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The best parameterization for parametric interpolation. (English) Zbl 1092.65014
The authors consider the problem of interpolation of curves and surfaces using parametric functions. The optimal parametrization conditions are obtained using the parametric continuation method. It is shown that the optimal parameter is the length of the curve to be interpolated (Theorem 1). For the parametric approximation of a surface, the optimal parametrization at each surface point is given by two orthogonal curves lying on the surface and passing trough this point. The optimal parameters are the lengths of the arcs of those curves.

65D17Computer aided design (modeling of curves and surfaces)
65D05Interpolation (numerical methods)
UNCMND; pchip
Full Text: DOI
[1] Faux, I. D.; Pratt, M. J.: Computational geometry for design and manufacture. (1979) · Zbl 0395.51001
[2] Hoschek, J.; Lasser, D.: Fundamentals of computer aided geometric design. (1993) · Zbl 0788.68002
[3] Kahaner, D.; Moler, C.; Nash, S.: Numerical methods and software. (1988) · Zbl 0744.65002
[4] Ortega, J. M.; Poole, W. G.: An introduction to numerical methods for differential equations. (1981) · Zbl 0472.65060
[5] Shalashilin, V. I.; Kuznetsov, E. B.: Parametric continuation and optimal parametrization in applied mathematics and mechanics. (2003) · Zbl 1040.65060
[6] Zav’yalov, Yu.S.; Leus, V. A.; Skorospelov, V. A.: Splines in engineering geometry. (1985)