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Pseudo-Simplicial Complexes from Maximal Locally Convex Functions

Summary: Pseudo-Simplicial Complexes
from Maximal Locally Convex Functions 
Franz Aurenhammer and Hannes Krasser
Institute for Theoretical Computer Science
Graz University of Technology, Graz, Austria
We introduce and discuss pseudo-simplicial complexes in R d as generalizations of
pseudo-triangulations in R 2 . Our approach is based on the concept of maximal locally
convex functions on polytopal domains.
1 Introduction
A pseudo-triangulation is a cell complex in the plane where each cell is a pseudo-triangle, i.e.,
a simple polygon with convex angles at exactly three vertices (the so-called corners). Figure 1
illustrates an example. Being an interesting and exible generalization of triangulations,
pseudo-triangulations have found their place in computational geometry. The scope of their
applications is broad, and they enjoy rich combinatorial and geometric properties; see e.g. [22,
11, 17, 10, 1, 16] and references therein. Unlike triangulations, pseudo-triangulations eluded
a meaningful generalization to higher dimensions so far. The de nition of pseudo-simplices
remained unclear, possibly because of the lack of an adequate de nition of corners of a


Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universitšt Graz


Collections: Computer Technologies and Information Sciences