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A Topological Hierarchy for Functions on Triangulated Surfaces
July/August 2004 (vol. 10 no. 4)
pp. 385-396

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.

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Index Terms:
Critical point theory, Morse-Smale complex, terrain data, simplification, multiresolution data structure.
Citation:
"A Topological Hierarchy for Functions on Triangulated Surfaces," IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 4, pp. 385-396, July-Aug. 2004, doi:10.1109/TVCG.2004.3
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