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In nature and in flow experiments particles form patterns of swirling motion in certain locations. Existing approaches identify these structures by considering the behavior of stream lines. However, in unsteady flows particle motion is described by path lines which generally gives different swirling patterns than stream lines. We introduce a novel… (More)

Figure 1: Flow behind a circular cylinder. Shown are vortex core lines in a certain frame of reference. Their evolution over time is tracked by our algorithm and depicted using transparent surfaces. Red color encodes the past while gray shows the future. ABSTRACT We introduce an approach to tracking vortex core lines in time-dependent 3D flow fields which… (More)

One of the reasons that topological methods have a limited popularity for the visualization of complex 3D flow fields is the fact that their topological structures contain a number of separating stream surfaces. Since these stream surfaces tend to hide each other as well as other topological features, for complex 3D topologies the visualizations become… (More)

Characteristic curves of vector fields include stream, path, and streak lines. Stream and path lines can be obtained by a simple vector field integration of an autonomous ODE system, i.e., they can be described as tangent curves of a vector field. This facilitates their mathematical analysis including the extraction of core lines around which stream or path… (More)

(a) 184 first order critical points. The box around the molecule represents the chosen area for topological simplification. (b) Topologically simplified representation with one higher order critical point elucidates the far field behavior of the benzene. Figure 1: Topological representations of the electrostatic field of the benzene molecule. ABSTRACT This… (More)

We present an approach to analyze mixing in flow fields by extracting vortex and strain features as extremal structures of derived scalar quantities that satisfy a duality property: They indicate vortical as well as high-strain (saddle-type) regions. Specifically, we consider the Okubo-Weiss criterion and the recently introduced M<sub>Z</sub> criterion.… (More)

Topological methods aim at the segmentation of a vector field into areas of different flow behavior. For 2D time-dependent vector fields, two such segmentations are possible: either concerning the behavior of stream lines, or of path lines. While stream line oriented topology is well established, we introduce path line oriented topology as a new… (More)

Bounded biharmonic Bounded triharmonic Bounded quatraharmonic Our quatraharmonic Unconstrained quatraharmonic Original Figure 1: Shape deformation: Recent works emphasize the importance of bounded control, but simply adding constant bounds to shape-aware smoothness energies of increasing order encourages more and more oscillation. Our framework efficiently… (More)

(a) Iconic representation. (b) Due to the shown separation surfaces, the topological skeleton of the vector field looks visually cluttered. (c) Visualization of the topological skeleton using saddle connectors. Figure 1: Topological representations of the benzene data set with 184 critical points. Abstract One of the reasons that topological methods have a… (More)

- Kuangyu Shi, Holger Theisel, Helwig Hauser, Tino Weinkauf, Kresimir Matkovic, Hans-Christian Hege +1 other
- 2006

We describe an approach to visually analyzing the dynamic behavior of 3D time-dependent flow fields by considering the behavior of the path lines. At selected positions in the 4D space-time domain, we compute a number of local and global properties of path lines describing relevant features of them. The resulting multivariate data set is analyzed by… (More)