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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| Veröffentlicht in: | Computer graphics forum Jg. 31; H. 3pt1; S. 945 - 954 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Oxford, UK
Blackwell Publishing Ltd
01.06.2012
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | 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. |
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| AbstractList | 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. 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. [PUBLICATION ABSTRACT] |
| Author | Jadhav, S. Bhatia, H. Bremer, P.-T. Levine, J. A. Pascucci, V. |
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| References_xml | – reference: Chen G., Mischaikow K., Laramee R. S., Zhang E.: Efficient Morse decompositions of vector fields. IEEE Trans. Vis. Comp. Grap. 14, 4 (2008), 848-862. 2, 3, 7. – reference: Theisel H., Weinkauf T., Hege H.-C., Seidel H.-P.: Topological methods for 2D time-dependent vector fields based on stream lines and path lines. IEEE Trans. Vis. Comp. Grap. 11, 4 (2005), 383-394. 2. – reference: Bresenham J.: Algorithm for computer control of a digital plotter. IBM Systems Journal 4, 1 (1965), 25-30. 4. – reference: Helgeland A., Reif B., Andreassen Ø., Wasberg C.: Visualization of vorticity and vortices in wall-bounded turbulent flows. IEEE Trans. Vis. Comp. Grap. 13, 5 (2007), 1055-1067. 1. – reference: Forman R.: Combinatorial vector fields and dynamical systems. Math. Z. 228, 4 (1998), 629-681. 2. – reference: Nielson G. M., Jung I.-H.: Tools for computing tangent curves for linearly varying vector fields over tetrahedral domains. IEEE Trans. Vis. Comp. 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| Title | A Quantized Boundary Representation of 2D Flows |
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