Implicit Convex Polygons |
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Authors: | Francisco Gómez Ferran Hurtado Suneeta Ramaswami Vera Sacristán Godfried Toussaint |
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Affiliation: | (1) Departemento de Matemática Aplicada, EU Informática, Universidad Politécnica de Madrid, Ctra. de Valencia Km 7, 28031 Madrid, Spain;(2) Departement de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain;(3) Department of Computer Science, 322 Business and Science Building, Rutgers University, Camden, NJ, 08102, U.S.A.;(4) School of Computer Science, McGill University, 3480 University, Montréal, Québec, Canada, H3A 2A7 |
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Abstract: | Convex polygons in the plane can be defined explicitly as an ordered list of vertices, or given implicitly, for example by a list of linear constraints. The latter representation has been considered in several fields such as facility location, robotics and computer graphics. In this paper, we investigate many fundamental geometric problems for implicitly represented polygons and give simple and fast algorithms that are easy to implement. We uncover an interesting partition of the problems into two classes: those that exhibit an (nlogn) lower bound on their complexity, and those that yield O(n) time algorithms via prune-and-search methods. |
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Keywords: | linear constraints linear programming geometric object representation prune-and-search complexity computational geometry |
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