Issue No. 04 - July/August (2004 vol. 10)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2004.3
<p><b>Abstract</b>—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.</p>
Critical point theory, Morse-Smale complex, terrain data, simplification, multiresolution data structure.
"A Topological Hierarchy for Functions on Triangulated Surfaces," in IEEE Transactions on Visualization & Computer Graphics, vol. 10, no. , pp. 385-396, 2004.