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abstract

Visualization of discrete gradient construction

Published: 13 June 2011 Publication History

Abstract

This video presents a visualization of a recent algorithm to compute discrete gradient fields on regular cell complexes. Discrete gradient fields are used in practical methods that robustly translate smooth Morse theory to combinatorial domains. We describe the stages of the algorithm, highlighting both its simplicity and generality.

References

[1]
H. Edelsbrunner and E. P. Mücke. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. In Symposium on Computational Geometry, pages 118--133, 1988.
[2]
R. Forman. A user's guide to discrete Morse theory. In Proc. of the 2001 Internat. Conf. on Formal Power Series and Algebraic Combinatorics, A special volume of Advances in Applied Mathematics, page 48, 2001.
[3]
A. Gyulassy, P.-T. Bremer, B. Hamann, and V. Pascucci. A practical approach to Morse-Smale complex computation: Scalability and generality. IEEE Trans. Vis. Comput. Graph., 14(6):1619--1626, 2008.
[4]
A. Gyulassy, P.-T. Bremer, B. Hamann, and V. Pascucci. Practical considerations in Morse-Smale complex computation. In Topological Methods in Visualization (TopoInVis), 2009.

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cover image ACM Conferences
SoCG '11: Proceedings of the twenty-seventh annual symposium on Computational geometry
June 2011
532 pages
ISBN:9781450306829
DOI:10.1145/1998196

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 13 June 2011

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Author Tags

  1. discrete gradient fields
  2. discrete morse theory
  3. regular cell complexes
  4. scalar field topology

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SoCG '11
SoCG '11: Symposium on Computational Geometry
June 13 - 15, 2011
Paris, France

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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