Hierarchical morse complexes for piecewise linear 2-manifolds

We present algorithms for constructing a hierarchy of increasingly coarse Morse complexes that decompose a piecewise linear 2-manifold. While Morse complexes are defined only in the smooth category, we extend the construction to the piecewise linear category by ensuring structural integrity and simulating differentiability. We then simplify Morse complexes by cancelling pairs of critical points in order of increasing persistence. Keywords. Computational topology, PL manifolds, Morse theory, topological persistence, hierarchy, algorithms, implementation, terrains.

• Type: Conference
• Year: 2001
• Where: COMPGEOM
• Authors: Herbert Edelsbrunner, John Harer, Afra Zomorodian
• Keywords: Coarse Morse Complexes, COMPGEOM 2001, Discrete Geometry, Morse Complexes, Piecewise Linear