| 1. |
- Shi, K., et al.
(författare)
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Extracting Separation Surfaces of Path Line Oriented Topology in Periodic 2D Time-Dependent Vector Fields
- 2007
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Ingår i: Journal of WSCG. - 1213-6964. ; 15:1, s. 75-82
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents an approach to extracting the separation surfaces from periodic 2D time-dependent vector fields based on a recently introduced path line oriented topology. This topology is based on critical path lines which repeat the same spatial cycle per time period. Around those path lines there are areas of similar asymptotic flow behavior basins which are captured by a 2D Poincare map as a discrete dynamical system. Due to pseudo discontinuities in this map and the discrete integration scheme, separatrices between the basins can not be obtained as integral curves. Instead we choose a point-wise approach to segment the Poincare map and apply computer vision algorithms to extract the 2D separation curves. Starting from those curves we integrate separation surfaces which partition the periodic 2D time-dependent vector field into areas of similar path line behavior. We apply our approach to a number of data sets to to demonstrate its utility.
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| 2. |
- Shi, K., et al.
(författare)
-
Path Line Attributes - an Information Visualization Approach to Analyzing the Dynamic Behavior of 3D Time-Dependent Flow Fields
- 2009
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Ingår i: Topology-Based Methods in Visualization II. - : Springer. ; , s. 75-88
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- 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 applying state-of-the-art information visualization approaches in the sense of a set of linked views (scatter plots, parallel coordinates, etc.) with interactive brushing and focus+context visualization. The selected path lines with certain properties are integrated and visualized as colored 3D curves. This approach allows an interactive exploration of intricate 4D flow structures. We apply our method to a number of flow data sets and describe how path line attributes are used for describing characteristic features of these flows.
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| 3. |
- Shi, K., et al.
(författare)
-
Path Line Oriented Topology for Periodic 2D Time-Dependent Vector Fields
- 2006
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Ingår i: Proc. Eurographics / IEEE VGTC Symposium on Visualization (EuroVis ’06). ; , s. 139-146
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Konferensbidrag (refereegranskat)abstract
- This paper presents an approach to extracting a path line oriented topological segmentation for periodic 2D time-dependent vector fields. Topological methods aiming in capturing the asymptotic behavior of path lines rarely exist because path lines are usually only defined over a fixed time-interval, making statements about their asymptotic behavior impossible. For the data class of periodic vector fields, this restriction does not apply any more. Our approach detects critical path lines as well as basins from which the path lines converge to the critical ones. We demonstrate our approach on a number of test data sets.
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| 4. |
- Shi, K., et al.
(författare)
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Finite-Time Transport Structures of Flow Fields
- 2008
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Ingår i: Proc. IEEE Pacific Visualization 2008. - : IEEE Computer Society. - 9781424419661 ; , s. 63-70
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Konferensbidrag (refereegranskat)abstract
- Modern experimental and computational fluid mechanics are increasingly concerned with the structure nature of fluid motion. Recent research has highlighted the analysis of one transport structure which is called Lagrangian coherent structure. However, the quantity nature of the flow transport is still unclear. In this paper, we focus on the transport characteristics of physical quantities and propose an approach to visualize the finite-time transport structure of quantity advection. This is similar to an integral convolution over a scalar field along path-lines of a flow field. Applied to a well chosen set of physical quantity fields this yields structures giving insights into the dynamical processes of the underlying flow. We demonstrate our approach on a number of test data sets.
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| 5. |
- Shi, K., et al.
(författare)
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Visualizing Transport Structures of Time-Dependent Flow Fields
- 2008
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Ingår i: IEEE Computer Graphics and Applications. - 0272-1716 .- 1558-1756. ; 28:5, s. 24-36
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Tidskriftsartikel (refereegranskat)abstract
- This article focuses on the transport characteristics of physical properties in fluids - in particular, visualizing the finite-time transport structure of property advection. Applied to a well-chosen set of property fields, the proposed approach yields structures giving insights into the underlying flow’s dynamic processes.
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| 6. |
- Theisel, H., et al.
(författare)
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Extraction of Parallel Vector Surfaces in 3D Time-Dependent Fields and Application to Vortex Core Line Tracking
- 2005
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Ingår i: Proc. IEEE Visualization 2005. - 0780394623 ; , s. 631-638
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Konferensbidrag (refereegranskat)abstract
- We introduce an approach to tracking vortex core lines in time-dependent 3D flow fields which are defined by the parallel vectors approach. They build surface structures in the 4D space-time domain. To extract them, we introduce two 4D vector fields which act as feature flow fields, i.e. their integration gives the vortex core structures. As part of this approach, we extract and classify local bifurcations of vortex core lines in space-time. Based on a 4D stream surface integration, we provide an algorithm to extract the complete vortex core structure. We apply our technique to a number of test data sets.
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| 7. |
- Theisel, H., et al.
(författare)
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Grid-Independent Detection of Closed Stream Lines in 2D Vector Fields
- 2004
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Ingår i: Proc. Vision, Modeling and Visualization. ; , s. 421-428
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 8. |
- Theisel, H., et al.
(författare)
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On the Applicability of Topological Methods for Complex Flow Data
- 2007
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Ingår i: Topology-based Methods in Visualization. - : Springer. ; , s. 105-120
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we study the applicability of topological methods for creating expressive, feature revealing visualizations of 3D vector fields. 3D vector fields can become very complex by having a high number of critical points and separatrices. Moreover, they may have a very sparse topology due to a small number of critical points or their total absence. We show that classical topological methods based on the extraction of separation surfaces are poorly suited for creating expressive visualizations of topologically complex fields. We show this fact by pointing out that the number of sectors of different flow behavior grows quadratically with the number of critical points – contrary to 2D vector fields. Although this limits the applicability of topological methods to a certain degree, we demonstrate the extensibility of this limit by using further simplifying methods like saddle connectors. For 3D vector fields with a very sparse topology, topological visualizations may fail to reveal the features inherent to the field. We show how to overcome this problem for a certain class of flow fields by removing the ambient part of the flow.
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| 9. |
- Theisel, H., et al.
(författare)
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Saddle Connectors - An Approach to Visualizing the Topological Skeleton of Complex 3D Vector Fields
- 2003
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Ingår i: Proc. IEEE Visualization 2003. ; , s. 225-232
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Konferensbidrag (refereegranskat)abstract
- One of the reasons that topological methods have a limited popularity for the visualization of complex 3D flow fields is the fact that such 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 cluttered and hardly interpretable. This paper proposes to use particular stream lines called saddle connectors instead of separating stream surfaces and to depict single surfaces only on user demand. We discuss properties and computational issues of saddle connectors and apply these methods to complex flow data. We show that the use of saddle connectors makes topological skeletons available as a valuable visualization tool even for topologically complex 3D flow data.
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| 10. |
- Theisel, H., et al.
(författare)
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Stream Line and Path Line Oriented Topology for 2D Time-Dependent Vector Fields
- 2004
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Ingår i: Proc. IEEE Visualization 2004. ; , s. 321-328
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Konferensbidrag (refereegranskat)abstract
- 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 visualization approach in this paper. As a contribution to stream line oriented topology we introduce new methods to detect global bifurcations like saddle connections and cyclic fold bifurcations. To get the path line oriented topology we segment the vector field into areas of attracting, repelling and saddle-like behavior of the path lines. We compare both kinds of topologies and apply them to a number of data sets.
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