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CCCG 2008, Montreal, Quebec, August 1315, 2008 Draining a Polygon

Summary: CCCG 2008, Montr´eal, Qu´ebec, August 13­15, 2008
Draining a Polygon
Rolling a Ball out of a Polygon
Greg Aloupis
Jean Cardinal
S´ebastien Collette
Ferran Hurtado
Stefan Langerman§
Joseph O'Rourke¶
We introduce the problem of draining water (or balls repre-
senting water drops) out of a punctured polygon (or a poly-
hedron) 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


Source: Aloupis, Greg - Département d'Informatique, Université Libre de Bruxelles


Collections: Mathematics; Computer Technologies and Information Sciences