article published Peer Bremer author Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Bernd Hamann author Valerio Pascucci author 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. IEEE2004 eng 1077-2626 1941-0506 1857996710.1109/TVCG.2004.3 104385 - 396 yes 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 P, Edelsbrunner H, Hamann B, Pascucci V. A topological hierarchy for functions on triangulated surfaces. <i>IEEE Transactions on Visualization and Computer Graphics</i>. 2004;10(4):385-396. doi:<a href="https://doi.org/10.1109/TVCG.2004.3">10.1109/TVCG.2004.3</a> Bremer, Peer, Herbert Edelsbrunner, Bernd Hamann, and Valerio Pascucci. “A Topological Hierarchy for Functions on Triangulated Surfaces.” <i>IEEE Transactions on Visualization and Computer Graphics</i>. IEEE, 2004. <a href="https://doi.org/10.1109/TVCG.2004.3">https://doi.org/10.1109/TVCG.2004.3</a>. P. Bremer, H. Edelsbrunner, B. Hamann, V. Pascucci, IEEE Transactions on Visualization and Computer Graphics 10 (2004) 385–396. P. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci, “A topological hierarchy for functions on triangulated surfaces,” <i>IEEE Transactions on Visualization and Computer Graphics</i>, vol. 10, no. 4. IEEE, pp. 385–396, 2004. Bremer, Peer, et al. “A Topological Hierarchy for Functions on Triangulated Surfaces.” <i>IEEE Transactions on Visualization and Computer Graphics</i>, vol. 10, no. 4, IEEE, 2004, pp. 385–96, doi:<a href="https://doi.org/10.1109/TVCG.2004.3">10.1109/TVCG.2004.3</a>. Bremer, P., Edelsbrunner, H., Hamann, B., &#38; Pascucci, V. (2004). A topological hierarchy for functions on triangulated surfaces. <i>IEEE Transactions on Visualization and Computer Graphics</i>. IEEE. <a href="https://doi.org/10.1109/TVCG.2004.3">https://doi.org/10.1109/TVCG.2004.3</a> 39842018-12-11T12:06:16Z2026-07-01T11:01:44Z