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

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons123492

Weinkauf,  Tino
Computer Graphics, MPI for Informatics, Max Planck Society;

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Citation

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.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0015-0DDF-2
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.