Visualizing Forman’s Discrete Vector Field

  • Thomas Lewiner
  • Helio Lopes
  • Geovan Tavares
Part of the Mathematics and Visualization book series (MATHVISUAL)

Summary

Morse theory has been considered to be a powerful tool in its applications to computational topology, computer graphics and geometric modeling. Forman introduced a discrete version of it, which is purely combinatorial. This opens Morse theory applications to a much larger scope.

The main objective of this work is to illustrate Forman’s theory. We intend to use some of Forman’s concepts to visually analyze the topology of an object. We present an algorithm to build a discrete gradient vector field on a cell complex as defined in Forman’s theory.

Keywords

Morse theory Forman theory vector field visualization 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Thomas Lewiner
    • 1
  • Helio Lopes
    • 1
  • Geovan Tavares
    • 1
  1. 1.Math&Media Laboratory, Department of MathematicsPontifical Catholic UniversityGávea, Rio de JaneiroBrazil

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