Tricubic interpolation in three dimensions
Article first published online: 3 MAR 2005
Copyright © 2005 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Volume 63, Issue 3, pages 455–471, 21 May 2005
How to Cite
Lekien, F. and Marsden, J. (2005), Tricubic interpolation in three dimensions. Int. J. Numer. Meth. Engng., 63: 455–471. doi: 10.1002/nme.1296
- Issue published online: 31 MAR 2005
- Article first published online: 3 MAR 2005
- Manuscript Accepted: 13 DEC 2004
- Manuscript Revised: 23 AUG 2004
- Manuscript Received: 13 MAY 2004
- Office of Naval Research. Grant Number: N00014-01-1-0208
- Office of Naval Research. Grant Number: N00014-02-1-0826
- computational dynamics
The purpose of this paper is to give a local tricubic interpolation scheme in three dimensions that is both C1 and isotropic. The algorithm is based on a specific 64 × 64 matrix that gives the relationship between the derivatives at the corners of the elements and the coefficients of the tricubic interpolant for this element. In contrast with global interpolation where the interpolated function usually depends on the whole data set, our tricubic local interpolation only uses data in a neighbourhood of an element. We show that the resulting interpolated function and its three first derivatives are continuous if one uses cubic interpolants. The implementation of the interpolator can be downloaded as a static and dynamic library for most platforms. The major difference between this work and current local interpolation schemes is that we do not separate the problem into three one-dimensional problems. This allows for a much easier and accurate computation of higher derivatives of the extrapolated field. Applications to the computation of Lagrangian coherent structures in ocean data are briefly discussed. Copyright © 2005 John Wiley & Sons, Ltd.