Draining a Polygon-or-Rolling a Ball Out of a Polygon

Authors

Greg Aloupis, Université Libre de Bruxelles
Jean Cardinal, Université Libre de Bruxelles
Sébastien Collette, Université Libre de Bruxelles
Ferran Hurtado, Universitat Politècnica de Catalunya
Stefan Langerman, Université Libre de Bruxelles
Joseph O'Rourke, Smith CollegeFollow

Document Type

Conference Proceeding

Publication Date

12-1-2008

Publication Title

Proceedings of the 20th Annual Canadian Conference on Computational Geometry, CCCG 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.

First Page

79

Last Page

82

Rights

© the authors

Comments

Archived as published.

Recommended Citation

Aloupis, Greg; Cardinal, Jean; Collette, Sébastien; Hurtado, Ferran; Langerman, Stefan; and O'Rourke, Joseph, "Draining a Polygon-or-Rolling a Ball Out of a Polygon" (2008). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/188