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

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.

Keywords

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 

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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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