Maximizing Adaptivity in Hierarchical Topological Models

We present an approach to hierarchically encode the topology of functions over triangulated surfaces. We describe the topology of a function by its Morse-Smale complex, a well known structure in computational topology. Following concepts of Morse theory, a Morse-Smale complex (and therefore a function’s topology) can be simplified by successively canceling pairs of critical points. We demonstrate how cancellations can be effectively encoded to produce a highly adaptive topology-based multi-resolution representation of a given function. Contrary to the approach of [4] we avoid encoding the complete complex in a traditional mesh hierarchy. Instead, we encode a reduced complex created by disregarding some topological constraints on the complex. The corresponding data is stored separately in a structure called cancellation forest. Conceptually, a cancellation forest consists of sets of critical points governed by the concepts of Morse theory. The combination of this new structure with ...

• Type: Conference
• Year: 2005
• Where: SMI
• Authors: Peer-Timo Bremer, Valerio Pascucci, Bernd Hamann
• Keywords: Morse Theory, Morse-Smale Complex, SMI 2005, Traditional Mesh Hierarchy