Name
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. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1109/TVCG.2004.3 | IEEE Trans. Vis. Comput. Graph. |
Keywords | Field | DocType |
geometric method,hierarchical data structure,terrain data,index terms— critical point theory,topological hierarchy,cancelling pair,data structure,simplification,simple notion,triangulated surface,preprocessing stage,morse-smale complex,reconstruction operation,multiresolution representation,morse-smale com- plex,multi-resolution data structure. i. introduction,critical point,computational geometry,data structures,mesh generation,graph theory,satisfiability,indexing terms | Graph theory,Data structure,Topology,Tree traversal,Computer science,Computational geometry,Theoretical computer science,Triangulation,Hierarchy,Hierarchical database model,Mesh generation | Journal |
Volume | Issue | ISSN |
10 | 4 | 1077-2626 |
Citations | PageRank | References |
93 | 3.26 | 23 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peer-Timo Bremer | 1 | 1446 | 82.47 |
| Herbert Edelsbrunner | 2 | 93 | 3.26 |
| Bernd Hamann | 3 | 93 | 3.26 |
| Valerio Pascucci | 4 | 3241 | 192.33 |