Manipulation of Pseudo-Triangular Surfaces

T. Hackl

Abstract:

This diploma thesis deals with pseudo-triangular surfaces and flipping therein, as introduced by Aichholzer et al. They defined a projectivity attribute for pseudo-triangulations and introduced a stability condition to decide it. Using a program from preliminary work of this thesis, we found a counter-example for concluding from stability to projectivity. Our aim is to redefine the stability-condition to be able to correctly conclude to projectivity in all cases. Our investigations lead to a proper combinatorial understanding of the projectivity of pseudo-triangulations. Thereby, we find a new class of cell complexes: punched pseudo-triangulations, which are a relaxation of pseudo-triangulations. In addition, we prove the existence of finite flipping sequences to the optimal surface that avoid the creation of non-pseudo-triangular cell complexes.

Reference: T. Hackl. Manipulation of pseudo-triangular surfaces. Master's thesis, IGI-TU Graz, Austria, 2004.