Abstract
In this paper, the problem of geometric interpolation of space data is considered. Cubic polynomial parametric curve is supposed to interpolate five points in three dimensional space. It is a case of a more general problem, i.e., the conjecture about the number of points in \(\mathbb{R}\) d which can be interpolated by parametric polynomial curve of degree n. The necessary and sufficient conditions are found which assure the existence and the uniqueness of the interpolating polynomial curve.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berger, M. S., Nonlinearity and Functional Analysis, Lectures on Nonlinear Problems in Mathematical Analysis, Academic Press, 1977.
de Boor, C., K. Höllig, and M. Sabin, High accuracy geometric Hermite interpolation, Comput. Aided Geom. Design, 4 (1987), pp. 269–278.
Feng, Y. Y., and J. Kozak, On spline interpolation of space data, in Mathematical Methods for Curves and Surfaces II, M. Dæhlen, T. Lyche, and L. L. Schumaker (eds.), Vanderbilt University Press, Nashville, 1998, pp. 167–174.
Höllig, K., and J. Koch, Geometric Hermite interpolation with maximal order and smoothness, Comput. Aided Geom. Design, 13 (1996), pp. 681–695.
Kozak, J., and E. Žagar, On curve interpolation in \(\mathbb{R}\) d, in Curve and Surface Fitting — Saint Malo 1999, A. Cohen, C. Rabut, and L. L. Schumaker (eds.), Vanderbilt University Press, Nashville, 2000, pp. 263–273.
Kozak, J., and E. Žagar, On geometric interpolation by polynomial curves, accepted for publication in SIAM Journal on Numerical Analysis.
Mørken, K., Parametric interpolation by quadratic polynomials in the plane, in Mathematical Methods for Curves and Surfaces, M. Dæhlen, T. Lyche, and L. L. Schumaker (eds.), Vanderbilt University Press, Nashville, 1995, pp. 385–402.
Mørken, K., and K. Scherer, A general framework for high-accuracy parametric interpolation, Math. Comp., 66 (1997), pp. 237–260.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer
About this paper
Cite this paper
Kozak, J., Žagar, E. (2005). Geometric Interpolation of Data in \(\mathbb{R}\) 3. In: Drmač, Z., Marušić, M., Tutek, Z. (eds) Proceedings of the Conference on Applied Mathematics and Scientific Computing. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3197-1_17
Download citation
DOI: https://doi.org/10.1007/1-4020-3197-1_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3196-0
Online ISBN: 978-1-4020-3197-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)