1st revision

Arrangement_on_surface_2/changes.txt

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+3.3.4 (15 Aug 2007)
+
+- First revision. This package replaces the obslete Arrangement_2 package

Arrangement_on_surface_2/dont_submit

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+Arrangement_on_surface_2.dxy
+benchmarks

Arrangement_on_surface_2/long_description.txt

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+Given a set C of planar curves, the arrangement A(C) is the
+subdivision of the plane into zero-dimensional, one-dimensional and
+two-dimensional cells, called vertices, edges and faces, respectively,
+induced by the curves in C. Arrangements are ubiquitous in the
+computational-geometry literature and have many applications
+in fields like motion planning, computer-aided design, geographical
+information systems, etc.
+
+The curves in C can intersect each other (a single curve may also
+be self-intersecting or may be comprised of several disconnected
+branches) and are not necessarily x-monotone. We construct a
+collection C'' of x-monotone subcurves that are pairwise disjoint in
+their interiors. We do it in two steps as follows. First, we decompose
+each curve in C into maximal x-monotone subcurves (and possibly
+isolated points), obtaining the collection C'. Note that an x-monotone
+curve cannot be self-intersecting. Then, we decompose each curve in
+C' into maximal connected subcurves not intersecting any other curve
+(or point) in C'. The collection C'' may also contain isolated points,
+if the curves of C contain such points. The arrangement induced by the
+collection C'' can be conveniently embedded as a planar graph, whose
+vertices are associated with curve endpoints or with isolated points,
+and whose edges are associated with subcurves. It is easy to see that
+A(C) = A(C''). This graph can be represented using a doubly-connected
+edge list data-structure (DCEL for short), which consists of
+containers of vertices, edges, and faces and maintains the incidence
+relations among these objects.
+
+This package can be used to construct, maintain, alter, and display
+arrangements in the plane. Once an arrangement is constructed, the
+package can be used to obtain results of various queries on the
+arrangement, such as point location. The package also includes generic
+implementations of two algorithmic frameworks, that are, computing the
+zone of an arrangement, and line-sweeping the plane, the arrangements
+is embedded on. These frameworks are used in turn in the
+implementations of other operations on arrangements. Computing the
+overlay of two arrangements, for example, is based on the sweep-line
+framework. 
+
+Arrangements and arrangement components can also be extended to store
+additional data. An important extension stores the construction
+history of the arrangement, such that it is possible to obtain the
+originating curve of an arrangement subcurve.

Arrangement_on_surface_2/maintainer

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+Ron Wein <wein@post.tau.ac.il>
+Efi Fogel <efif@post.tau.ac.il>
+Ophir Setter <ophirset@post.tau.ac.il>
+Shlomo Golubev <golubevs@post.tau.ac.il>