Draining a polygon-or-rolling a ball out of a polygon

  • Authors:

  • Greg Aloupis;Jean Cardinal;Sébastien Collette;Ferran Hurtado;Stefan Langerman;Joseph Orourke

  • Affiliations:

  • Université Libre de Bruxelles (ULB), CP212, Bld. du Triomphe, 1050 Brussels, Belgium;Université Libre de Bruxelles (ULB), CP212, Bld. du Triomphe, 1050 Brussels, Belgium;Université Libre de Bruxelles (ULB), CP212, Bld. du Triomphe, 1050 Brussels, Belgium;Universitat Politècnica de Catalunya, Jordi Girona 1-3, E-08034 Barcelona, Spain;Université Libre de Bruxelles (ULB), CP212, Bld. du Triomphe, 1050 Brussels, Belgium;Smith College, Northampton, MA 01063, USA

  • Venue:
  • Computational Geometry: Theory and Applications
  • Year:
  • 2014

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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(n^2logn) 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.