Vector Field Topology Analysis and Application in Visualization

Abstract

Abstract: Vector field topology analysis is an important tool of feature-based visualization of vector fields. As a frontier research of flow field visualization, topology analysis extracts the topological structures as vector fields' features, helps uses filter important data, and reduce the occlusion and visual cluster. Based on mathematical definitions related to vector field topology analysis, different methods were introduced along with their advantages and shortcomings, and a knowledge system of vector field topology analysis was well-established. The applications and significance of topology analysis were explored to play a greater role, and the combination with other visualization techniques was discussed.

Key words: vector fields, topology analysis, critical points, separatrix, FTLE, Lagrangian coherent structures

CLC Number:

TP391

Li Chao, Wu Lingda, Zhao Bin. Vector Field Topology Analysis and Application in Visualization[J]. Journal of System Simulation, 2015, 27(10): 2352-2358.

References

[1] Hansen C D, Johnson C R.The visualization handbook [M]. USA: Academic Press, 2005.
[2] Klassen R V Harrington. Shadowed hedgehogs: a technique for visualizing 2D slices of 3D vector fields [C]// Proceedings of the 2nd Conference on Visualization'91. USA: IEEE Computer Society Press, 1991.
[3] 唐泽圣. 三维数据场可视化 [M]. 北京: 清华大学出版社, 1999.
[4] 周迪斌. 基于纹理的高质量矢量可视化研究 [D]. 杭州: 浙江大学, 2008.
[5] Helman J L, Hesselink L.Visualizing vector field topology in fluid flows[J]. IEEE Computer Graphics and Applications (S0272-1716), 1991, 11(3): 36-46.
[6] Tricoche X, Scheuermann G, Hagen H.A topology simplification method for 2D vector fields.[C]// Proceedings, Visualization 2000. USA: IEEE, 2000.
[7] Tricoche X, Scheuermann G, Hagen H.Continuous topology simplification of planar vector fields[C]// Proceedings of the Conference on Visualization'01. USA: IEEE Computer Society, 2001.
[8] Theisel H, Weinkauf T, Hege H, et al. Saddle connectors-an approach to visualizing the topological skeleton of complex 3D vector fields[C]// Visualization, 2003, VIS 2003. USA: IEEE, 2003.
[9] Weinkauf T, Theisel H, Hege H, et al. Boundary Switch Connectors for Topological Visualization of Complex 3D Vector Fields[C]// VisSym, 2004. Germany: Springer Berlin Heidelberg, 2004: 183-192.
[10] Theisel H, Weinkauf T, Hege H, et al. On the Applicability of Topological Methods for Complex Flow Data[M]. Hauser H, Hagen H, Theisel H. Germany: Springer Berlin Heidelberg, 2007: 105-120.
[11] De Leeuw W, Van Liere R.Collapsing flow topology using area metrics [C]// Proceedings of the Conference on Visualization'99: celebrating ten years. USA: IEEE Computer Society Press, 1999.
[12] Weinkauf T, Theisel H, Shi K, et al. Extracting higher order critical points and topological simplification of 3D vector fields[C]// Visualization, 2005, VIS 05. USA: IEEE, 2005.
[13] Shadden S C, Lekien F, Marsden J E.Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows[J]. Physica D: Nonlinear Phenomena (S0167-2789), 2005, 212(3): 271-304.
[14] Haller G.A variational theory of hyperbolic Lagrangian coherent structures[J]. Physica D: Nonlinear Phenomena (S0167-2789), 2011, 240(7): 574-598.
[15] Tang W, Chan P W, Haller G.Accurate extraction of Lagrangian coherent structures over finite domains with application to flight data analysis over Hong Kong International Airport[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science (S1054-1500), 2010, 20(1): 17502.
[16] Sadlo F, Peikert R.Efficient visualization of Lagrangian coherent structures by filtered AMR ridge extraction[J]. Visualization and Computer Graphics, IEEE Transactions on (S1077-2626), 2007, 13(6): 1456-1463.
[17] Garth C, Gerhardt F, Tricoche X, et al. Efficient computation and visualization of coherent structures in fluid flow applications[J]. Visualization and Computer Graphics, IEEE Transactions on (S1077-2626), 2007, 13(6): 1464-1471.
[18] Lipinski D, Mohseni K.A ridge tracking algorithm and error estimate for efficient computation of Lagrangian coherent structures[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science (S1054-1500), 2010, 20(1): 17504.
[19] Miron P, Vétel J, Garon A, et al. Anisotropic mesh adaptation on Lagrangian coherent structures[J]. Journal of Computational Physics (S0021-9991), 2012, 231(19): 6419-6437.
[20] Conti C, Rossinelli D, Koumoutsakos P.GPU and APU computations of Finite Time Lyapunov Exponent fields[J]. Journal of Computational Physics (S0021-9991), 2012, 231(5): 2229-2244.
[21] Leung S.An Eulerian approach for computing the finite time Lyapunov exponent[J]. Journal of computational physics (S0021-9991), 2011, 230(9): 3500-3524.