 
Summary: Straight Skeletons for General Polygonal Figures
in the Plane
OSWIN AICHHOLZER
FRANZ AURENHAMMER
Institute for Theoretical Computer Science
Graz University of Technology
Klosterwiesgasse 32/2, A8010 Graz, Austria
foaich,aureng@igi.tugraz.ac.at
Abstract: A novel type of skeleton for general polygonal figures, 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 worstcase running time is O(n 3 log n), but the algorithm can be expected
to be practically efficient, and it is easy to implement.
We also show that the concept of S(G) is flexible 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 offering an alternative to Voronoitype 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.
