A topological hierarchy for functions on triangulated surfaces Bremer, Peer Edelsbrunner, Herbert ; https://orcid.org/0000-0002-9823-6833 Hamann, Bernd Pascucci, Valerio 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. IEEE 2004 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/3984 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1109/TVCG.2004.3 info:eu-repo/semantics/altIdentifier/issn/1077-2626 info:eu-repo/semantics/altIdentifier/e-issn/1941-0506 info:eu-repo/semantics/altIdentifier/pmid/18579967 info:eu-repo/semantics/closedAccess