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.
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References
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)
Cattiaux-Huillard, I., Albrecht, G., Hernández-Mederos, V.: Optimal parameterization of rational quadratic curves. Computer Aided Geometric Design 26(7), 725–732 (2009)
Costantini, P., Farouki, R., Manni, C., Sestini, A.: Computation of optimal composite re-parameterizations. Computer Aided Geometric Design 18(9), 875–897 (2001)
Farouki, R.: Optimal parameterizations. Computer Aided Geometric Design 14(2), 153–168 (1997)
Farouki, R., Sakkalis, T.: Real rational curves are not unit speed. Computer Aided Geometric Design 8(2), 151–157 (1991)
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)
Jüttler, B.: A vegetarian approach to optimal parameterizations. Computer Aided Geometric Design 14(9), 887–890 (1997)
Patterson, R., Bajaj, C.: Curvature adjusted parameterization of curves. Computer Science Technical Report CSD-TR-907, Paper 773, Purdue University, USA (1989)
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)
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)
Wang, D. (ed.): Selected Lectures in Symbolic Computation. Tsinghua University Press, Beijing (2003) (in Chinese)
Yang, J., Wang, D., Hong, H.: Improving angular speed uniformity by reparameterization (preprint, submitted for publication, January 2012)
Zoutendijk, G.: Methods of Feasible Directions: A Study in Linear and Nonlinear Programming. Elsevier Publishing Company, Amsterdam (1960)
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Yang, J., Wang, D., Hong, H. (2012). Improving Angular Speed Uniformity by Optimal C 0 Piecewise Reparameterization. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol 7442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32973-9_29
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DOI: https://doi.org/10.1007/978-3-642-32973-9_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32972-2
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