 
Summary: PseudoSimplicial Complexes
from Maximal Locally Convex Functions
Franz Aurenhammer and Hannes Krasser
Institute for Theoretical Computer Science
Graz University of Technology, Graz, Austria
fauren,hkrasserg@igi.tugraz.at
Abstract
We introduce and discuss pseudosimplicial complexes in R d as generalizations of
pseudotriangulations in R 2 . Our approach is based on the concept of maximal locally
convex functions on polytopal domains.
1 Introduction
A pseudotriangulation is a cell complex in the plane where each cell is a pseudotriangle, i.e.,
a simple polygon with convex angles at exactly three vertices (the socalled corners). Figure 1
illustrates an example. Being an interesting and
exible generalization of triangulations,
pseudotriangulations 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, pseudotriangulations eluded
a meaningful generalization to higher dimensions so far. The denition of pseudosimplices
remained unclear, possibly because of the lack of an adequate denition of corners of a
polytope.
