A topological hierarchy for functions on triangulated surfaces.
June 28th, 2008 | by admin |A topological hierarchy for functions on triangulated surfaces.
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.
Bremer PT, Edelsbrunner H, Hamann B, Pascucci V.
IEEE.