{"abstract":[{"text":"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.","lang":"eng"}],"title":"A topological hierarchy for functions on triangulated surfaces","publist_id":"2139","volume":10,"date_updated":"2021-01-12T07:53:39Z","page":"385 - 396","intvolume":"        10","publisher":"IEEE","author":[{"full_name":"Bremer, Peer-Timo","first_name":"Peer","last_name":"Bremer"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Herbert Edelsbrunner","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Hamann, Bernd","first_name":"Bernd","last_name":"Hamann"},{"full_name":"Pascucci, Valerio","first_name":"Valerio","last_name":"Pascucci"}],"issue":"4","month":"07","doi":"10.1109/TVCG.2004.3","_id":"3984","type":"journal_article","extern":1,"publication":"IEEE Transactions on Visualization and Computer Graphics","date_created":"2018-12-11T12:06:16Z","status":"public","citation":{"mla":"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>.","ieee":"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.","ista":"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.","apa":"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>","chicago":"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>.","ama":"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>","short":"P. Bremer, H. Edelsbrunner, B. Hamann, V. Pascucci, IEEE Transactions on Visualization and Computer Graphics 10 (2004) 385–396."},"date_published":"2004-07-01T00:00:00Z","day":"01","year":"2004","publication_status":"published","quality_controlled":0}