@inproceedings{TheiselSahnerWeinkaufetal.2005, author = {Theisel, Holger and Sahner, Jan and Weinkauf, Tino and Hege, Hans-Christian and Seidel, Hans-Peter}, title = {Extraction of parallel vector surfaces in 3D time-dependent fields and application to vortex core line tracking}, series = {Proc. IEEE Visualization 2005}, booktitle = {Proc. IEEE Visualization 2005}, address = {Minneapolis, USA}, pages = {559 -- 566}, year = {2005}, language = {en} } @article{WeinkaufHegeTheisel2012, author = {Weinkauf, Tino and Hege, Hans-Christian and Theisel, Holger}, title = {Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields}, series = {Computer Graphics Forum}, volume = {31}, journal = {Computer Graphics Forum}, number = {2pt4}, doi = {10.1111/j.1467-8659.2012.03063.x}, pages = {825 -- 834}, year = {2012}, abstract = {We present the first general scheme to describe all four types of characteristic curves of flow fields - stream, path, streak, and time lines - as tangent curves of a derived vector field. Thus, all these lines can be obtained by a simple integration of an autonomous ODE system. Our approach draws on the principal ideas of the recently introduced tangent curve description of streak lines. We provide the first description of time lines as tangent curves of a derived vector field, which could previously only be constructed in a geometric manner. Furthermore, our scheme gives rise to new types of curves. In particular, we introduce advected stream lines as a parameter-free variant of the time line metaphor. With our novel mathematical description of characteristic curves, a large number of feature extraction and analysis tools becomes available for all types of characteristic curves, which were previously only available for stream and path lines. We will highlight some of these possible applications including the computation of time line curvature fields and the extraction of cores of swirling advected stream lines.}, language = {en} } @misc{GuentherKuhnHegeetal., 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}, 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} } @misc{KuhnEngelkeRoessletal., 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}, 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., 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}, series = {Computer Graphics Forum}, 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}, language = {en} }