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Reduced data for curve modeling – applications in graphics, computer vision and physics

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In this paper we consider the problem of modeling curves in R n via interpolation with out apriori specified interpolation knots. We discuss two approaches to estimate missing knots{ti}mi=0 for non-parametric data(i.e.collection of points {qi}mi=0, where qiRn). The first approach (uniforme valuation) is based on blind guess in which knots {ˆti}mi=0 are chosen uniformly. The second approach (cumulative chord parameterization), incorporates the geometry of the distribution of data points.More precisely the difference ˆti+1−ˆti is equal to the Euclidean distance between data points qi+1 and qi. The second method partially compensates for the loss of the information carried by the reduced data. We also present the application of the above schemes for fitting non-parametric data in computer graphics (light-source motion rendering),in computer vision (image segmentation)and in physics (high velocity particles trajectory modeling).Though experiments are conducted for points in R2 and R3 the entire method is equally applicable in Rn.
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  • Faculty of Mathematics and Information, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
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  • Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences – SGGW, Nowoursynowska 159, 02-776 Warsaw, Poland
autor
  • Faculty of Mathematics and Information, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
Bibliografia
  • 1. Bradski G., Kaehler A.: Learning OpenCV. O’Reilly Media 2008.
  • 2. de Boor C.: A Practical Guide to Splines. Applied Mathematical Sciences, Springer 2001.
  • 3. Floater M.S.: Chordal cubic spline interpolation is fourth order accurate. IMA Jouarnal of Numerical Analysis, 26, 2006, 25-33.
  • 4. Kozera R., Noakes L.: C1 interpolation with cumulative chord cubics. Fundamenta Informaticae, 31(3-4), 2004, 285-301.
  • 5. Kozera R.: Curve modeling via interpolation based on multidimensional reduced data. Studia Informatica, 25(4B), 2004.
  • 6. Lenik K., Korga S.: Deform 3D and SolidWorks FEM tests in conditions of sliding friction. Archives of Materials Science and Engineering, 56, 2012, 89-92.
  • 7. Lenik K., Korga S.: The application of a tribotester prototype to sliding friction simulations and wear computations by means of FEM. Les problemes contemporains du technosphere et delaformation des cadres dingenieurs, 2011, 61-64.
  • 8. Noakes L., Kozera R.: Cumulative chords and piecewise-quadratics and piecewise-cubics. In Geometric Properies of Incomplete Data, Eds R. Klette, R. Kozera, L. Noakes and J. Weickert, Computational Imaging and Vision. Springer, 31, 2006, 59-75.
  • 9. Paliszewski P., Szczygiel I.: Modelowanie numeryczne procesu napełniania cylindra silnika ZI (in English: Flow simulation inside the IC engine). Postępy Nauki i Techniki – Advances in Science and Technology, 15, 2012, 116-122.
  • 10. Phong B.T.: Illumination for Computer Generated Pictures Commun. ACM (1975).
  • 11. Piegl L., Tiler W.: The NURBS Book. Springer, 1995.
  • 12. Pinsky A.A., Yavorsky B.M.: Fundamentals of Physics. Volume II. MIR Publishers 1975.
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