mirror of https://github.com/CGAL/cgal
70 lines
2.2 KiB
TeX
70 lines
2.2 KiB
TeX
\begin{ccRefClass} {Triangle_3<Kernel>}
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\ccDefinition An object $t$ of the class \ccRefName\ is a triangle in
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the three-dimensional Euclidean space $\E^3$. As the triangle is not
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a full-dimensional object there is only a test whether a point lies on
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the triangle or not.
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\ccCreation
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\ccCreationVariable{t}
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\ccHidden \ccConstructor{Triangle_3();}
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{introduces an uninitialized variable \ccVar.}
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\ccHidden \ccConstructor{Triangle_3(const Triangle_3<Kernel> &u);}
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{copy constructor.}
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\ccConstructor{Triangle_3(const Point_3<Kernel> &p,
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const Point_3<Kernel> &q,
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const Point_3<Kernel> &r);}
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{introduces a triangle \ccVar\ with vertices $p$, $q$ and $r$.}
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\ccOperations
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\ccHidden \ccMethod{Triangle_3<Kernel> & operator=(const Triangle_3<Kernel> &t2);}
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{Assignment.}
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\ccMethod{bool operator==(const Triangle_3<Kernel> &t2) const;}
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{Test for equality: two triangles t and $t_2$ are equal, iff there
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exists a cyclic permutation of the vertices of $t2$, such that
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they are equal to the vertices of~\ccVar.}
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\ccMethod{bool operator!=(const Triangle_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 3 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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\ccMethod{Plane_3<Kernel> supporting_plane();}
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{returns the supporting plane of \ccVar, with same
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orientation.}
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\ccPredicates
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\ccMethod{bool is_degenerate() const;}
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{{\ccVar} is degenerate if its vertices are collinear.}
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\ccMethod{bool has_on(const Point_3<Kernel> &p) const;}
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{A point is on \ccVar, if it is on a vertex, an edge or the
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face of \ccVar.}
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\ccHeading{Miscellaneous}
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\ccMethod{Kernel::FT squared_area() const;}
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{returns a square of the area 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{Triangle_3<Kernel> transform(const Aff_transformation_3<Kernel> &at) const;}
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{returns the triangle 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::Triangle_3} \\
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\end{ccRefClass}
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