Visualizing Forman s discrete vector field

Visualizing Forman s discrete vector field
Thomas Lewiner, Hélio Lopes, Geovan Tavares

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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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 = {\url{http://thomas.lewiner.org/pdfs/morse_visu_vismath.pdf}}
}