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Computational methods for discrete parametric \(\ell_1\) and \(\ell_\infty\) curve fitting. (English) Zbl 0963.68208

Summary: The paper is devoted to \(\ell_1\) and \(\ell_\infty\) approximation with parametric spline curves. We discuss the questions of existence and uniqueness of solutions. With the help of a suitable linearization of the Euclidean norm, we derive method for computing the approximating spline curves. The method uses linear and quadratic programming in order to find the solution.

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
41A15 Spline approximation

Software:

FITPACK
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References:

[1] Hoschek J., Fundamentals of Computer Aided Geometric Design (1993) · Zbl 0788.68002
[2] W. Heidrich, R. Bartels and G. Labahn, Curves and Surfaces with Applications in CAGD, eds. A. Le Mehaute, C. Rabut and L. L. Schumaker (Vanderbilt University Press, Nashville, 1997) pp. 177–184. · Zbl 0938.65024
[3] DOI: 10.1093/comjnl/9.3.318 · Zbl 0168.14905 · doi:10.1093/comjnl/9.3.318
[4] DOI: 10.1137/0710069 · Zbl 0266.65016 · doi:10.1137/0710069
[5] DOI: 10.1007/978-1-4612-6333-3 · doi:10.1007/978-1-4612-6333-3
[6] Schumaker L. L., Spline Functions: Basic Theory (1981)
[7] Dierckx P., Curve and Surface Fitting with Splines (1993) · Zbl 0782.41016
[8] DOI: 10.1007/BFb0063201 · doi:10.1007/BFb0063201
[9] Fletcher R., Practical Methods of Optimization (1990) · Zbl 0905.65002
[10] DOI: 10.1016/0021-9045(69)90033-1 · Zbl 0181.17604 · doi:10.1016/0021-9045(69)90033-1
[11] DOI: 10.1007/978-3-0348-7376-5_12 · doi:10.1007/978-3-0348-7376-5_12
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