Grid-independent Detection of Closed Stream Lines in 2D Vector Fields

We present a new approach to detecting isolated closed stream lines in 2D vector fields. This approach is based on the idea of transforming the 2D vector field into an appropriate 3D vector field such that detecting closed stream lines in 2D is equivalent to intersecting certain stream surfaces in 3D. Contrary to pre-existing methods, our approach does not rely on any underlying grid structure of the vector field. We demonstrate the applicability and stability by applying it to a test data set.

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

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

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

[4]  Hans-Peter Seidel,et al.  Topological Construction and Visualization of Higher Order 3D Vector Fields , 2004, Comput. Graph. Forum.

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

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

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

[8]  Al Globus,et al.  A tool for visualizing the topology of three-dimensional vector fields , 1991, Proceeding Visualization '91.

[9]  Lambertus Hesselink,et al.  Feature comparisons of vector fields using Earth mover's distance , 1998, Proceedings Visualization '98 (Cat. No.98CB36276).

[10]  Jeff P. Hultquist,et al.  Constructing stream surfaces in steady 3D vector fields , 1992, Proceedings Visualization '92.

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

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

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

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

[15]  Gerik Scheuermann,et al.  Detection and Visualization of Closed Streamlines in Planar Flows , 2001, IEEE Trans. Vis. Comput. Graph..

[16]  Holger Theisel,et al.  Vector Field Metrics Based on Distance Measures of First Order Critical Points , 2002, WSCG.

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

[18]  Hans-Christian Hege,et al.  amira: A Highly Interactive System for Visual Data Analysis , 2005, The Visualization Handbook.

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

[20]  Detlev Stalling,et al.  Fast texture based algorithms for vector field visualization , 1999 .

[21]  HesselinkLambertus,et al.  Representation and Display of Vector Field Topology in Fluid Flow Data Sets , 1989 .

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

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

[24]  D. Asimov Notes on the Topology of Vector Fields and Flows , 2003 .

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

[26]  Rüdiger Westermann,et al.  Topology-Preserving Smoothing of Vector Fields , 2001, IEEE Trans. Vis. Comput. Graph..

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

[28]  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..