@article{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}, series = {Computer Graphics Forum}, volume = {35}, journal = {Computer Graphics Forum}, number = {3}, doi = {10.1111/cgf.12914}, pages = {381 -- 390}, language = {en} } @misc{GuentherKuhnHegeetal., author = {G{\"u}nther, Tobias and Kuhn, Alexander and Hege, Hans-Christian and Gross, Markus and Theisel, Holger}, title = {Progressive Monte-Carlo Rendering of Atmospheric Flow Features Across Scales}, series = {69th Annual Meeting of the APS Division of Fluid Dynamics, Gallery of Fluid Motion, Nov 20-22, 2016, Portland, OR, USA.}, journal = {69th Annual Meeting of the APS Division of Fluid Dynamics, Gallery of Fluid Motion, Nov 20-22, 2016, Portland, OR, USA.}, doi = {10.1103/APS.DFD.2016.GFM.P0030}, abstract = {To improve existing weather prediction and reanalysis capabilities, high-resolution and multi-modal climate data becomes an increasingly important topic. The advent of increasingly dense numerical simulation of atmospheric phenomena, provides new means to better understand dynamic processes and to visualize structural flow patterns that remain hidden otherwise. In the presented illustrations we demonstrate an advanced technique to visualize multiple scales of dense flow fields and Lagrangian patterns therein, simulated by state-of-the-art simulation models for each scale. They provide a deeper insight into the structural differences and patterns that occur on each scale and highlight the complexity of flow phenomena in our atmosphere.}, 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} }