The Visual Computer

, Volume 32, Issue 12, pp 1563–1578 | Cite as

2D Vector field approximation using linear neighborhoods

  • Stefan Koch
  • Jens Kasten
  • Alexander Wiebel
  • Gerik Scheuermann
  • Mario Hlawitschka
Original Article


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.


I.6.6. Flow visualization, simulation output analysis I.6.9.b Flow visualization, computing methodologies I.3.8 Computer graphics, applications, computer applications J.2 Physical sciences and engineering, physics 



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Stefan Koch
    • 1
  • Jens Kasten
    • 1
  • Alexander Wiebel
    • 2
  • Gerik Scheuermann
    • 1
  • Mario Hlawitschka
    • 1
  1. 1.Institute of Computer ScienceLeipzig UniversityLeipzigGermany
  2. 2.Coburg University of Applied SciencesCoburgGermany

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