Local bilinear computation of Jacobi sets

Klötzl, Daniel; Krake, Tim; Zhou, Youjia; Hotz, Ingrid; Wang, Bei; Weiskopf, Daniel

doi:10.1007/s00371-022-02557-4

Title: Local bilinear computation of Jacobi sets

Journal Article · Thu Jun 30 00:00:00 EDT 2022 · The Visual Computer

DOI:https://doi.org/10.1007/s00371-022-02557-4· OSTI ID:1874619

; Krake, Tim;

;

Abstract We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.

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Research Organization:: Univ. of Utah, Salt Lake City, UT (United States)

Sponsoring Organization:: USDOE Office of Science (SC); German Research Foundation (DFG); Swedish Research Council (VR); National Science Foundation (NSF)

Grant/Contract Number:: DOE DE-SC0021015; SC0021015; DFG 270852890-GRK 2160/2; DFG 251654672-TRR 161; 2019-05487; NSF IIS-1910733

OSTI ID:: 1874619

Alternate ID(s):: OSTI ID: 1976622

Journal Information:: The Visual Computer, Journal Name: The Visual Computer Vol. 38 Journal Issue: 9-10; ISSN 0178-2789

Publisher:: Springer Science + Business MediaCopyright Statement

Country of Publication:: Germany

Language:: English

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