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Summary: Draining a Polygon
or
Rolling a Ball out of a Polygon
Greg Aloupis
Jean Cardinal
S´ebastien Collette
Ferran Hurtado§
Stefan Langerman¶
Joseph O'Rourke
September 15, 2008
Abstract
We introduce the problem of draining water (or balls representing
water drops) out of a punctured polygon (or a polyhedron) by rotating the
shape. For 2D polygons, we obtain combinatorial bounds on the number
of holes needed, both for arbitrary polygons and for special classes of
polygons. We detail an O(n2
log n) algorithm that finds the minimum
number of holes needed for a given polygon, and argue that the complexity
remains polynomial for polyhedra in 3D. We make a start at characterizing
the 1-drainable shapes, those that only need one hole.
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