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Space-Time Flow Visualization of Dynamics in 2D Lagrangian Coherent Structures

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Computer Vision, Imaging and Computer Graphics. Theory and Application

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 359))

Abstract

Stretching and compression in tangent directions of Lagrangian coherent structures (LCS) are of particular interest in the vicinity of hyperbolic trajectories and play a key role in turbulence and mixing. Since integration of hyperbolic trajectories is difficult, we propose to visualize them in 2D time-dependent vector fields by space-time intersection curves of LCS. LCS are present as ridge lines in the 2D finite-time Lyapunov exponent (FTLE) field and as ridge surfaces in its 3D space-time domain. We extract these ridge surfaces from the forward and reverse FTLE field and intersect them. Due to their advection property, LCS become stream surfaces in 3D space-time. This allows us to use line integral convolution on the LCS to visualize their intrinsic dynamics, in particular around hyperbolic trajectories. To reduce occlusion, we constrain the LCS to space-time bands around their intersection curves. We evaluate our approach using synthetic, simulated, and measured vector fields.

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Author information

Authors and Affiliations

  1. University of Stuttgart, Germany

    Filip Sadlo, Sven Bachthaler & Daniel Weiskopf

  2. Karlsruhe Institute of Technology, Germany

    Carsten Dachsbacher

Authors
  1. Filip Sadlo
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  2. Sven Bachthaler
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  3. Carsten Dachsbacher
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  4. Daniel Weiskopf
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Editor information

Editors and Affiliations

  1. Xerox Research Centre Europe, 6 ch. de Maupertuis, 38240, Meylan, France

    Gabriela Csurka

  2. Aalborg University, Niels Jernes Vej 14, 3-215A, 9220, Aalborg Ø, Denmark

    Martin Kraus

  3. Department of Computer Science, University of Wales, Swansea, UK

    Robert S. Laramee

  4. LISA-ISTIA, Université d’Angers, 62, avenue Notre-Dame du Lac, 49000, Angers, France

    Paul Richard

  5. Departamento de Sistemas e Informática, Escola Superior de Tecnologia do IPS, Rua do Vale de Chaves Estefanilha, 2910, Setúbal, Portugal

    José Braz

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Sadlo, F., Bachthaler, S., Dachsbacher, C., Weiskopf, D. (2013). Space-Time Flow Visualization of Dynamics in 2D Lagrangian Coherent Structures. In: Csurka, G., Kraus, M., Laramee, R.S., Richard, P., Braz, J. (eds) Computer Vision, Imaging and Computer Graphics. Theory and Application. Communications in Computer and Information Science, vol 359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38241-3_10

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  • DOI: https://doi.org/10.1007/978-3-642-38241-3_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38240-6

  • Online ISBN: 978-3-642-38241-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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