A New Approach to Vector Field Interpolation, Classification and Robust Critical Points Detection Using Radial Basis Functions

  • Vaclav Skala
  • Michal Smolik
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 765)


Visualization of vector fields plays an important role in many applications. Vector fields can be described by differential equations. For classification null points, i.e. points where derivation is zero, are used. However, if vector field data are given in a discrete form, e.g. by data obtained by simulation or a measurement, finding of critical points is difficult due to huge amount of data to be processed and differential form usually used. This contribution describes a new approach for vector field null points detection and evaluation, which enables data compression and easier fundamental behavior visualization. The approach is based on implicit form representation of vector fields.


Critical points Vector field classification Vector field topology Approximation Data acquisition Visualization Radial basis functions RBF Interpolation Approximation 



The author would like to thank to colleagues at the University of West Bohemia and to anonymous reviewers for their comments, which helped to improve the manuscript significantly. Special thanks also belong to Pavel Šnejdar for MATLAB additional programming and images generation.

Research was supported by the Czech Science Foundation, No. GA 17–05534S and partially by SGS 2016-013.


  1. Goldman, R.: Curvature formulas for implicit curves and surfaces. Comput. Aided Geom. Des. 22, 632–658 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Helman, J., Hesselink, L.: Representation and display of vector field topology in fluid flow data sets. IEEE Comput. 22(8), 27–36 (1989)CrossRefGoogle Scholar
  3. Koch, S., Kasten, J., Wiebel, A., Scheuermann, G., Hlawitschka, M.: Vector field approximation using linear neighborhoods. Vis. Comput. 32(12), 1563–1578 (2015)CrossRefGoogle Scholar
  4. Majdisova, Z., Skala, V.: Radial basis function approximations: comparison and applications. Appl. Math. Model. 51, 728–743 (2017)MathSciNetCrossRefGoogle Scholar
  5. Scheuermann, G., Krüger, H., Menzel, M., Rockwood, A.: Visualizing non-linear vector field topology. IEEE Trans. Visual. Comput. Graph. 4(2), 109–116 (1998)CrossRefGoogle Scholar
  6. Smolik, M., Skala, V.: Classification of critical points using a second order derivative. In: ICCS 2017, Procedia Computer Science, pp. 2373–2377. Elsevier (2017a)CrossRefGoogle Scholar
  7. Smolik, M., Skala, V.: Spherical RBF vector field interpolation: experimental study. In: SAMI, pp. 431–434. IEEE (2017b)Google Scholar
  8. Thiesel, H.: Vector field curvature and applications. Ph.D. Thesis. Univ. of Rostock (1995)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer Science and Engineering, Faculty of Applied SciencesUniversity of West BohemiaPlzenCzech Republic

Personalised recommendations