title: Weighted straight skeletons in the plane.
abstract: We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights.
authors: David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 1A2, Canada.
authors: Therese
authors: T
authors: Biedl
authors: Universität Salzburg, FB Computerwissenschaften, 5020 Salzburg, Austria.
authors: Martin
authors: M
authors: Held
authors: Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria.
authors: Stefan
authors: S
authors: Huber
authors: Universität Salzburg, FB Computerwissenschaften, 5020 Salzburg, Austria.
authors: Dominik
authors: D
authors: Kaaser
authors: Universität Salzburg, FB Computerwissenschaften, 5020 Salzburg, Austria.
authors: Peter
authors: P
authors: Palfrader
keywords: Ambiguity; Characterization; Generalization; Positive and negative weights; Straight skeleton