Weighted Straight Skeletons In The Plane

In this paper, we investigate the weighted straight skele-ton from a geometric, graph-theoretical and combinato-rial point of view. We start with a thorough defini-tion, shed light on an ambiguity issue in the procedural definition, and propose solutions. We investigate the geometry of faces and the roof model and we discuss in which cases the straight skeleton is connected. Fi-nally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may con-tain cycles, and we discuss under which circumstances the weighted straight skeleton still behaves similar to its unweighted pendant.