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IEEE Trans Vis Comput Graph. 2004 Jul-Aug;10(4):385-96. doi: 10.1109/TVCG.2004.3.

A topological hierarchy for functions on triangulated surfaces.

Author information

1
Center for Image Processing and Integrated Computing, Department of Science, University of California, Davis, CA 95616, USA. tbremer@ucdavis.edu

Abstract

We combine topological and geometric methods to construct a multiresolution representation for a function over a two-dimensional domain. In a preprocessing stage, we create the Morse-Smale complex of the function and progressively simplify its topology by cancelling pairs of critical points. Based on a simple notion of dependency among these cancellations, we construct a hierarchical data structure supporting traversal and reconstruction operations similarly to traditional geometry-based representations. We use this data structure to extract topologically valid approximations that satisfy error bounds provided at runtime.

PMID:
18579967
DOI:
10.1109/TVCG.2004.3
[Indexed for MEDLINE]
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