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Efi Fogel 2006-03-30 23:08:06 +00:00
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@ -379,6 +379,7 @@ Boolean_set_operations_2/doc_tex/Boolean_set_operations_2/fig/unique.eps -text
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Boolean_set_operations_2/examples/Boolean_set_operations_2/test.dxf -text
Boolean_set_operations_2/long_description.txt -text
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Boolean_set_operations_2/long_description.txt Executable file
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This package consists of the implementation of Boolean set-operations
on point sets bounded by weekly x-monotone curves in 2-dimensional
Euclidean space. (Continuous planar curves or vertical segments.} In
particular, it contains the implementation of regularized Boolean
set-operations, intersection predicates, and point containment predicates.
A regularized Boolean set-operation op* can be obtained by first
taking the interior of the resultant point set of an ordinary Boolean
set-operation (P op Q) and then by taking the closure [Hoff]. That is,
(P op* Q = closure(interior(P op Q)). Regularized Boolean
set-operations appear in Constructive Solid Geometry (CSG), because
regular sets are closed under regularized Boolean set-operations, and
because regularization eliminates lower dimensional features, namely
isolated vertices and antennas, thus simplifying and restricting the
representation to physically meaningful solids. Our package provides
regularized operations on polygons and general polygons, where the
edges of a general polygon may be general x-monotone curves, rather
than being simple line segments.
[Hoff] Christoph M. Hoffmann, "Solid Modeling",
"Handbook of Discrete and Computational Geometry",
editors Jacob E. Goodman and Joseph O'Rourke,
Chapman & Hall/CRC, 2nd edition, 2004, 56, "1257--1278"