Maximizing adaptivity in hierarchical topological models using cancellation trees

Abstract

We present a highly adaptive hierarchical representation of the topology of functions defined over two-manifold domains. Guided by the theory of Morse–Smale complexes, we encode dependencies between cancellations of critical points using two independent structures: a traditional mesh hierarchy to store connectivity information and a new structure called cancellation trees to encode the configuration of critical points. Cancellation trees provide a powerful method to increase adaptivity while using a simple, easy-to-implement data structure. The resulting hierarchy is significantly more flexible than the one previously reported (IEEE Trans. Vis. Comput. Graph. 10(4):385–396, 2004). In particular, the resulting hierarchy is guaranteed to be of logarithmic height.