A topological hierarchy for functions on triangulated surfaces

P. Bremer, H. Edelsbrunner, B. Hamann, V. Pascucci, IEEE Transactions on Visualization and Computer Graphics 10 (2004) 385–396.

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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.
Publishing Year
Date Published
2004-07-01
Journal Title
IEEE Transactions on Visualization and Computer Graphics
Volume
10
Issue
4
Page
385 - 396
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Bremer P, Edelsbrunner H, Hamann B, Pascucci V. A topological hierarchy for functions on triangulated surfaces. IEEE Transactions on Visualization and Computer Graphics. 2004;10(4):385-396. doi:10.1109/TVCG.2004.3
Bremer, P., Edelsbrunner, H., Hamann, B., & Pascucci, V. (2004). A topological hierarchy for functions on triangulated surfaces. IEEE Transactions on Visualization and Computer Graphics, 10(4), 385–396. https://doi.org/10.1109/TVCG.2004.3
Bremer, Peer, Herbert Edelsbrunner, Bernd Hamann, and Valerio Pascucci. “A Topological Hierarchy for Functions on Triangulated Surfaces.” IEEE Transactions on Visualization and Computer Graphics 10, no. 4 (2004): 385–96. https://doi.org/10.1109/TVCG.2004.3.
P. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci, “A topological hierarchy for functions on triangulated surfaces,” IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 4, pp. 385–396, 2004.
Bremer P, Edelsbrunner H, Hamann B, Pascucci V. 2004. A topological hierarchy for functions on triangulated surfaces. IEEE Transactions on Visualization and Computer Graphics. 10(4), 385–396.
Bremer, Peer, et al. “A Topological Hierarchy for Functions on Triangulated Surfaces.” IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 4, IEEE, 2004, pp. 385–96, doi:10.1109/TVCG.2004.3.

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