mirror of https://github.com/CGAL/cgal
Fixing sweep line section.
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@ -48,39 +48,14 @@
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%concept, which is a refinement thereof instead (see
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%Chapter~\ref{I1_ChapterArrangement}).
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\subsection*{Sweep Line}
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%-------------------------------------------------
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The \ccc{Planar Map with Intersections} packge contains a sweep line
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utility. The sweep line algorithm can be used to build a planar map
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much quicker than in an incremental way, where each curve is
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inserted after the other. Two global functions are provided.
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The function \ccc{sweep_to_construct_planar_map} builds a planar map
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as a result of the call. Mind that it is possible to call this
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function also with an instance the \ccc{Planar_map_2} class rather
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than an instance of \ccc{Planar_map_with_intersections_2}. If no
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additional insertion of intersecting or non $x$-monotone curves are
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planned follwing the building of the map, then it would be more
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efficient (in running time) and less demanding (in traits class
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functionality) to use an instance of the former.
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The function \ccc{sweep_to_produce_planar_map_subcurves} does not
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build a planar map but rather collects the $x$-monotone pairwise
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disjoint subcurves in a container. It is possible to tune the
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function so that it will avoid to produce repetitions of overlapping
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subcurves in the container or not.
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The sweep line utility calculates intersections of curves. The
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\ccc{PlanarMapWithIntersectionTraits_2} concepts requires this
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very functionality. Thus, the sweep line functions have to use
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traits classes that model the above concept. This is true even for
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the case where an instance of \ccc{Planar_map_2<Dcel, Traits>} is built.
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See the sweep line functions reference pages for implementation
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details (\ccc{sweep_to_construct_planar_map}\lcTex{
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\ccRefPage{CGAL::sweep_to_construct_planar_map}} and
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\ccc{sweep_to_produce_planar_map_subcurves}\lcTex{
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\ccRefPage{CGAL::sweep_to_produce_planar_map_subcurves}}).
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\subsection*{Sweep line:}
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The construction of a \ccc{Planar map} can be done using a sweep
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line technique rather than iteratively inserting one curve after another.
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The sweep line algorithm perfomrs better, but is done statically and therefore
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requires the list of curves in advance.
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Due to the sweep line technique, inserting curves which are interior intersect,
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overlap or non $x$-monotone is supported.
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The interface is given in chapter ~\ref{I1_ChapterPlanarMap}.
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\begin{ccAdvanced}
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@ -48,39 +48,14 @@
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%concept, which is a refinement thereof instead (see
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%Chapter~\ref{I1_ChapterArrangement}).
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\subsection*{Sweep Line}
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%-------------------------------------------------
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The \ccc{Planar Map with Intersections} packge contains a sweep line
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utility. The sweep line algorithm can be used to build a planar map
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much quicker than in an incremental way, where each curve is
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inserted after the other. Two global functions are provided.
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The function \ccc{sweep_to_construct_planar_map} builds a planar map
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as a result of the call. Mind that it is possible to call this
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function also with an instance the \ccc{Planar_map_2} class rather
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than an instance of \ccc{Planar_map_with_intersections_2}. If no
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additional insertion of intersecting or non $x$-monotone curves are
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planned follwing the building of the map, then it would be more
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efficient (in running time) and less demanding (in traits class
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functionality) to use an instance of the former.
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The function \ccc{sweep_to_produce_planar_map_subcurves} does not
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build a planar map but rather collects the $x$-monotone pairwise
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disjoint subcurves in a container. It is possible to tune the
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function so that it will avoid to produce repetitions of overlapping
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subcurves in the container or not.
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The sweep line utility calculates intersections of curves. The
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\ccc{PlanarMapWithIntersectionTraits_2} concepts requires this
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very functionality. Thus, the sweep line functions have to use
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traits classes that model the above concept. This is true even for
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the case where an instance of \ccc{Planar_map_2<Dcel, Traits>} is built.
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See the sweep line functions reference pages for implementation
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details (\ccc{sweep_to_construct_planar_map}\lcTex{
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\ccRefPage{CGAL::sweep_to_construct_planar_map}} and
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\ccc{sweep_to_produce_planar_map_subcurves}\lcTex{
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\ccRefPage{CGAL::sweep_to_produce_planar_map_subcurves}}).
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\subsection*{Sweep line:}
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The construction of a \ccc{Planar map} can be done using a sweep
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line technique rather than iteratively inserting one curve after another.
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The sweep line algorithm perfomrs better, but is done statically and therefore
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requires the list of curves in advance.
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Due to the sweep line technique, inserting curves which are interior intersect,
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overlap or non $x$-monotone is supported.
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The interface is given in chapter ~\ref{I1_ChapterPlanarMap}.
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\begin{ccAdvanced}
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