TY - CHAP A1 - Theisel, Holger A1 - Weinkauf, Tino A1 - Hege, Hans-Christian A1 - Seidel, Hans-Peter T1 - Stream line and path line oriented topology for 2D time-dependent vector fields T2 - Proc. IEEE Visualization 2004 Y1 - 2004 U6 - https://doi.org/10.1109/VIS.2004.99 SP - 321 EP - 328 CY - Austin, U.S.A. ER - TY - CHAP A1 - Weinkauf, Tino A1 - Theisel, Holger A1 - Hege, Hans-Christian A1 - Seidel, Hans-Peter T1 - Topological construction and visualization of higher order 3D vector fields T2 - Computer Graphics Forum Y1 - 2004 U6 - https://doi.org/10.1109/VISUAL.2005.1532842 VL - 23(3) SP - 469 EP - 478 CY - Grenoble, France ER - TY - CHAP A1 - Weinkauf, Tino A1 - Theisel, Holger ED - Skala, Václav T1 - Vector Field Metrics Based on Distance Measures of First Order Critical Points T2 - Journal of WSCG, Short Communication Papers Y1 - 2002 VL - 10 SP - 121 EP - 128 ER - TY - CHAP A1 - Weinkauf, Tino A1 - Theisel, Holger ED - Skala, Václav T1 - Curvature Measures of 3D Vector Fields and their Applications T2 - Journal of WSCG Y1 - 2002 UR - http://www.zib.de/weinkauf/ U6 - https://doi.org/10.1109/TPAMI.2006.36 VL - 10 SP - 507 EP - 514 ER - TY - CHAP A1 - Weinkauf, Tino A1 - Theisel, Holger A1 - Hege, Hans-Christian A1 - Seidel, Hans-Peter T1 - Boundary switch connectors for topological visualization of complex 3D vector fields T2 - Proc. Joint Eurographics - IEEE TCVG Symposium on Visualization (VisSym ’04) Y1 - 2004 SP - 183 EP - 192 CY - Konstanz, Germany ER - TY - CHAP A1 - Theisel, Holger A1 - Weinkauf, Tino A1 - Hege, Hans-Christian A1 - Seidel, Hans-Peter T1 - Saddle Connectors - An Approach to Visualizing the Topological Skeleton of Complex 3D Vector Fields T2 - Proc. IEEE Visualization 2003 Y1 - 2003 U6 - https://doi.org/10.1109/VISUAL.2003.1250376 SP - 225 EP - 232 CY - Seattle ER - TY - GEN A1 - Kuhn, Alexander A1 - Engelke, Wito A1 - Rössl, Christian A1 - Hadwiger, Markus A1 - Theisel, Holger T1 - Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy N2 - Lagrangian Coherent Structures (LCS) have become a widespread and powerful method to describe dynamic motion patterns in time-dependent flow fields. The standard way to extract LCS is to compute height ridges in the Finite Time Lyapunov Exponent (FTLE) field. In this work, we present an alternative method to approximate Lagrangian features for 2D unsteady flow fields that achieves subgrid accuracy without additional particle sampling. We obtain this by a geometric reconstruction of the flow map using additional material constraints for the available samples. In comparison to the standard method, this allows for a more accurate global approximation of LCS on sparse grids and for long integration intervals. The proposed algorithm works directly on a set of given particle trajectories and without additional flow map derivatives. We demonstrate its application for a set of computational fluid dynamic examples, as well as trajectories acquired by Lagrangian methods, and discuss its benefits and limitations. T3 - ZIB-Report - 13-71 KW - time-dependent vector fields KW - flow field visualization KW - Lagrangian Coherent Structures (LCS) KW - finite-time Lyapunov exponents (FTLE) KW - time lines Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43050 SN - 1438-0064 ER - TY - JOUR A1 - Kuhn, Alexander A1 - Engelke, Wito A1 - Rössl, Christian A1 - Hadwiger, Markus A1 - Theisel, Holger T1 - Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy JF - Computer Graphics Forum Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43990 SN - 0934-5892 VL - 33 SP - 222 EP - 234 PB - Wiley Blackwell ER - TY - JOUR A1 - Oeltze, Steffen A1 - Lehmann, Dirk J. A1 - Kuhn, Alexander A1 - Janiga, Gábor A1 - Theisel, Holger A1 - Preim, Bernhard T1 - Blood Flow Clustering and Applications in Virtual Stenting of Intracranial Aneurysms JF - IEEE Transactions on Visualization and Computer Graphics, 2014 Y1 - 2013 U6 - https://doi.org/10.1109/TVCG.2013.2297914 SN - 0934-5892 VL - 20 IS - 5 SP - 686 EP - 701 ER - TY - GEN A1 - Günther, Tobias A1 - Kuhn, Alexander A1 - Hege, Hans-Christian A1 - Theisel, Holger T1 - MCFTLE: Monte Carlo Rendering of Finite-Time Lyapunov Exponent Fields N2 - Traditionally, Lagrangian fields such as finite-time Lyapunov exponents (FTLE) are precomputed on a discrete grid and are ray casted afterwards. This, however, introduces both grid discretization errors and sampling errors during ray marching. In this work, we apply a progressive, view-dependent Monte Carlo-based approach for the visualization of such Lagrangian fields in time-dependent flows. Our ap- proach avoids grid discretization and ray marching errors completely, is consistent, and has a low memory consumption. The system provides noisy previews that con- verge over time to an accurate high-quality visualization. Compared to traditional approaches, the proposed system avoids explicitly predefined fieldline seeding structures, and uses a Monte Carlo sampling strategy named Woodcock tracking to distribute samples along the view ray. An acceleration of this sampling strategy requires local upper bounds for the FTLE values, which we progressively acquire during the rendering. Our approach is tailored for high-quality visualizations of complex FTLE fields and is guaranteed to faithfully represent detailed ridge surface structures as indicators for Lagrangian coherent structures (LCS). We demonstrate the effectiveness of our approach by using a set of analytic test cases and real-world numerical simulations. T3 - ZIB-Report - 16-21 KW - Picture/Image Generation, Display algorithms, Three-Dimensional Graphics and Realism, Raytracing Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59054 SN - 1438-0064 N1 - By mistake the fourth author Hans-Christian Hege has been ommitted in the journal publication ER -