A NEW APPROACH FOR THE GEODESIC VORONOI DIAGRAM OF POINTS IN A SIMPLEPOLYGON AND OTHER RESTRICTED POLYGONAL DOMAINS

We introduce a new method for computing the geodesic Voronoi diagram o f point sites in a simple polygon and other restricted polygonal domai ns. Our method combines a sweep of the polygonal domain with the mergi ng step of a usual divide-and-conquer algorithm. The time complexity i s O((n + k) log(n + k)) where n is the number of vertices and k is the number of points, improving upon previously known bounds. Space is O( n + k). Other polygonal domains where our method is applicable include (among others) a polygonal domain of parallel disjoint line segments and a polygonal domain of rectangles in the L-1 metric.