The State of the Art in Flow Visualization: Structure-Based Techniques

Flow visualization has been a very active subfield of scientific visualization in recent years. From the resulting large variety of methods this paper discusses structure-based techniques. The aim of these approaches is to partition the flow in areas of common behavior. Based on this partitioning, subsequent visualization techniques can be applied. A classification is suggested and advantages/disadvantages of the different techniques are discussed as well.

[1]  Jiann-Liang Chen,et al.  Normalized-cut algorithm for hierarchical vector field data segmentation , 2003, IS&T/SPIE Electronic Imaging.

[2]  Hans-Peter Seidel,et al.  Eurographics/ Ieee-vgtc Symposium on Visualization (2006) Path Line Oriented Topology for Periodic 2d Time-dependent Vector Fields , 2022 .

[3]  Gerik Scheuermann,et al.  Locating Closed Streamlines in 3D Vector Fields , 2002, VisSym.

[4]  A. Perry,et al.  Critical Points in Flow Patterns , 1975 .

[5]  Bernd Hamann,et al.  Topological segmentation in three-dimensional vector fields , 2004, IEEE Transactions on Visualization and Computer Graphics.

[6]  Robert van Liere,et al.  Visualization of Global Flow Structures Using Multiple Levels of Topology , 1999, VisSym.

[7]  Robert S. Laramee,et al.  The State of the Art , 2015 .

[8]  Harald Garcke,et al.  A Phase Field Model for Continuous Clustering on Vector Fields , 2001, IEEE Trans. Vis. Comput. Graph..

[9]  K. Polthier,et al.  Variational Approach to Vector Field Decomposition , 2000, VisSym.

[10]  Helwig Löffelmann,et al.  Visualizing Poincaré Maps together with the Underlying Flow , 1997, VisMath.

[11]  Wenbin Chen,et al.  Segmentation of discrete vector fields , 2006, IEEE Transactions on Visualization and Computer Graphics.

[12]  Hans-Peter Seidel,et al.  Extracting higher order critical points and topological simplification of 3D vector fields , 2005, VIS 05. IEEE Visualization, 2005..

[13]  Suresh K. Lodha,et al.  Topology preserving compression of 2D vector fields , 2000, Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145).

[14]  Hans-Peter Seidel,et al.  Feature Flow Fields , 2003, VisSym.

[15]  Hans-Peter Seidel,et al.  Boundary switch connectors for topological visualization of complex 3D vector fields , 2004, VISSYM'04.

[16]  Gerik Scheuermann,et al.  Multifield visualization using local statistical complexity , 2007, IEEE Transactions on Visualization and Computer Graphics.

[17]  Robert S. Laramee,et al.  The State of the Art in Flow Visualisation: Feature Extraction and Tracking , 2003, Comput. Graph. Forum.

[18]  Konstantin Mischaikow,et al.  Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition , 2007, IEEE Transactions on Visualization and Computer Graphics.

[19]  Hans-Peter Seidel,et al.  Stream line and path line oriented topology for 2D time-dependent vector fields , 2004, IEEE Visualization 2004.

[20]  Robert S. Laramee,et al.  Feature Extraction and Visualisation of Flow Fields , 2002, Eurographics.

[21]  Filip Sadlo,et al.  Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction , 2007, IEEE Transactions on Visualization and Computer Graphics.

[22]  Martin Rumpf,et al.  Flow field clustering via algebraic multigrid , 2004, IEEE Visualization 2004.

[23]  Guang-Zhong Yang,et al.  A Data Clustering and Streamline Reduction Method for 3D MR Flow Vector Field Simplification , 2004, MICCAI.

[24]  Alexandru Telea,et al.  Simplified representation of vector fields , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[25]  Robert S. Laramee,et al.  The State of the Art in Flow Visualization: Dense and Texture‐Based Techniques , 2004, Comput. Graph. Forum.

[26]  Hans Hagen,et al.  Tracking Closed Streamlines in Time Dependent Planar Flows , 2001, VMV.

[27]  G. Haller Distinguished material surfaces and coherent structures in three-dimensional fluid flows , 2001 .

[28]  Qiang Du,et al.  Centroidal Voronoi tessellation based algorithms for vector fields visualization and segmentation , 2004, IEEE Visualization 2004.

[29]  Joerg Meyer,et al.  Pathline predicates and unsteady flow structures , 2008, The Visual Computer.

[30]  Helwig Löffelmann,et al.  Enhancing the Visualization of Characteristic Structures in Dynamical Systems , 1998, Visualization in Scientific Computing.

[31]  Holger Theisel Designing 2D Vector Fields of Arbitrary Topology , 2002, Comput. Graph. Forum.

[32]  Hans Hagen,et al.  Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications , 2007, IEEE Transactions on Visualization and Computer Graphics.

[33]  Christian Rössl,et al.  Combining topological simplification and topology preserving compression for 2D vector fields , 2003, 11th Pacific Conference onComputer Graphics and Applications, 2003. Proceedings..

[34]  Robert van Liere,et al.  Collapsing flow topology using area metrics , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[35]  Hans-Peter Seidel,et al.  Grid-independent Detection of Closed Stream Lines in 2D Vector Fields , 2004, VMV.

[36]  Bernd Hamann,et al.  Construction of vector field hierarchies , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[37]  Lambertus Hesselink,et al.  Automated analysis of fluid flow topology , 1989, Photonics West - Lasers and Applications in Science and Engineering.

[38]  Bernd Hamann,et al.  Improving Topological Segmentation of Three-dimensional Vector Fields , 2003, VisSym.

[39]  Gerik Scheuermann,et al.  Streamline Predicates as Flow Topology Generalization , 2007, Topology-based Methods in Visualization.

[40]  Hans Hagen,et al.  Continuous topology simplification of planar vector fields , 2001, Proceedings Visualization, 2001. VIS '01..

[41]  Gerik Scheuermann,et al.  Efficient construction of flow structures , 2007 .

[42]  Gerik Scheuermann,et al.  Visualizing Nonlinear Vector Field Topology , 1998, IEEE Trans. Vis. Comput. Graph..

[43]  M. S. Chong,et al.  A general classification of three-dimensional flow fields , 1990 .

[44]  Xavier Tricoche,et al.  Generalized Streak Lines: Analysis and Visualization of Boundary Induced Vortices , 2007, IEEE Transactions on Visualization and Computer Graphics.

[45]  A. Rockwood,et al.  Visualization of higher order singularities in vector fields , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

[46]  Lambertus Hesselink,et al.  Surface representations of two- and three-dimensional fluid flow topology , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

[47]  Hans Hagen,et al.  Topology-Based Visualization of Time-Dependent 2D Vector Fields , 2001, VisSym.

[48]  Hans Hagen,et al.  Topology tracking for the visualization of time-dependent two-dimensional flows , 2002, Comput. Graph..

[49]  Filip Sadlo,et al.  Visualizing Lagrangian Coherent Structures and Comparison to Vector Field Topology , 2009, Topology-Based Methods in Visualization II.

[50]  Christian Rössl,et al.  Compression of 2D Vector Fields Under Guaranteed Topology Preservation , 2003, Comput. Graph. Forum.

[51]  Hans Hagen,et al.  Vector and Tensor Field Topology Simplification on Irregular Grids , 2001, VisSym.

[52]  Gerik Scheuermann,et al.  Streamline Predicates , 2006, IEEE Transactions on Visualization and Computer Graphics.

[53]  Konrad Polthier,et al.  Identifying Vector Field Singularities Using a Discrete Hodge Decomposition , 2002, VisMath.

[54]  Lambertus Hesselink,et al.  Visualizing vector field topology in fluid flows , 1991, IEEE Computer Graphics and Applications.

[55]  Lambertus Hesselink,et al.  Representation and display of vector field topology in fluid flow data sets , 1989, Computer.

[56]  Hans-Peter Seidel,et al.  Saddle connectors - an approach to visualizing the topological skeleton of complex 3D vector fields , 2003, IEEE Visualization, 2003. VIS 2003..

[57]  H. Hagen,et al.  A topology simplification method for 2D vector fields , 2000, Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145).

[58]  M. S. Chong,et al.  A Description of Eddying Motions and Flow Patterns Using Critical-Point Concepts , 1987 .

[59]  Hans-Peter Seidel,et al.  Path Line Attributes - an Information Visualization Approach to Analyzing the Dynamic Behavior of 3D Time-Dependent Flow Fields , 2009, Topology-Based Methods in Visualization II.

[60]  Santiago V. Lombeyda,et al.  Vector Field Analysis and Visualization through Variational Clustering , 2005, EuroVis.

[61]  Lambertus Hesselink,et al.  Topology visualization of the optical power flow through a novel C-shaped nano-aperture , 2004, IEEE Visualization 2004.

[62]  Hans-Peter Seidel,et al.  Topological methods for 2D time-dependent vector fields based on stream lines and path lines , 2005, IEEE Transactions on Visualization and Computer Graphics.