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  Topology Preserving Thinning of Vector Fields on Triangular Meshes

Theisel, H., Rössl, C., & Seidel, H.-P. (2004). Topology Preserving Thinning of Vector Fields on Triangular Meshes. In N. A. Dodgson, M. S. Floater, & M. A. Sabin (Eds.), Advances in Multiresolution for Geometric Modelling (pp. 353-366). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2B61-D Version Permalink: https://hdl.handle.net/21.11116/0000-000F-2943-8
Genre: Book Chapter

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 Creators:
Theisel, Holger1, Author           
Rössl, Christian1, Author           
Seidel, Hans-Peter1, Author                 
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

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 Abstract: We consider the topology of piecewise linear vector fields whose domain is a
piecewise linear 2-manifold, i.e. a triangular mesh. Such vector fields can
describe simulated 2-dimensional flows, or they may reflect geometric
properties of the underlying mesh. We introduce a thinning technique which
preserves the complete topology of the vector field, i.e. the critical points
and separatrices. As the theoretical foundation, we have shown in an earlier
paper that for local modiØcations of a vector field, it is possible to decide
entirely by a local analysis whether or not the global topology is preserved.
This result is applied in a number of compression algorithms which are based on
a repeated local modification of the vector field, namely a repeated
edge-collapse of the underlying piecewise linear domain.

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Language(s): eng - English
 Dates: 2005-05-242004
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 231898
Other: Local-ID: C125675300671F7B-786D77D58525CD29C1256E77004B68B3-trs:tptfv:04
DOI: 10.1007/3-540-26808-1_20
BibTex Citekey: Theisel-et-al_AMGM04
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Title: Advances in Multiresolution for Geometric Modelling
Source Genre: Book
 Creator(s):
Dodgson, Neil A.1, Editor
Floater, Michael S.1, Editor
Sabin, Malcom A.1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 353 - 366 Identifier: ISBN: 3-540-21462-3

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Title: Mathematics and Visualization
Source Genre: Series
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Pages: - Volume / Issue: - Sequence Number: - Start / End Page: - Identifier: ISSN: 1612-3786