Output-Sensitive Parallel Algorithm for Polygon Clipping

Abstract

Polygon clipping is one of the complex operations in computational geometry. It is a primitive operation in many fields such as Geographic Information Systems (GIS), Computer Graphics and VLSI CAD. Sequential algorithms for this problem are in abundance in literature but there are very few parallel algorithms solving it in its most general form. We present the first output-sensitive CREW PRAM algorithm, which can perform polygon clipping in O(logn) time using (n + k + k') processors, where n is the number of vertices, k is the number of edge intersections and k' is the additional temporary vertices introduced due to the partitioning of polygons. The current best algorithm by Karinthi, Srinivas, and Almasi [1] does not handle self-intersecting polygons, is not output-sensitive and must employ ⊝(n2) processors to achieve O(logn) time. Our algorithm is developed from the first principles and it is superior to [1] in cost. It yields a practical implementation on multicores and demonstrates 30x speedup for real-world dataset. Our algorithm can perform the typical clipping operations including intersection, union, and difference.