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Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition
Guoning Chen, Konstantin Mischaikow, Robert S. Laramee, Pawel Pilarczyk,
and Eugene Zhang
Paper (PDF, 3.94 Mb).
This material is based upon work supported by the National Science Foundation under Grant No. CCF-0546881.
Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).
Design and control of vector fields is critical for many visualization
and graphics tasks such as vector field visualization, fluid simulation,
and texture synthesis. The fundamental qualitative structures associated
with vector fields are fixed points, periodic orbits, and separatrices.
In this paper we provide a new technique that allows for the systematic
1. Two vector fields (top) and their corresponding Entity Connection graphs (bottom). The field in the left contains sources (green dots), sinks (red dots), saddles (blue dots), repelling periodic orbits (green loops), and attacting periodic orbits (red loops). The field in the right is obtained by performing flow smoothing inside the region indicated by the white loop.
2. CFD simulation of the tumble motion inside a combustion chamber (left). Through user-guided smoothing, the major features remain while noises are removed (right).
3. Example fields created using our design system. Our novel streamline-based visualization technique allows periodic orbits and separatrices to be maintained in the display.
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