Improving the global continuity of the natural neighbor interpolation. (English) Zbl 1116.68626
Laganà, Antonio (ed.) et al., Computational science and its applications — ICCSA 2004. International conference, Assisi, Italy, May 14–17, 2004. Proceedings, Part III. Berlin: Springer (ISBN 3-540-22057-7/pbk). Lecture Notes in Computer Science 3045, 71-80 (2004).
Summary: The natural neighbor interpolation is a potential interpolation method for multidimensional data. However, only globally \(C^{1}\) interpolants have been known so far. This paper proposes a globally \(C^{2}\) 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 \(C^{k}\) 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.
For the entire collection see [Zbl 1051.68016].
For the entire collection see [Zbl 1051.68016].
MSC:
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
