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Vector Field Second Order Derivative Approximation and Geometrical Characteristics

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Computational Science and Its Applications – ICCSA 2017 (ICCSA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10404))

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Abstract

Vector field is mostly linearly approximated for the purpose of classification and description. This approximation gives us only basic information of the vector field. We will show how to approximate the vector field with second order derivatives, i.e. Hessian and Jacobian matrices. This approximation gives us much more detailed description of the vector field. Moreover, we will show the similarity of this approximation with conic section formula.

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References

  1. Agranovsky, A., Camp, D., Joy, K.I., Childs, H.: Subsampling-based compression and flow visualization. In: IS&T/SPIE Electronic Imaging, International Society for Optics and Photonics (2015)

    Google Scholar 

  2. Balduzzi, F., Bianchini, A., Maleci, R., Ferrara, G., Ferrari, L.: Critical issues in the CFD simulation of Darrieus wind turbines. Renew. Energy 85, 419–435 (2016)

    Article  Google Scholar 

  3. Benbourhim, M.N., Bouhamidi, A.: Approximation of vectors fields by thin plate splines with tension. J. Approx. Theory 136(2), 198–229 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cabrera, D.A.C., González-Casanova, P., Gout, C., Juárez, L.H., Reséndizd, L.R.: Vector field approximation using radial basis functions. J. Comput. Appl. Math. 240, 163–173 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Forsberg, A., Chen, J., Laidlaw, D.: Comparing 3D vector field visualization methods: a user study. IEEE Trans. Vis. Comput. Graph. 15(6), 1219–1226 (2009)

    Article  Google Scholar 

  6. Helman, J., Hesselink, L.: Representation and display of vector field topology in fluid flow data sets. IEEE Comput. 22(8), 27–36 (1989)

    Article  Google Scholar 

  7. Koch, S., Kasten, J., Wiebel, A., Scheuermann, G., Hlawitschka, M.: 2D Vector field approximation using linear neighborhoods. Vis. Comput. 32, 1563–1578 (2015)

    Article  Google Scholar 

  8. Laidlaw, D.H., Kirby, R.M., Jackson, C.D., Davidson, J.S., Miller, T.S., Da Silva, M., Warrenand, W.H., Tarr, M.J.: Comparing 2D vector field visualization methods: a user study. IEEE Trans. Vis. Comput. Graph. 11(1), 59–70 (2005)

    Article  Google Scholar 

  9. Lage, M., Petronetto, F., Paiva, A., Lopes, H., Lewiner, T., Tavares, G.: Vector field reconstruction from sparse samples with applications. In: 19th Brazilian Symposium on Computer Graphics and Image Processing, SIBGRAPI (2006)

    Google Scholar 

  10. de Leeuw, W., van Liere, R.: Collapsing flow topology using area metrics. In: Proceedings of IEEE Visualization 1999, pp. 349–354 (1999)

    Google Scholar 

  11. Lu, K., Chaudhuri, A., Lee, T.Y., Shen, H.W., Wong, P.C.: Exploring vector fields with distribution-based streamline analysis. PacificVis, pp. 257–264 (2013)

    Google Scholar 

  12. Peng, C., Teng, Y., Hwang, B., Guo, Z., Wang, L.P.: Implementation issues and benchmarking of lattice Boltzmann method for moving rigid particle simulations in a viscous flow. Comput. Math. Appl. 72(2), 349–374 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Philippou, P.A., Strickland, R.N.: Vector field analysis and synthesis using threedimensional phase portraits. Graph. Models Image Process. 59(6), 446–462 (1997)

    Article  Google Scholar 

  14. Scheuermann, G., Krüger, H., Menzel, M., Rockwood, A.: Visualizing non-linear vector field topology. IEEE Trans. Vis. Comput. Graph. 4(2), 109–116 (1998)

    Article  Google Scholar 

  15. Skraba, P., Rosen, P., Wang, B., Chen, G., Bhatia, H., Pascucci, V.: Critical point cancellation in 3D vector fields: robustness and discussion. IEEE Trans. Vis. Comput. Graph. (2016)

    Google Scholar 

  16. Skraba, P., Wang, B., Chen, G., Rosen, P.: 2D vector field simplification based on robustness. In: Pacific Visualization Symposium (PacificVis), IEEE, pp. 49–56 (2014)

    Google Scholar 

  17. Smolik, M., Skala, V.: Spherical RBF vector field interpolation: experimental study. SAMI 2017, pp. 431–434, Slovakia (2017)

    Google Scholar 

  18. Smolik, M., Skala, V.: Vector field interpolation with radial basis functions. SIGRAD 2016, pp. 15–21, Sweden (2016)

    Google Scholar 

  19. Weinkauf, T., Theisel, H., Shi, K., Hege, H.-C., Seidel, H.-P.: Extracting higher order critical points and topological simplification of 3D vector fields. In: Proceedings of IEEE Visualization 2005, pp. 559–566, Minneapolis, U.S.A. (2005)

    Google Scholar 

  20. Westermann, R., Johnson, C., Ertl, T.: Topology-preserving smoothing of vector fields. IEEE Trans.Vis. Comput. Graph 7(3), 222–229 (2001)

    Article  Google Scholar 

  21. Wischgoll, T., Scheuermann, G.: Detection and visualization of closed streamlines in planar flows. IEEE Trans. Vis. Comput. Graph. 7(2), 165–172 (2001)

    Article  Google Scholar 

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Acknowledgments

The authors would like to thank their colleagues at the University of West Bohemia, Plzen, for their comments and suggestions, their valuable comments and hints provided. The research was supported by projects Czech Science Foundation (GACR) No. 17-05534S and partly by SGS 2016-013.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic

    Michal Smolik & Vaclav Skala

Authors
  1. Michal Smolik
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  2. Vaclav Skala
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Corresponding author

Correspondence to Michal Smolik .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Trieste, Trieste, Italy

    Giuseppe Borruso

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  9. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  10. University of Trieste, Trieste, Italy

    Alfredo Cuzzocrea

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Smolik, M., Skala, V. (2017). Vector Field Second Order Derivative Approximation and Geometrical Characteristics. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10404. Springer, Cham. https://doi.org/10.1007/978-3-319-62392-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-62392-4_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62391-7

  • Online ISBN: 978-3-319-62392-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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