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Compression of 2D Vector Fields Under Guaranteed Topology Preservation
Author(s) -
Theisel H.,
Rössl Ch.,
Seidel H.P.
Publication year - 2003
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.00680
Subject(s) - topology (electrical circuits) , compression (physics) , extension topology , computer science , data compression , domain (mathematical analysis) , vector field , mathematics , field (mathematics) , piecewise , algorithm , discrete mathematics , general topology , pure mathematics , geometry , mathematical analysis , combinatorics , topological space , materials science , composite material
In this paper we introduce a new compression technique for 2D vector fields which preserves the complete topology, i.e., the critical points and the connectivity of the separatrices. As the theoretical foundation of the algorithm, we show in a theorem that for local modifications 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 compression algorithm which is based on a repeated local modification of the vector field ‐ namely a repeated edge collapse of the underlying piecewise linear domain. We apply the compression technique to a number of data sets with a complex topology and obtain significantly improved compression ratios in comparison to pre‐existing topology‐preserving techniques.