Summary: Consistent Cell-Decomposition of
Homeomorphic Simplicial Surfaces
Philipp Manuel Beckmann
22nd January 2006
Institute for Mathematics
Technical University of Berlin
Die selbständige und eigenhändige Anfertigung versichere ich an Eides Statt.
Surface representations of 3D-objects play a central role in many branches of
computer science, e.g., in computer graphics, digital geometry processing, vi-
sualisation and also in many numerical applications. Apart from the acquisition
of models, typical tasks in these areas include the modification and alteration of
certain visual, geometrical or topological aspects of the surfaces. Applications
range from cutting and gluing operations to texture mapping or surface modelling.
One particular interest focuses on the construction of homeomorphisms between
topologically identical surfaces. These 1-1-correspondences open the possibility
to compare models of different (but perhaps similar) shape in a computationally