mirror of https://github.com/CGAL/cgal
87 lines
3.0 KiB
TeX
87 lines
3.0 KiB
TeX
\begin{ccRefClass} {Line_3<Kernel>}
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\ccDefinition
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An object \ccStyle{l} of the data type \ccRefName\ is a directed
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straight line in the three-dimensional Euclidean space $\E^3$.
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\ccCreation
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\ccCreationVariable{l}
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\ccHidden \ccConstructor{Line_3();}
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{introduces an uninitialized variable \ccVar.}
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\ccHidden \ccConstructor{Line_3(const Line_3<Kernel> &h);}
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{copy constructor.}
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\ccConstructor{Line_3(const Point_3<Kernel> &p, const Point_3<Kernel> &q);}
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{introduces a line \ccVar\ passing through the points $p$ and $q$.
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Line \ccVar\ is directed from $p$ to $q$.}
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\ccConstructor{Line_3(const Point_3<Kernel> &p, const Direction_3<Kernel>&d)}
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{introduces a line \ccVar\ passing through point $p$ with
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direction $d$.}
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\ccConstructor{Line_3(const Point_3<Kernel> &p, const Vector_3<Kernel>&v)}
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{introduces a line \ccVar\ passing through point $p$ and
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oriented by $v$.}
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\ccConstructor{Line_3(const Segment_3<Kernel> &s);}
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{returns the line supporting the segment $s$,
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oriented from source to target.}
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\ccConstructor{Line_3(const Ray_3<Kernel> &r);}
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{returns the line supporting the ray $r$, with the
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same orientation.}
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\ccOperations
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\ccSetThreeColumns{Direction_3<Kernel> }{}{\hspace*{8.5cm}}
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\ccHidden \ccMethod{Line_3<Kernel> & operator=(const Line_3<Kernel> &h);}
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{Assignment.}
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\ccMethod{bool operator==(const Line_3<Kernel> &h) const;}
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{Test for equality: two lines are equal, iff they have a non
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empty \ccHtmlNoLinksFrom{intersection} and the same direction.}
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\ccMethod{bool operator!=(const Line_3<Kernel> &h) const;}
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{Test for inequality.}
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\ccMethod{Point_3<Kernel> projection(const Point_3<Kernel> &p) const;}
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{returns the orthogonal \ccHtmlNoLinksFrom{projection} of $p$ on \ccVar.}
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\ccMethod{Point_3<Kernel> point(int i) const;}
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{returns an arbitrary point on \ccVar. It holds
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\ccStyle{point(i) = point(j)}, iff \ccStyle{i=j}.}
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\ccPredicates
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\ccMethod{bool is_degenerate() const;}
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{returns \ccc{true} iff line \ccVar\ is degenerated to a point.}
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\ccMethod{bool has_on(const Point_3<Kernel> &p) const;}
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{returns \ccc{true} iff \ccc{p} lies on \ccVar.}
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\ccHeading{Miscellaneous}
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\ccMethod{Plane_3<Kernel> perpendicular_plane(const Point_3<Kernel> &p) const;}
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{returns the plane perpendicular to \ccVar\ passing through $p$.}
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\ccMethod{Line_3<Kernel> opposite() const;}
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{returns the line with opposite direction.}
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\ccMethod{Vector_3<Kernel> to_vector() const;}
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{returns a vector having the same direction as \ccVar.}
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\ccMethod{Direction_3<Kernel> direction() const;}
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{returns the direction of \ccVar.}
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\ccMethod{Line_3<Kernel> transform(const Aff_transformation_3<Kernel> &t) const;}
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{returns the line obtained by applying $t$ on a point on \ccVar\
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and the direction of \ccVar.}
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\ccSeeAlso
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\ccRefConceptPage{Kernel::Line_3}
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\end{ccRefClass}
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