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  Cusps of Characteristic Curves and Intersection-aware Visualization of Path and Streak Lines

Weinkauf, T., Theisel, H., & Sorkine, O. (2012). Cusps of Characteristic Curves and Intersection-aware Visualization of Path and Streak Lines. In R. Peikert, H. Hauser, H. Car, & R. Fuchs (Eds.), Topological Methods in Data Analysis and Visualization II (pp. 161-176). New York, NY: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0015-0DDF-2 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0019-F649-4
Genre: Book Chapter

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 Creators:
Weinkauf, Tino1, Author           
Theisel, Holger2, Author           
Sorkine, Olga2, Author
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              
2External Organizations, ou_persistent22              

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 Abstract: We analyze characteristic curves of vector fields and report on locations where they have cusps in their spatial projection, i.e., isolated points on the curve with abruptly turning tangent direction. Cusps appear in places where a projection of the corresponding tangent curve vector field exhibits critical points. We show that such cusps are only possible for streak and path lines, whereas they cannot appear on stream and time lines. Cusps turn out to be closely related to self-intersections of characteristic curves. We utilize this information in a new algorithm to create uncluttered static visualizations of path and streak lines.

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Language(s): eng - English
 Dates: 2012
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: Other: Local-ID: FE4F273CA66F880CC1257AD90033934C-weinkauf12b
DOI: 10.1007/978-3-642-23175-9_11
BibTex Citekey: weinkauf12b
 Degree: -

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Title: Topological Methods in Data Analysis and Visualization II
  Subtitle : Theory, Algorithms, and Applications
Source Genre: Book
 Creator(s):
Peikert, Ronald1, Editor
Hauser, Helwig1, Editor
Car, Hamish1, Editor
Fuchs, Raphael1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: New York, NY : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 161 - 176 Identifier: ISBN: 978-3-642-23174-2
ISBN: 978-3-642-23175-9

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