mirror of https://github.com/CGAL/cgal
Editing of text, especially adding the fact that pmwx handles non x-monotone curves and about the sweep line.
This commit is contained in:
Shai Hirsch
parent
300ed9df0a
commit
3cfa35b6af
|
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@ -24,44 +24,61 @@
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\subsection*{Introduction}
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\ccRefLabel{pmwx_ref_intro}
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The planar map with intersections class extends the planar map
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class. The planar map with intersections adds insertion functions
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that handle intersections and overlapping among the curves of the
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planar map. The basic types of the planar map (vertex, halfedge,
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face, Dcel, etc.) are kept. \ccc{Planar_map_with_intersections_2}
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is templated with the planar map class it derives from.
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The \ccc{Planar Map with Intersections} package extends the
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functionality of the \ccc{Planar Map} package. Morover, the class
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\ccc{Planar_map_with_intersections_2} extends the class
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\ccc{Planar_map_2}. The \ccc{Planar Map with Intersections} package
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supports insertion functions that handle non $x$-monotone curves and
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intersections and overlappings among the curves of the planar
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map. The basic types of the \ccc{Planar Map} package (vertex,
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halfedge, face, Dcel, etc.) are
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kept. \ccc{Planar_map_with_intersections_2} is templated with the
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planar map class it derives from.
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\subsection*{Planar Map with Intersections Traits Class}
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%-----------------------------------------------
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Since the planar map with intersections has an additional
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functionality of intersecting curves it needs additional
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functionality of the traits class. We describe the planar map with
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intersections traits concept following in this chapter.
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Nevertheless, we do not have specific implementation of this
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concept, and we use the arrangement traits instead (see
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Chapter~\ref{I1_ChapterArrangement}).
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Since the planar map with intersections has an additional
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functionality of handling non $x$-monotone and intersecting curves
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it needs additional functionality of the traits class. We describe
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the \ccc{Planar_map_with_intersections_traits} concept following in
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this chapter. Nevertheless, we do not have specific implementation
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of this concept, and we use models of the \ccc{Arrangement_traits}
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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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\subsection*{Sweep Line}
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%-------------------------------------------------
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The \ccc{Planar Map With Intersections} contains a sweep lines algorithm.
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Given a collection of intersecting (possibly overlapping or non $x$-monotone)
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curves the algorithm calculates the intersection points. As a result, the
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collection of pairwise interior disjoint subcurves can be produced, or,
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alternatively, a subdivion is being built.
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This subdivion can be either of the type \ccc{Planar Map With Intersections} or of the
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type \ccc{Planar map}.However, the \ccStyle{Sweep line} is a part of
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\ccStyle {Planar Map With Intersections} package since
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the traits used here are those defined in that package, due to calcluations as finding
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intersections, overlapping and $x$-monotony.
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Using sweep line technique, and building a \ccc{Planar Map With Intersections} is most
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usefull when users have a primar list of curves,
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but inserting intersecting curves each at a time will be needed afterward.
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See the sweep line functions reference pages for implementation details.
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\ccc{sweep_to_construct_planar_map}\lcTex{
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(\ccRefPage{CGAL::sweep_to_construct_planar_map})},
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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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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{Planar_map_with_intersection_traits} 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} 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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\begin{ccAdvanced}
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@ -127,8 +144,9 @@ Total number of edges 5
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\subsection*{Functions}
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\ccRefIdfierPage{CGAL::sweep_to_construct_planar_map<Curve_iterator,Planar_map>(Curve_iterator curves_begin, Curve_iterator curves_end, Planar_map &result);}\\
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\ccRefIdfierPage{CGAL::sweep_to_produce_planar_map_subcurves<Curve_iterator,Traits,Containe>(Curve_iterator curves_begin, Curve_iterator curves_end, Container &subcurves, bool overlapping = false);}
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\ccRefIdfierPage{CGAL::sweep_to_construct_planar_map}\\
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\ccRefIdfierPage{CGAL::sweep_to_produce_planar_map_subcurves}\\
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\end{ccTexOnly}
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@ -59,51 +59,67 @@
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\section{Introduction}
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\paragraph{2D Planar Map with Intersections:} Given a collection $C$ of (possibly
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intersecting) $x$-monotone curves in the plane, we construct a
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collection $C'$ as follows: We decompose each curve in $C$ into
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maximal connected pieces not intersecting any other curve in $C$.
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This way we obtain the collection $C'$ of $x$-monotone, pairwise
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interior disjoint curves.
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Constructing the {\it planar map with intersection} of the curves
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in $C$ gives the {\it planar map}(see
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Chapter~\ref{I1_ChapterPlanarMap}) induced by the curves in $C'$.
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\paragraph{2D Planar Map with Intersections:}
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Given a collection $C$ of (possibly intersecting and not necessarily
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$x$-monotone curves in the plane, we construct a collection $C''$ in
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two steps, as follows: First, we decompose each curve in C intor
|
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maximal x-monotone curves, thus obtaining the collection
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$C'$. Second, We decompose each curve in $C'$ into maximal connected
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pieces not intersecting any other curve in $C'$. This way we obtain
|
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the collection $C''$ of $x$-monotone, pairwise interior disjoint
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curves. Constructing the {\it planar map with intersection} of the
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curves in $C$ gives the {\it planar map}(see
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Chapter~\ref{I1_ChapterPlanarMap}) induced by the curves in $C''$.
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Planar map with intersections extends the functionality of planar
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map by enabling simple insertion of intersecting $x$-monotone
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curves. The planar map with intersections class has different
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insertion functions but it uses the same data structures of the
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planar map. Therefore, any functionality of the planar map is also
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supported here (e.g., traversal of planar map features, point
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location queries). However, The planar map with intersections
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needs additional intersection functions in the geometric traits
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class. Note that if one needs to build a planar map of
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$x$-monotone, pairwise interior disjoint curves, then it would be
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more efficient (in running time) and less demanding (in traits
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class functionality) to use the planar map class.
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The \ccc{Planar Map with Intersections} package extends the
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functionality of the \ccc{Planar Map} package by enabling simple
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insertion of intersecting not necessarily $x$-monotone curves. The
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\ccc{Planar_map_with_intersections_2} class has different insertion
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functions but it uses the same data structures of the planar
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map. Therefore, almost any functionality of the planar map is also
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supported here (e.g., traversal of planar map features, point
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location queries and I/O operations are suppoerted but infinite
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objects are not supported). However, the planar map with
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intersections needs additional intersection functions in the
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geometric traits class. Note that if one needs to build a planar map
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of $x$-monotone, pairwise interior disjoint curves, then it would be
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more efficient (in running time) and less demanding (in traits class
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functionality) to use the planar map class.
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\paragraph{Degeneracies}
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Like the \ccc{Planar Map} package (see
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Chapter~\ref{I1_ChapterPlanarMap}), the \ccc{Planar Map with
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Intersections} package can deal with $x$-degenerate input (including
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vertical segments). However, while in the planar map the input
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curves were assumed to be non intersecting in their interiors, there
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is no such assumption when using planar map with
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intersections. Furthermore, overlapping curves are supported. If two
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curves overlap the traits intersection function returns the two
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endpoints of the common part.
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\paragraph{Degeneracies} Like the planar map class (see
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Chapter~\ref{I1_ChapterPlanarMap}), the planar map with intersections class can deal with
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$x$-degenerate input (including vertical segments). However, while in the
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planar map the input curves were assumed to be non
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intersecting in their interiors, there is no such assumption when using
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planar map with intersections. Furthermore, overlapping curves are
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supported. If two curves overlap the traits intersection function returns
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the two endpoints of the common part.
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\paragraph{Sweep line}
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A \ccc{Planar Map with Intersections} can be built incrementally by
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inserting one curve after the other into the map. For a big number
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of curves it is much faster to perfrom the sweep line algorithm on
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the collection of input curves. A sweep line utility is supported as
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part of the package. The utility can either build the induced planar
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map or rather collect the pairwise interior disjoint subcurves
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computed in a container.
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\paragraph{Sweep line:}
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As mentioned in Chapter ~\ref{I1_ChapterPlanarMap}),
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inserting interior intersecting curves, overlap or non $x$-monotone to \ccc{Planar map}
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is available due to the sweep line algorithm.
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When using the sweep line technique it is also possible to report only
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the resulting subcurves induced by the input curves.
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The sweep line algorithm will use the traits classes defined for \ccc{Planar Maps with Intersections}.
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If no additional insertions of intersecting curves are planned
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following the building of the map it is possible to perform a sweep
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line operation that will build the simpler class \ccc{Planar_map_2}.
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This is possible since the output of the sweep line operation is a
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collection of $x$-monotone pairwise interior disjoint, which are
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supported by the \ccc{Planar Map} package. The result of applying
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the sweep line algorithm to a collection of curves and a non-empty
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map is equal to that of applying the algorithm to the union of the
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planar map curves and the collection of input curves. Simply put,
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the intersections of input curves and planar map curves are also
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calculated.
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%******************************************************************************
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\section{Example Programs}
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%---------------------------------------------------
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\subsection{Simple Example of a Segment Planar Map with Intersections}
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@ -129,14 +145,17 @@ Edges of the planar map:
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\end{verbatim}
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\subsubsection{Example of Sweep line}
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\label{ssec:example1}
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The following example demonstrates the usage of the \ccc {Sweep line} algorithm.
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It constructs a planar map out of four segments --- $(0,0)-(1,1)$ , $(0,1)-(1,0)$ ,
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$(0,0)-(1,0)$ and $(0,1)-(1,1)$ , two of them are intersecting in their interior.
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The resulting planar map will contain all the disjoint interior sub segments obtained
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by the calculation of the \ccc {Sweep line} algorithm. For clearness, we printed all the
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halfedges of the resulting planar map to the standard output using the I/O functions for \ccc{Planar map}.
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\subsection{Example of Sweep Line}
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\label{ssec:example1_sweep}
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The following example demonstrates the usage of the \ccc {Sweep
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line} algorithm. It constructs a planar map out of four segments
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--- $(0,0)-(1,1)$ , $(0,1)-(1,0)$ , $(0,0)-(1,0)$ and $(0,1)-(1,1)$
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(an hourglass shape), two of them are intersecting in their
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interior. The resulting planar map will contain all the disjoint
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interior sub segments obtained by the calculation of the sweep
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line algorithm. For clarity, we printed all the halfedges of the
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resulting planar map to the standard output using the I/O functions
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for the \ccc{Planar map} package.
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\ccIncludeExampleCode{Sweep_line/example1.C}
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@ -24,44 +24,61 @@
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\subsection*{Introduction}
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\ccRefLabel{pmwx_ref_intro}
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|
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The planar map with intersections class extends the planar map
|
||||
class. The planar map with intersections adds insertion functions
|
||||
that handle intersections and overlapping among the curves of the
|
||||
planar map. The basic types of the planar map (vertex, halfedge,
|
||||
face, Dcel, etc.) are kept. \ccc{Planar_map_with_intersections_2}
|
||||
is templated with the planar map class it derives from.
|
||||
The \ccc{Planar Map with Intersections} package extends the
|
||||
functionality of the \ccc{Planar Map} package. Morover, the class
|
||||
\ccc{Planar_map_with_intersections_2} extends the class
|
||||
\ccc{Planar_map_2}. The \ccc{Planar Map with Intersections} package
|
||||
supports insertion functions that handle non $x$-monotone curves and
|
||||
intersections and overlappings among the curves of the planar
|
||||
map. The basic types of the \ccc{Planar Map} package (vertex,
|
||||
halfedge, face, Dcel, etc.) are
|
||||
kept. \ccc{Planar_map_with_intersections_2} is templated with the
|
||||
planar map class it derives from.
|
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|
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\subsection*{Planar Map with Intersections Traits Class}
|
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%-----------------------------------------------
|
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Since the planar map with intersections has an additional
|
||||
functionality of intersecting curves it needs additional
|
||||
functionality of the traits class. We describe the planar map with
|
||||
intersections traits concept following in this chapter.
|
||||
Nevertheless, we do not have specific implementation of this
|
||||
concept, and we use the arrangement traits instead (see
|
||||
Chapter~\ref{I1_ChapterArrangement}).
|
||||
Since the planar map with intersections has an additional
|
||||
functionality of handling non $x$-monotone and intersecting curves
|
||||
it needs additional functionality of the traits class. We describe
|
||||
the \ccc{Planar_map_with_intersections_traits} concept following in
|
||||
this chapter. Nevertheless, we do not have specific implementation
|
||||
of this concept, and we use models of the \ccc{Arrangement_traits}
|
||||
concept, which is a refinement thereof instead (see
|
||||
Chapter~\ref{I1_ChapterArrangement}).
|
||||
|
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\subsection*{Sweep line}
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\subsection*{Sweep Line}
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%-------------------------------------------------
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The \ccc{Planar Map With Intersections} contains a sweep lines algorithm.
|
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Given a collection of intersecting (possibly overlapping or non $x$-monotone)
|
||||
curves the algorithm calculates the intersection points. As a result, the
|
||||
collection of pairwise interior disjoint subcurves can be produced, or,
|
||||
alternatively, a subdivion is being built.
|
||||
This subdivion can be either of the type \ccc{Planar Map With Intersections} or of the
|
||||
type \ccc{Planar map}.However, the \ccStyle{Sweep line} is a part of
|
||||
\ccStyle {Planar Map With Intersections} package since
|
||||
the traits used here are those defined in that package, due to calcluations as finding
|
||||
intersections, overlapping and $x$-monotony.
|
||||
Using sweep line technique, and building a \ccc{Planar Map With Intersections} is most
|
||||
usefull when users have a primar list of curves,
|
||||
but inserting intersecting curves each at a time will be needed afterward.
|
||||
|
||||
See the sweep line functions reference pages for implementation details.
|
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\ccc{sweep_to_construct_planar_map}\lcTex{
|
||||
(\ccRefPage{CGAL::sweep_to_construct_planar_map})},
|
||||
\ccc{sweep_to_produce_planar_map_subcurves}\lcTex{
|
||||
(\ccRefPage{CGAL::sweep_to_produce_planar_map_subcurves})},
|
||||
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{Planar_map_with_intersection_traits} 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} 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}}).
|
||||
|
||||
|
||||
\begin{ccAdvanced}
|
||||
|
|
@ -127,8 +144,9 @@ Total number of edges 5
|
|||
|
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|
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\subsection*{Functions}
|
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\ccRefIdfierPage{CGAL::sweep_to_construct_planar_map<Curve_iterator,Planar_map>(Curve_iterator curves_begin, Curve_iterator curves_end, Planar_map &result);}\\
|
||||
\ccRefIdfierPage{CGAL::sweep_to_produce_planar_map_subcurves<Curve_iterator,Traits,Containe>(Curve_iterator curves_begin, Curve_iterator curves_end, Container &subcurves, bool overlapping = false);}
|
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\ccRefIdfierPage{CGAL::sweep_to_construct_planar_map}\\
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\ccRefIdfierPage{CGAL::sweep_to_produce_planar_map_subcurves}\\
|
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|
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\end{ccTexOnly}
|
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|
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|
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|
|
|
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|
|
@ -59,51 +59,67 @@
|
|||
|
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\section{Introduction}
|
||||
|
||||
\paragraph{2D Planar Map with Intersections:} Given a collection $C$ of (possibly
|
||||
intersecting) $x$-monotone curves in the plane, we construct a
|
||||
collection $C'$ as follows: We decompose each curve in $C$ into
|
||||
maximal connected pieces not intersecting any other curve in $C$.
|
||||
This way we obtain the collection $C'$ of $x$-monotone, pairwise
|
||||
interior disjoint curves.
|
||||
Constructing the {\it planar map with intersection} of the curves
|
||||
in $C$ gives the {\it planar map}(see
|
||||
Chapter~\ref{I1_ChapterPlanarMap}) induced by the curves in $C'$.
|
||||
\paragraph{2D Planar Map with Intersections:}
|
||||
Given a collection $C$ of (possibly intersecting and not necessarily
|
||||
$x$-monotone curves in the plane, we construct a collection $C''$ in
|
||||
two steps, as follows: First, we decompose each curve in C intor
|
||||
maximal x-monotone curves, thus obtaining the collection
|
||||
$C'$. Second, We decompose each curve in $C'$ into maximal connected
|
||||
pieces not intersecting any other curve in $C'$. This way we obtain
|
||||
the collection $C''$ of $x$-monotone, pairwise interior disjoint
|
||||
curves. Constructing the {\it planar map with intersection} of the
|
||||
curves in $C$ gives the {\it planar map}(see
|
||||
Chapter~\ref{I1_ChapterPlanarMap}) induced by the curves in $C''$.
|
||||
|
||||
Planar map with intersections extends the functionality of planar
|
||||
map by enabling simple insertion of intersecting $x$-monotone
|
||||
curves. The planar map with intersections class has different
|
||||
insertion functions but it uses the same data structures of the
|
||||
planar map. Therefore, any functionality of the planar map is also
|
||||
supported here (e.g., traversal of planar map features, point
|
||||
location queries). However, The planar map with intersections
|
||||
needs additional intersection functions in the geometric traits
|
||||
class. Note that if one needs to build a planar map of
|
||||
$x$-monotone, pairwise interior disjoint curves, then it would be
|
||||
more efficient (in running time) and less demanding (in traits
|
||||
class functionality) to use the planar map class.
|
||||
The \ccc{Planar Map with Intersections} package extends the
|
||||
functionality of the \ccc{Planar Map} package by enabling simple
|
||||
insertion of intersecting not necessarily $x$-monotone curves. The
|
||||
\ccc{Planar_map_with_intersections_2} class has different insertion
|
||||
functions but it uses the same data structures of the planar
|
||||
map. Therefore, almost any functionality of the planar map is also
|
||||
supported here (e.g., traversal of planar map features, point
|
||||
location queries and I/O operations are suppoerted but infinite
|
||||
objects are not supported). However, the planar map with
|
||||
intersections needs additional intersection functions in the
|
||||
geometric traits class. Note that if one needs to build a planar map
|
||||
of $x$-monotone, pairwise interior disjoint curves, then it would be
|
||||
more efficient (in running time) and less demanding (in traits class
|
||||
functionality) to use the planar map class.
|
||||
|
||||
\paragraph{Degeneracies}
|
||||
Like the \ccc{Planar Map} package (see
|
||||
Chapter~\ref{I1_ChapterPlanarMap}), the \ccc{Planar Map with
|
||||
Intersections} package can deal with $x$-degenerate input (including
|
||||
vertical segments). However, while in the planar map the input
|
||||
curves were assumed to be non intersecting in their interiors, there
|
||||
is no such assumption when using planar map with
|
||||
intersections. Furthermore, overlapping curves are supported. If two
|
||||
curves overlap the traits intersection function returns the two
|
||||
endpoints of the common part.
|
||||
|
||||
\paragraph{Degeneracies} Like the planar map class (see
|
||||
Chapter~\ref{I1_ChapterPlanarMap}), the planar map with intersections class can deal with
|
||||
$x$-degenerate input (including vertical segments). However, while in the
|
||||
planar map the input curves were assumed to be non
|
||||
intersecting in their interiors, there is no such assumption when using
|
||||
planar map with intersections. Furthermore, overlapping curves are
|
||||
supported. If two curves overlap the traits intersection function returns
|
||||
the two endpoints of the common part.
|
||||
\paragraph{Sweep line}
|
||||
A \ccc{Planar Map with Intersections} can be built incrementally by
|
||||
inserting one curve after the other into the map. For a big number
|
||||
of curves it is much faster to perfrom the sweep line algorithm on
|
||||
the collection of input curves. A sweep line utility is supported as
|
||||
part of the package. The utility can either build the induced planar
|
||||
map or rather collect the pairwise interior disjoint subcurves
|
||||
computed in a container.
|
||||
|
||||
\paragraph{Sweep line:}
|
||||
As mentioned in Chapter ~\ref{I1_ChapterPlanarMap}),
|
||||
inserting interior intersecting curves, overlap or non $x$-monotone to \ccc{Planar map}
|
||||
is available due to the sweep line algorithm.
|
||||
When using the sweep line technique it is also possible to report only
|
||||
the resulting subcurves induced by the input curves.
|
||||
The sweep line algorithm will use the traits classes defined for \ccc{Planar Maps with Intersections}.
|
||||
If no additional insertions of intersecting curves are planned
|
||||
following the building of the map it is possible to perform a sweep
|
||||
line operation that will build the simpler class \ccc{Planar_map_2}.
|
||||
This is possible since the output of the sweep line operation is a
|
||||
collection of $x$-monotone pairwise interior disjoint, which are
|
||||
supported by the \ccc{Planar Map} package. The result of applying
|
||||
the sweep line algorithm to a collection of curves and a non-empty
|
||||
map is equal to that of applying the algorithm to the union of the
|
||||
planar map curves and the collection of input curves. Simply put,
|
||||
the intersections of input curves and planar map curves are also
|
||||
calculated.
|
||||
|
||||
%******************************************************************************
|
||||
|
||||
|
||||
|
||||
\section{Example Programs}
|
||||
%---------------------------------------------------
|
||||
\subsection{Simple Example of a Segment Planar Map with Intersections}
|
||||
|
|
@ -129,14 +145,17 @@ Edges of the planar map:
|
|||
\end{verbatim}
|
||||
|
||||
|
||||
\subsubsection{Example of Sweep line}
|
||||
\label{ssec:example1}
|
||||
The following example demonstrates the usage of the \ccc {Sweep line} algorithm.
|
||||
It constructs a planar map out of four segments --- $(0,0)-(1,1)$ , $(0,1)-(1,0)$ ,
|
||||
$(0,0)-(1,0)$ and $(0,1)-(1,1)$ , two of them are intersecting in their interior.
|
||||
The resulting planar map will contain all the disjoint interior sub segments obtained
|
||||
by the calculation of the \ccc {Sweep line} algorithm. For clearness, we printed all the
|
||||
halfedges of the resulting planar map to the standard output using the I/O functions for \ccc{Planar map}.
|
||||
\subsection{Example of Sweep Line}
|
||||
\label{ssec:example1_sweep}
|
||||
The following example demonstrates the usage of the \ccc {Sweep
|
||||
line} algorithm. It constructs a planar map out of four segments
|
||||
--- $(0,0)-(1,1)$ , $(0,1)-(1,0)$ , $(0,0)-(1,0)$ and $(0,1)-(1,1)$
|
||||
(an hourglass shape), two of them are intersecting in their
|
||||
interior. The resulting planar map will contain all the disjoint
|
||||
interior sub segments obtained by the calculation of the sweep
|
||||
line algorithm. For clarity, we printed all the halfedges of the
|
||||
resulting planar map to the standard output using the I/O functions
|
||||
for the \ccc{Planar map} package.
|
||||
|
||||
\ccIncludeExampleCode{Sweep_line/example1.C}
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue