A Quantized Boundary Representation of 2D Flows

Analysis and visualization of complex vector fields remain major challenges when studying large scale simulation of physical phenomena. The primary reason is the gap between the concepts of smooth vector field theory and their computational realization. In practice, researchers must choose between e...

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Bibliographic Details
Published in:Computer graphics forum 2012-06, Vol.31 (3pt1), p.945-954
Main Authors: Levine, J. A., Jadhav, S., Bhatia, H., Pascucci, V., Bremer, P.-T.
Format: Article
Language:English
Subjects:
Computer graphics
Computer simulation
Field theory
G.1.2 [Numerical Analysis]: Approximation-Approximation of surfaces and contours
I.3.6 [Computer Graphics]: Methodology and Techniques-Graphics data structures and data types
Invariants
Mathematical analysis
Numerical analysis
Preserves
Quantization
Representations
Simulation
Studies
Topological manifolds
Vectors (mathematics)
Visualization
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Summary:Analysis and visualization of complex vector fields remain major challenges when studying large scale simulation of physical phenomena. The primary reason is the gap between the concepts of smooth vector field theory and their computational realization. In practice, researchers must choose between either numerical techniques, with limited or no guarantees on how they preserve fundamental invariants, or discrete techniques which limit the precision at which the vector field can be represented. We propose a new representation of vector fields that combines the advantages of both approaches. In particular, we represent a subset of possible streamlines by storing their paths as they traverse the edges of a triangulation. Using only a finite set of streamlines creates a fully discrete version of a vector field that nevertheless approximates the smooth flow up to a user controlled error bound. The discrete nature of our representation enables us to directly compute and classify analogues of critical points, closed orbits, and other common topological structures. Further, by varying the number of divisions (quantizations) used per edge, we vary the resolution used to represent the field, allowing for controlled precision. This representation is compact in memory and supports standard vector field operations.
ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2012.03087.x