Computational Topology for Shape Modeling

(Invited Paper) Proc. Shape Modeling International '99, Univ. Aizu, Japan, Mar. 1999, pp. 36-45

This paper expands the role of the new field of computational topology by surveying methods for incorporating connectedness in shape modeling. Two geometric representations in particular, recurrent models and implicit surfaces, can (often unpredictably) become connected or disconnected based on typical changes in modeling parameters. Two methodologies for controlling connectedness are identified: connectedness loci and Morse theory. The survey concludes by identifying several open problems remaining in shape modeling for computational topology to solve.

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