Last update: Sept. 30, 2003
Lehrstuhl Graphische Datenverarbeitung
Institute of Computer Science, University of Hannover
The three fundamental problems of geometric modeling can be summarized as:
In this seminar we present contributions to the first two of those three fundamental problems of geometric modeling. We give an overview on geometrical and analytical methods useful to characterize and construct shape. In this context we explain that stable umbilics, spectra of Laplace operators and Medial axes can be employed to classify the shape of surfaces, images and solids. The approach suggesting to distinguish shapes by using the spectra of the Laplace - and of the Laplace Beltrami - operator appears to be new in the areas of geometric modeling, CAD and Computer Graphics in general.
A major part of this lecture discusses distance geometric concepts such as medial axes and cut loci. Here we present geometric concepts such as geodesic Medial Axes and geodesic Voronoi diagrams being generalizations of their classical counter parts to curved surfaces. In the latter cases the geodesic distance between two surface points is defined via the shortest surface path joining the two points. This part of the seminar gives special attention to geodesic medial axes and to geodesic Voronoi diagrams.
Finally we indicate that the medial axis transform provides geometric tools that might be employed to develop intuitive user interfaces useful to mould shape via haptic man/machine interaction.
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