## MCFTLE: Monte Carlo Rendering of Finite-Time Lyapunov Exponent Fields

Please always quote using this URN: urn:nbn:de:0297-zib-59054
• 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.

Author: Tobias Günther, Alexander Kuhn, Hans-Christian Hege, Holger Theisel ZIB-Report Picture/Image Generation, Display algorithms, Three-Dimensional Graphics and Realism, Raytracing 65-XX NUMERICAL ANALYSIS A. General Literature 00.00.00 GENERAL 2016/04/04 ZIB-Report (16-21) 1438-0064 By mistake the fourth author Hans-Christian Hege has been ommitted in the journal publication Appeared in: Computer Graphics Forum 35 (2016) 381-390 https://doi.org/10.1111/cgf.12914