Tobias Günther, Alexander Kuhn and Holger Theisel
MCFTLE: Monte Carlo Rendering of FiniteTime Lyapunov Exponent Fields
Computer Graphics Forum (Proc. EuroVis), 2016Abstract:Traditionally, Lagrangian fields such as finitetime 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, viewdependent Monte Carlobased approach for the visualization of such Lagrangian fields in timedependent flows. Our approach avoids grid discretization and ray marching errors completely, is consistent, and has a low memory consumption. The system provides noisy previews that converge over time to an accurate highquality 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 highquality 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 realworld numerical simulations.Download
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