Discrete & Computational Geometry

, Volume 30, Issue 1, pp 87–107

Hierarchical Morse—Smale Complexes for Piecewise Linear 2-Manifolds

  •  Edelsbrunner
  •  Harer
  •  Zomorodian

DOI: 10.1007/s00454-003-2926-5

Cite this article as:
Edelsbrunner, Harer & Zomorodian Discrete Comput Geom (2003) 30: 87. doi:10.1007/s00454-003-2926-5

Abstract. We present algorithms for constructing a hierarchy of increasingly coarse Morse—Smale complexes that decompose a piecewise linear 2-manifold. While these 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—Smale complexes by canceling pairs of critical points in order of increasing persistence.

Copyright information

© 2003 Springer-Verlag New York Inc.

Authors and Affiliations

  •  Edelsbrunner
    • 1
  •  Harer
    • 2
  •  Zomorodian
    • 3
  1. 1.Department of Computer Science, Duke University, Durham, NC 27708, USA edels@cs.duke.edu and Raindrop Geomagic, Research Triangle Park, NC 27709, USA US
  2. 2.Department of Mathematics, Duke University, Durham, NC 27708, USA harer@math.duke.edu US
  3. 3.Department of Computer Science, University of Illinois, Urbana, IL 61801, USA afra@cs.stanford.eduUS

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