Visualizing Forman's Discrete Vector Field

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.

[1]  John Hart.  Morse Theory for Implicit Surface Modeling , 1997, VisMath.

[2]  Tosiyasu L. Kunii,et al.  Surface coding based on Morse theory , 1991, IEEE Computer Graphics and Applications.

[3]  Jarek Rossignac,et al.  Edgebreaker: a simple compression for surfaces with handles , 2002, SMA '02.

[4]  Discrete Morse Complexes , 2000, math/0011234.

[5]  Jarek Rossignac,et al.  Grow & fold: compression of tetrahedral meshes , 1999, SMA '99.

[6]  Jesse Freeman,et al.  in Morse theory, , 1999 .

[7]  Herbert Edelsbrunner,et al.  Auditory Morse Analysis of Triangulated Manifolds , 1997, VisMath.

[8]  Hélio Lopes,et al.  Structural operators for modeling 3-manifolds , 1997, SMA '97.

[9]  Gert Vegter,et al.  Computational Topology , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[10]  Manoj K. Chari.  On discrete Morse functions and combinatorial decompositions , 2000, Discret. Math..

[11]  Herbert Edelsbrunner,et al.  An incremental algorithm for Betti numbers of simplicial complexes , 1993, SCG '93.

[12]  Jarek Rossignac,et al.  Grow & fold: compressing the connectivity of tetrahedral meshes , 2000, Comput. Aided Des..

[13]  C. Berge.  Graphes et hypergraphes , 1970 .

[14]  John C. Hart,et al.  Computational topology for shape modeling , 1999, Proceedings Shape Modeling International '99. International Conference on Shape Modeling and Applications.

[15]  Ömer Egecioglu,et al.  A Computationally Intractable Problem on Simplicial Complexes , 1996, Comput. Geom..

[16]  A. Blumberg.  BASIC TOPOLOGY , 2002 .

[17]  Herbert Edelsbrunner,et al.  Hierarchical morse complexes for piecewise linear 2-manifolds , 2001, SCG '01.

[18]  Thomas Lewiner,et al.  Optimal discrete Morse functions for 2-manifolds , 2003, Comput. Geom..

[19]  Stephen Weingram,et al.  The Topology of CW Complexes , 1969 .

[20]  R. Forman.  Morse Theory for Cell Complexes , 1998 .