Certified Computation of Planar Morse-Smale Complexes of Smooth Functions

The Morse-Smale complex is an important tool for global topological analysis in various problems of computational geometry and topology. Algorithms for Morse-Smale complexes have been presented in case of piecewise linear manifolds. However, previous research in this field does not provide certified methods in the case of smooth functions. In the current paper we use interval methods to compute a topologically correct approximation of Morse-Smale complex of smooth functions of two variables. The algorithm can also compute approximations that are arbitrarily close to the true geometric complex. Preliminary implementation results are reported. To Appear, ACM Symposium on Computational Geometry (SoCG) 2012.