mirror of https://github.com/CGAL/cgal
110 lines
3.9 KiB
TeX
110 lines
3.9 KiB
TeX
\begin{ccRefClass} {Segment_3<Kernel>}
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\ccDefinition An object $s$ of the data type \ccRefName\ is a directed
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straight line segment in the three-dimensional Euclidean space $\E^3$, i.e.\ a
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straight line segment $[p,q]$ connecting two points $p,q \in
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\R^3$. The segment is topologically closed, i.e.\ the end
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points belong to it. Point $p$ is called the {\em source} and $q$
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is called the {\em target} of $s$. The length of $s$ is the
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Euclidean distance between $p$ and $q$. Note that there is only a function
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to compute the square of the length, because otherwise we had to
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perform a square root operation which is not defined for all
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number types, which is expensive, and may not be exact.
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\ccCreation
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\ccCreationVariable{s}
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\ccHidden \ccConstructor{Segment_3();}
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{introduces an uninitialized variable \ccVar.}
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\ccHidden \ccConstructor{Segment_3(const Segment_3<Kernel> &q);}
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{copy constructor.}
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\ccConstructor{Segment_3(const Point_3<Kernel> &p, const Point_3<Kernel> &q);}
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{introduces a segment \ccVar\ with source $p$
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and target $q$. It is directed from the source towards
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the target.}
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\ccOperations
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%\ccSetTwoOfThreeColumns{5cm}{4cm}
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\ccHidden \ccMethod{Segment_3<Kernel> & operator=(const Segment_3<Kernel> &q);}
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{Assignment.}
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\ccMethod{bool operator==(const Segment_3<Kernel> &q) const;}
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{Test for equality: Two segments are equal, iff their sources and
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targets are equal.}
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\ccMethod{bool operator!=(const Segment_3<Kernel> &q) const;}
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{Test for inequality.}
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\ccMethod{Point_3<Kernel> source() const;}
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{returns the source of \ccVar.}
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\ccGlue
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\ccMethod{Point_3<Kernel> target() const;}
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{returns the target of \ccVar.}
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\ccMethod{Point_3<Kernel> min() const;}
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{returns the point of \ccVar\ with smallest coordinate (lexicographically).}
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\ccMethod{Point_3<Kernel> max() const;}
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{returns the point of \ccVar\ with largest coordinate (lexicographically).}
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\ccMethod{Point_3<Kernel> vertex(int i) const;}
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{returns source or target of \ccVar: \ccStyle{vertex(0)} returns
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the source, \ccStyle{vertex(1)} returns the target.
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The parameter \ccStyle{i} is taken modulo 2, which gives
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easy access to the other vertex.}
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\ccMethod{Point_3<Kernel> point(int i) const;}
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{returns \ccStyle{vertex(i)}.}
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\ccGlue
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\ccMethod{Point_3<Kernel> operator[](int i) const;}
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{returns \ccStyle{vertex(i)}.}
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\ccMethod{Kernel::FT squared_length() const;}
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{returns the squared length of \ccVar. }
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\ccMethod{Vector_3<Kernel> to_vector() const;}
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{returns the vector \ccVar.\ccc{target()} - \ccVar.\ccc{source()}.}
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\ccMethod{Direction_3<Kernel> direction() const;}
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{returns the direction from source to target.}
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\ccMethod{Segment_3<Kernel> opposite() const; }
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{returns a segment with source and target interchanged.}
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\ccMethod{Line_3<Kernel> supporting_line() const;}
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{returns the line $l$ passing through \ccVar. Line $l$ has the
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same orientation as segment \ccVar, that is
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from the source to the target of \ccVar.}
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\ccMethod{bool is_degenerate() const;}
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{segment \ccVar\ is degenerate, if source and target fall together.}
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\ccMethod{bool has_on(const Point_3<Kernel> &p) const;}
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{A point is on \ccVar, iff it is equal to the source or target
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of \ccVar, or if it is in the interior of \ccVar.}
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%
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% \ccMethod{bool collinear_has_on(const Point_3<Kernel> &p) const;}
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% {checks if point $p$ is on segment~\ccVar. This function is faster
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% than function \ccStyle{has_on()}.
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% \ccPrecond $p$ is collinear to \ccVar.}
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%
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\ccMethod{Bbox_3 bbox() const;}
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{returns a bounding box containing~\ccVar.}
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\ccMethod{Segment_3<Kernel> transform(const Aff_transformation_3<Kernel> &t) const;}
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{returns the segment obtained by applying $t$ on the source
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and the target of \ccVar.}
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\ccSeeAlso
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\ccRefConceptPage{Kernel::Segment_3}\\
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\end{ccRefClass}
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