Visualizing Forman s discrete vector field

Thomas Lewiner; Hélio Lopes; Geovan Tavares

Discrete Topology

Visualizing Forman s discrete vector field

Thomas Lewiner, Hélio Lopes, Geovan Tavares

Visualization and Mathematics III (VisMath 2002): pp. 95-112 (May 2002)

Selected for publication in IEEE TVCG

Visualizing Forman s discrete vector field

abstract

Abstract

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 Morse-Forman s discrete gradient vector field on a cell complex.

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PDF paper908 KB PPT presentation2.4 MB

cite

BibTeX

@incollection{morse_visu_vismath,
  author        = {Thomas Lewiner and Hélio Lopes and Geovan Tavares},
  title         = {Visualizing Forman s discrete vector field},
  year          = {2002},
  month         = {may},
  booktitle     = {Visualization and Mathematics III (VisMath 2002)},
  pages         = {95--112},
  editor        = {Hans-Christian Hege and Konrad Polthier},
  publisher     = {Springer},
  address       = {Heidelberg},
  url           = {https://thomas.lewiner.org/pdfs/morse_visu_vismath.pdf}
}