Straight skeleton

The shrinking process, the straight skeleton (blue) and the roof model.

In geometry, a straight skeleton is a method of representing a polygon by a topological skeleton. It is similar in some ways to the medial axis but differs in that the skeleton is composed of straight line segments, while the medial axis of a polygon may involve parabolic curves. However, both are homotopy-equivalent to the underlying polygon.[1]

Straight skeletons were first defined for simple polygons by Aichholzer et al. (1995),[2] and generalized to planar straight-line graphs (PSLG) by Aichholzer & Aurenhammer (1996).[3] In their interpretation as projection of roof surfaces, they are already extensively discussed by G. A. Peschka (1877).[4]

  1. ^ Huber, Stefan (2018). "The Topology of Skeletons and Offsets" (PDF). Proceedings of the 34th European Workshop on Computational Geometry (EuroCG'18)..
  2. ^ Aichholzer, Oswin; Aurenhammer, Franz; Alberts, David; Gärtner, Bernd (1995). "A novel type of skeleton for polygons". Journal of Universal Computer Science. 1 (12): 752–761. doi:10.1007/978-3-642-80350-5_65. MR 1392429..
  3. ^ Aichholzer, Oswin; Aurenhammer, Franz (1996). "Straight skeletons for general polygonal figures in the plane". Proc. 2nd Ann. Int. Conf. Computing and Combinatorics (COCOON '96). Lecture Notes in Computer Science. Vol. 1090. Springer-Verlag. pp. 117–126.
  4. ^ Peschka, Gustav A. (1877). Kotirte Ebenen: Kotirte Projektionen und deren Anwendung; Vorträge. Brünn: Buschak & Irrgang. doi:10.14463/GBV:865177619..