Implicit Convex Polygons

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Implicit Convex Polygons
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 (n log n) lower bound on their complexity, and those that yield O(n) time algorithms via prune-and-search methods. Mathematics Subject Classifications (2000): 52B55, 68Q25, 68Q17, 68U05. Key words: linear constraints, linear programming, geometric object representation, prune-andsearch, complexity, computational geometry.
Francisco Gómez, Ferran Hurtado, Suneeta Ra
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 2002
Where JMMA
Authors Francisco Gómez, Ferran Hurtado, Suneeta Ramaswami, Vera Sacristan, Godfried T. Toussaint
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