Fixing sweep line section.

This commit is contained in:
Ester Ezra 2001-06-28 18:22:59 +00:00
parent 7232ec7234
commit f497579c09
2 changed files with 16 additions and 66 deletions

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

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