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Tricubic interpolation in three dimensions
Author(s) -
Lekien F.,
Marsden J.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1296
Subject(s) - interpolation (computer graphics) , trilinear interpolation , computation , nearest neighbor interpolation , spline interpolation , multivariate interpolation , mathematics , stairstep interpolation , isotropy , bilinear interpolation , finite element method , algorithm , computer science , engineering , physics , motion (physics) , artificial intelligence , statistics , quantum mechanics , structural engineering
The purpose of this paper is to give a local tricubic interpolation scheme in three dimensions that is both C 1 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.