Resolving intersection, union and difference of two simple polygons based on minimum circle

Abstract

A new algorithm for Boolean operation of two simple polygons based on minimum circle was presented. Polygon P and Q were initialized to counter-clockwise direction, and the edges connecting to each intersection point of P and Q were arranged in sequential order. Then, all minimum circles were found using the minimum turning angle rule. These minimum circles were classified according to edges direction in P and Q. Intersection, union, and difference of the two polygons are corresponding to different kinds of minimum circles. The algorithm run in time O((n+m+k)logd) in a worst presented case, where n and m were the vertex numbers of the two polygons respectively, k was the numbers of intersection points, and d was the number of polygon’s monotonic chain. The algorithm has explicit geometric significance, and well resolves the problems in special cases, such as overlapped edges, and operation edges intersection at the vertex of edges.