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A topological hierarchy for functions on triangulated surfaces

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4 Author(s)
Bremer, P.-T. ; Dept. of Comput. Sci., California Univ., Davis, CA, USA ; Hamann, B. ; Edelsbrunner, H. ; Pascucci, V.

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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Visualization and Computer Graphics, IEEE Transactions on  (Volume:10 ,  Issue: 4 )