MCFTLE: Monte Carlo Rendering of Finite-Time Lyapunov Exponent Fields
Günther T, Kuhn A, Theisel H (2016)
Publication Type: Journal article
Publication year: 2016
Journal
Book Volume: 35
Pages Range: 381-390
Journal Issue: 3
DOI: 10.1111/cgf.12914
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 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 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.
Authors with CRIS profile
Involved external institutions
Otto-von-Guericke-Universität Magdeburg
Germany (DE)
Konrad-Zuse-Zentrum für Informationstechnik / Zuse Institute Berlin (ZIB)
Germany (DE)
Germany (DE)
Konrad-Zuse-Zentrum für Informationstechnik / Zuse Institute Berlin (ZIB)
Germany (DE)
How to cite
APA:
Günther, T., Kuhn, A., & Theisel, H. (2016). MCFTLE: Monte Carlo Rendering of Finite-Time Lyapunov Exponent Fields. Computer Graphics Forum, 35(3), 381-390. https://dx.doi.org/10.1111/cgf.12914
MLA:
Günther, Tobias, Alexander Kuhn, and Holger Theisel. "MCFTLE: Monte Carlo Rendering of Finite-Time Lyapunov Exponent Fields." Computer Graphics Forum 35.3 (2016): 381-390.
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