A multi-resolution data structure for two-dimensional Morse-Smale functions
Peer‐Timo Bremer, Herbert Edelsbrunner, Bernd Hamann, Valerio Pascucci · IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control · 2004
We combine topological and geometric methods to construct a multi-resolution data structure for functions over two-dimensional domains. Starting with the Morse-Smale complex, we construct a topological hierarchy by progressively canceling critical points in pairs. Concurrently, we create a geometric hierarchy by adapting the geometry to the changes in topology. The data structure supports mesh traversal operations similarly to traditional multi-resolution representations.