Discrete & Computational Geometry

, Volume 30, Issue 1, pp 87–107 | Cite as

Hierarchical Morse—Smale Complexes for Piecewise Linear 2-Manifolds

  •  Edelsbrunner
  •  Harer
  •  Zomorodian

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.


Structural Integrity Piecewise Linear Smale Complex Linear Category Smooth Category 
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Copyright information

© Springer-Verlag New York Inc. 2003

Authors and Affiliations

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

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