@inproceedings{TheiselWeinkaufHegeetal.2004, author = {Theisel, Holger and Weinkauf, Tino and Hege, Hans-Christian and Seidel, Hans-Peter}, title = {Stream line and path line oriented topology for 2D time-dependent vector fields}, booktitle = {Proc. IEEE Visualization 2004}, address = {Austin, U.S.A.}, doi = {10.1109/VIS.2004.99}, pages = {321 -- 328}, year = {2004}, language = {en} } @inproceedings{WeinkaufTheiselHegeetal.2004, author = {Weinkauf, Tino and Theisel, Holger and Hege, Hans-Christian and Seidel, Hans-Peter}, title = {Topological construction and visualization of higher order 3D vector fields}, volume = {23(3)}, booktitle = {Computer Graphics Forum}, address = {Grenoble, France}, doi = {10.1109/VISUAL.2005.1532842}, pages = {469 -- 478}, year = {2004}, language = {en} } @inproceedings{WeinkaufTheisel2002, author = {Weinkauf, Tino and Theisel, Holger}, title = {Vector Field Metrics Based on Distance Measures of First Order Critical Points}, volume = {10}, booktitle = {Journal of WSCG, Short Communication Papers}, editor = {Skala, V{\´a}clav}, pages = {121 -- 128}, year = {2002}, language = {en} } @inproceedings{WeinkaufTheisel2002, author = {Weinkauf, Tino and Theisel, Holger}, title = {Curvature Measures of 3D Vector Fields and their Applications}, volume = {10}, booktitle = {Journal of WSCG}, editor = {Skala, V{\´a}clav}, doi = {10.1109/TPAMI.2006.36}, pages = {507 -- 514}, year = {2002}, language = {en} } @inproceedings{WeinkaufTheiselHegeetal.2004, author = {Weinkauf, Tino and Theisel, Holger and Hege, Hans-Christian and Seidel, Hans-Peter}, title = {Boundary switch connectors for topological visualization of complex 3D vector fields}, booktitle = {Proc. Joint Eurographics - IEEE TCVG Symposium on Visualization (VisSym '04)}, address = {Konstanz, Germany}, pages = {183 -- 192}, year = {2004}, language = {en} } @inproceedings{TheiselWeinkaufHegeetal.2003, author = {Theisel, Holger and Weinkauf, Tino and Hege, Hans-Christian and Seidel, Hans-Peter}, title = {Saddle Connectors - An Approach to Visualizing the Topological Skeleton of Complex 3D Vector Fields}, booktitle = {Proc. IEEE Visualization 2003}, address = {Seattle}, doi = {10.1109/VISUAL.2003.1250376}, pages = {225 -- 232}, year = {2003}, language = {en} } @misc{KuhnEngelkeRoessletal.2013, author = {Kuhn, Alexander and Engelke, Wito and R{\"o}ssl, Christian and Hadwiger, Markus and Theisel, Holger}, title = {Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43050}, year = {2013}, abstract = {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.}, language = {en} } @article{KuhnEngelkeRoessletal.2014, author = {Kuhn, Alexander and Engelke, Wito and R{\"o}ssl, Christian and Hadwiger, Markus and Theisel, Holger}, title = {Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy}, volume = {33}, journal = {Computer Graphics Forum}, publisher = {Wiley Blackwell}, issn = {0934-5892}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43990}, pages = {222 -- 234}, year = {2014}, language = {en} } @article{OeltzeLehmannKuhnetal.2014, author = {Oeltze, Steffen and Lehmann, Dirk J. and Kuhn, Alexander and Janiga, G{\´a}bor and Theisel, Holger and Preim, Bernhard}, title = {Blood Flow Clustering and Applications in Virtual Stenting of Intracranial Aneurysms}, volume = {20}, journal = {IEEE Transactions on Visualization and Computer Graphics, 2014}, number = {5}, organization = {Otto-von-Guericke-Universit{\"a}t Magdeburg}, issn = {0934-5892}, doi = {10.1109/TVCG.2013.2297914}, pages = {686 -- 701}, year = {2014}, language = {en} } @misc{GuentherKuhnHegeetal.2016, author = {G{\"u}nther, Tobias and Kuhn, Alexander and Hege, Hans-Christian and Theisel, Holger}, title = {MCFTLE: Monte Carlo Rendering of Finite-Time Lyapunov Exponent Fields}, issn = {1438-0064}, doi = {10.1111/cgf.12914}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59054}, year = {2016}, abstract = {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.}, language = {en} }