Mediale-Achsen-Rücktransformation in Riemannschen Mannigfaltigkeiten

Cem Dogan, Leibniz Universität Hannover, Masterarbeit
05/2007

The Medial Axis is the set of centers of all maximally inscribed spheres. This geometric concept is used for object representation and, together with the Medial Axis Inverse Transform (MAIT), for modeling of solids by editing their medial surface and a radius function.

Extending the three-dimensional Euclidean to the Riemannian situation allows to treat physical and technical problems that can be modeled with an adapted metric.

The Geodesic Medial Modeler (GMM) is a tool to design the Medial Axis as a tensor spline surface and to deform the Euclidean space locally. It performs the associated MAIT calculations in real time and visualizes the resulting envelope in the three-dimensional parameter space.

Kontakt: Franz-Erich Wolter