Hierarchical morse complexes for piecewise linear 2-manifolds

Authors:
Herbert Edelsbrunner;John Harer;Afra Zomorodian
Affiliations:
Dept. of Computer Science, Duke University, Durham, Raindrop Geomagic, RTP, North Carolina;Department of Mathematics, Duke University, Durham, North Carolina;Dept. of Computer Science, University of Illinois, Urbana, Illinois
Venue:
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Year:
2001

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Abstract

We present algorithms for constructing a hierarchy of increasingly coa rse 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.