F. Aurenhammer and H. Krasser
Pseudo-triangulations are interesting and flexible generalizations of
triangulations that have found their place in computational geometry. Unlike
triangulations, pseudo-triangulations eluded a meaningful generalization to
higher dimensions so far. In this paper, we define pseudo-simplices and
pseudo-simplicial complexes in d-space in a way consistent to
pseudo-triangulations in the plane. Flip operations in pseudo-complexes are
specified, as combinations of flips in pseudo-triangulations, and of
bistellar flips in simplicial complexes. Our results are based on the concept
of maximal locally convex functions on polyhedral domains, that allows us to
unify several well-known structures, namely pseudo-triangulations,
constrained Delaunay triangulations, and regular simplicial complexes.
Reference: F. Aurenhammer and H. Krasser.
In Proc. European Workshop on Computational Geometry EuroCG
'05, pages 85-88, Eindhoven, The Netherlands, 2005.