Abstract

We combine topological and geometric methods to construct a multi-resolution representation for functions over two-dimensional domains. In a preprocessing stage, we create the Morse-Smale complex of the function and progressively simplify its topology by canceling 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 geometrybased representations. We use this data structure to extract topologically valid approximations that satisfy error bounds provided at run-time.

Citations