Improving the Global Continuity of the Natural Neighbor Interpolation
The natural neighbor interpolation is a potential interpolation method for multidimensional data. However, only globally C1 interpolants have been known so far. This paper proposes a globally C2 interpolant, and write it in an explicit form. When the data are supplied to the interpolant from a third-degree polynomial, the interpolant can reproduce that polynomial exactly. The idea used to derive the interpolant is applicable to obtain a globally Ck interpolant for an arbitrary non-negative integer k. Hence, this paper gets rid of the continuity limitation of the natural neighbor interpolation, and thus leads it to a new research stage.
Unable to display preview. Download preview PDF.
- 2.Sibson, R.: A brief description of natural neighbour interpolation. In: Barnett, V. (ed.) Interpreting Multivariate Data, pp. 21–36. John Wiley & Sons, Chichester (1981)Google Scholar
- 5.Thiessen, A.H.: Precipitation averages for large areas. Monthly Weather Review 39, 1082–1084 (1911)Google Scholar
- 6.Preparata, F.P., Shamos, M.I.: Computational Geometry. Springer, Heidelberg (1985)Google Scholar
- 7.de Boor, C.: B-form basics. In: Farin, G. (ed.) Geometric Modeling: Algorithms and New Trends, pp. 131–148. SIAM, Philadelphia (1987)Google Scholar