cgal/Kernel_23/doc_tex/Kernel_23_ref/Segment_2.tex

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\begin{ccRefClass} {Segment_2<Kernel>}
\ccDefinition An object $s$ of the data type \ccRefName\ is a directed
straight line segment in the two-dimensional Euclidean plane $\E^2$, i.e.\ a
straight line segment $[p,q]$ connecting two points $p,q$
\ccTexHtml{$\in$}{in}
$\R^2$. The segment is topologically closed, i.e.\ the end
points belong to it. Point $p$ is called the {\em source} and $q$
is called the {\em target} of $s$. The length of $s$ is the
Euclidean distance between $p$ and $q$. Note that there is only a function
to compute the square of the length, because otherwise we had to
perform a square root operation which is not defined for all
number types, which is expensive, and may not be exact.
\ccCreation
\ccCreationVariable{s}
\ccHidden \ccConstructor{Segment_2();}
{introduces an uninitialized variable \ccVar.}
\ccHidden \ccConstructor{Segment_2(const Segment_2<Kernel> &q);}
{copy constructor.}
\ccConstructor{Segment_2(const Point_2<Kernel> &p, const Point_2<Kernel> &q);}
{introduces a segment \ccVar\ with source $p$
and target $q$. The segment is directed from the source towards
the target.}
\ccOperations
%\ccSetTwoOfThreeColumns{5cm}{4cm}
\ccSetThreeColumns{Direction_2<Kernel> & }{}{\hspace*{7.5cm}}
\ccHidden \ccMethod{Segment_2<Kernel> & operator=(const Segment_2<Kernel> &q);}
{Assignment.}
\ccMethod{bool operator==(const Segment_2<Kernel> &q) const;}
{Test for equality: Two segments are equal, iff their sources and
targets are equal.}
\ccMethod{bool operator!=(const Segment_2<Kernel> &q) const;}
{Test for inequality.}
\ccMethod{Point_2<Kernel> source() const;}
{returns the source of \ccVar.}
\ccMethod{Point_2<Kernel> target() const;}
{returns the target of \ccVar.}
\ccGlue
\ccMethod{Point_2<Kernel> min() const;}
{returns the point of \ccVar\ with lexicographically smallest coordinate.}
\ccMethod{Point_2<Kernel> max() const;}
{returns the point of \ccVar\ with lexicographically largest coordinate.}
\ccMethod{Point_2<Kernel> vertex(int i) const;}
{returns source or target of \ccVar: \ccStyle{vertex(0)} returns
the source of \ccVar, \ccStyle{vertex(1)} returns the target of \ccVar.
The parameter \ccStyle{i} is taken modulo 2, which gives
easy access to the other vertex. }
\ccMethod{Point_2<Kernel> point(int i) const;}
{returns \ccStyle{vertex(i)}.}
\ccMethod{Point_2<Kernel> operator[](int i) const;}
{returns \ccStyle{vertex(i)}.}
\ccMethod{Kernel::FT squared_length() const;}
{returns the squared length of \ccVar. }
\ccMethod{Direction_2<Kernel> direction() const;}
{returns the direction from source to target of \ccVar.}
\ccMethod{Vector_2<Kernel> to_vector() const;}
{returns the vector \ccVar.\ccc{target()} - \ccVar.\ccc{source()}.}
\ccMethod{Segment_2<Kernel> opposite() const; }
{returns a segment with source and target point interchanged.}
\ccMethod{Line_2<Kernel> supporting_line() const;}
{returns the line $l$ passing through \ccVar. Line $l$ has the
same orientation as segment \ccVar.}
\ccPredicates
\ccMethod{bool is_degenerate() const;}
{segment \ccVar\ is degenerate, if source and target are equal.}
\ccMethod{bool is_horizontal() const;}
{}
\ccGlue
\ccMethod{bool is_vertical() const;}
{}
\ccMethod{bool has_on(const Point_2<Kernel> &p) const;}
{A point is on \ccVar, iff it is equal to the source or target
of \ccVar, or if it is in the interior of \ccVar.}
\ccMethod{bool collinear_has_on(const Point_2<Kernel> &p) const;}
{checks if point $p$ is on segment~\ccVar. This function is faster
than function \ccStyle{has_on()}.
\ccPrecond $p$ is on the supporting line of \ccVar.}
\ccHeading{Miscellaneous}
\ccMethod{Bbox_2 bbox() const;}
{returns a bounding box containing~\ccVar.}
\ccMethod{Segment_2<Kernel> transform(const Aff_transformation_2<Kernel> &t) const;}
{returns the segment obtained by applying $t$ on the source
and the target of \ccVar.}
\ccSeeAlso
\ccRefConceptPage{Kernel::Segment_2}\\
\end{ccRefClass}