Straight Skeletons for General Polygonal Figures in the Plane

A novel type of skeleton for general polygonal gures, the straight skeleton S(G) of a planar straight line graph G, is introduced and discussed. Exact bounds on the size of S(G) are derived. The straight line structure of S(G) and its lower combinatorial complexity may make S(G) preferable to the widely used Voronoi diagram (or medial axis) of G in several applications. We explain why S(G) has no Voronoi diagram based interpretation and why standard construction techniques fail to work. A simple O(n) space algorithm for constructing S(G) is proposed. The worst-case running time is O(n 3 log n), but the algorithm can be expected to be practically eecient, and it is easy to implement. We also show that the concept of S(G) is exible enough to allow an individual weighting of the edges and vertices of G, without changes in the maximal size of S(G), or in the method of construction. Apart from ooering an alternative to Voronoi-type skeletons, these generalizations of S(G) have applications to the reconstruction of a geographical terrain from a given river map, and to the construction of a polygonal roof above a given layout of ground walls.