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2D Vector field approximation using linear neighborhoods

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Abstract

We present a vector field approximation for two-dimensional vector fields that preserves their topology and significantly reduces the memory footprint. This approximation is based on a segmentation. The flow within each segmentation region is approximated by an affine linear function. The implementation is driven by four aims: (1) the approximation preserves the original topology; (2) the maximal approximation error is below a user-defined threshold in all regions; (3) the number of regions is as small as possible; and (4) each point has the minimal approximation error. The generation of an optimal solution is computationally infeasible. We discuss this problem and provide a greedy strategy to efficiently compute a sensible segmentation that considers the four aims. Finally, we use the region-wise affine linear approximation to compute a simplified grid for the vector field.

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Acknowledgments

We thank Markus Rütten, Guillaume Daviller, and Bernd Noack for providing the simulation datasets. Special thanks go to the FAnToM development group for providing the visualization software. We also thank Roxana Bujack and Sebastian Volke for the fruitful discussions. S. Koch and J. Kasten were supported by the European Social Fund (Appl. No. 100098251).

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Authors and Affiliations

  1. Institute of Computer Science, Leipzig University, Augustusplatz 10, 04109, Leipzig, Germany

    Stefan Koch, Jens Kasten, Gerik Scheuermann & Mario Hlawitschka

  2. Coburg University of Applied Sciences, Friedrich-Streib-Str.2, 96450, Coburg, Germany

    Alexander Wiebel

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  1. Stefan Koch
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  2. Jens Kasten
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  3. Alexander Wiebel
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  4. Gerik Scheuermann
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  5. Mario Hlawitschka
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Correspondence to Stefan Koch.

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Koch, S., Kasten, J., Wiebel, A. et al. 2D Vector field approximation using linear neighborhoods. Vis Comput 32, 1563–1578 (2016). https://doi.org/10.1007/s00371-015-1140-9

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  • DOI: https://doi.org/10.1007/s00371-015-1140-9

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