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