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Pseudo-Tetrahedral Complexes Franz Aurenhammer and Hannes Krasser

Summary: Pseudo-Tetrahedral Complexes
Franz Aurenhammer and Hannes Krasser 
1 Introduction
A pseudo-triangulation is a cell complex in the plane
whose cells are pseudo-triangles, i.e., simple polygons
with exactly three convex vertices (so-called corners).
Being an interesting and exible generalization of tri-
angulations, pseudo-triangulations have found their
place in computational geometry; see e.g. [8, 11, 7, 1]
and references therein.
Unlike triangulations, pseudo-triangulations eluded
a meaningful generalization to higher dimensions so
far. In this paper, we de ne pseudo-simplices and
pseudo-simplicial complexes in d-space in a way con-
sistent to pseudo-triangulations in the plane. Flip op-
erations in pseudo-complexes are speci ed, as combi-
nations of ips in pseudo-triangulations [11, 1], and
of bistellar ips in simplicial complexes [9, 5, 4]. Our
results are based on the concept of maximal locally
convex functions on polyhedral domains [1], that al-


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


Collections: Computer Technologies and Information Sciences