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4. , High accurate rational approximation of parametric curves, Computer Aided Geometric Design 10 (1993), 293-313. 5. Epstein, M. , On the influence of parametrization in parametric interpolation, SIAMJ. Numer. Anal. 13 (1976), 261-268. 6. , Curves and Surfaces for Computer Aided Geometric Design, Academic Press, San Diego, 1988. 7. Floater, M. , Arc length estimation and the convergence of parametric polynomial interpolation, preprint, CMA, Oslo (2005). 8. Floater, M. , Chordal cubic spline interpolation is fourth order accurate, IMA J.
Widder, D. , The Laplace Transform, 8th printing, Princeton University Press, Princeton, 1972. 29. , Approximationsordnung und Regularitat von Differentialoperatoren, Habilitationsschrift, Gerhard-Mercator-Universitat Duisburg, 1996. This Page is Intentionally Left Blank Topics in Multivariate Approximation and Interpolation K. V. All rights reserved 23 Three Families of Nonlinear Subdivision Schemes Nira Dyn School of Mathematical Sciences, Tel-Aviv University, Israel Abstract Three families of nonlinear subdivision schemes, derived from linear schemes, are reviewed.
This same property holds for any quadrature method with positive weights and degree of precision at least two. 3. Examples Figure 9 shows the C 1 cubic spline built from cubic 2-point Hermite interpolation, based on chordal parameter values. In this figure and in all subsequent similar figures, the black curve is the original and the grey one the approximation. Figure 10 shows the C 2 quintic splines built from quintic 2-point Hermite interpolation, based on chordal parameter values, and the improved parameter values.