel::Tetrahedron_3} \\
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\end{ccRefClass}
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