Advertisement

Improving Angular Speed Uniformity by Optimal C0 Piecewise Reparameterization

  • Jing Yang
  • Dongming Wang
  • Hoon Hong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7442)

Abstract

We adapt the C 0 piecewise Möbius transformation to compute a C 0 piecewise-rational reparameterization of any plane curve that approximates to the arc-angle parameterization of the curve. The method proposed on the basis of this transformation can achieve highly accurate approximation to the arc-angle parameterization. A mechanism is developed to optimize the transformation using locally optimal partitioning of the unit interval. Experimental results are provided to show the effectiveness and efficiency of the reparameterization method.

Keywords

Parametric plane curve angular speed uniformity optimal piecewise Möbius transformation locally optimal partition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (10th printing). United States Government Printing, Washington, D.C (1972)zbMATHGoogle Scholar
  2. 2.
    Cattiaux-Huillard, I., Albrecht, G., Hernández-Mederos, V.: Optimal parameterization of rational quadratic curves. Computer Aided Geometric Design 26(7), 725–732 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Costantini, P., Farouki, R., Manni, C., Sestini, A.: Computation of optimal composite re-parameterizations. Computer Aided Geometric Design 18(9), 875–897 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Farouki, R.: Optimal parameterizations. Computer Aided Geometric Design 14(2), 153–168 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Farouki, R., Sakkalis, T.: Real rational curves are not unit speed. Computer Aided Geometric Design 8(2), 151–157 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Gil, J., Keren, D.: New approach to the arc length parameterization problem. In: Straßer, W. (ed.) Prodeedings of the 13th Spring Conference on Computer Graphics, Budmerice, Slovakia, June 5–8, pp. 27–34. Comenius University, Slovakia (1997)Google Scholar
  7. 7.
    Jüttler, B.: A vegetarian approach to optimal parameterizations. Computer Aided Geometric Design 14(9), 887–890 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Patterson, R., Bajaj, C.: Curvature adjusted parameterization of curves. Computer Science Technical Report CSD-TR-907, Paper 773, Purdue University, USA (1989)Google Scholar
  9. 9.
    Sendra, J.R., Winkler, F., Pérez-Díaz, S.: Rational Algebraic Curves: A Computer Algebra Approach. Algorithms and Computation in Mathematics, vol. 22. Springer, Heidelberg (2008)zbMATHCrossRefGoogle Scholar
  10. 10.
    Walter, M., Fournier, A.: Approximate arc length parameterization. In: Velho, L., Albuquerque, A., Lotufo, R. (eds.) Prodeedings of the 9th Brazilian Symposiun on Computer Graphics and Image Processing, Fortaleza-CE, Brazil, October 29-November 1, pp. 143–150. Caxambu, SBC/UFMG (1996)Google Scholar
  11. 11.
    Wang, D. (ed.): Selected Lectures in Symbolic Computation. Tsinghua University Press, Beijing (2003) (in Chinese)Google Scholar
  12. 12.
    Yang, J., Wang, D., Hong, H.: Improving angular speed uniformity by reparameterization (preprint, submitted for publication, January 2012)Google Scholar
  13. 13.
    Zoutendijk, G.: Methods of Feasible Directions: A Study in Linear and Nonlinear Programming. Elsevier Publishing Company, Amsterdam (1960)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jing Yang
    • 1
  • Dongming Wang
    • 2
  • Hoon Hong
    • 3
  1. 1.LMIB – School of Mathematics and Systems ScienceBeihang UniversityBeijingChina
  2. 2.Laboratoire d’Informatique de Paris 6CNRS – Université Pierre et Marie CurieParis cedex 05France
  3. 3.Department of MathematicsNorth Carolina State UniversityRaleighUSA

Personalised recommendations