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Tricubic interpolation in three dimensions

Lekien, F. and Marsden, J. (2005) Tricubic interpolation in three dimensions. International Journal for Numerical Methods in Engineering, 63 (3). pp. 455-471. ISSN 0029-5981. http://resolver.caltech.edu/CaltechAUTHORS:20100823-110032644

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/nme.1296DOIUNSPECIFIED
http://onlinelibrary.wiley.com/doi/10.1002/nme.1296/abstract?globalMessage=0PublisherUNSPECIFIED
Additional Information:© 2005 John Wiley & Sons, Ltd. Received 13 May 2004 Revised 23 August 2004. Accepted 13 December 2004. Article first published online: 3 MAR 2005. This project was supported by the Office of Naval Research through ONR contract N00014-01-1- 0208 and the AOSN-II project under ONR contract N00014-02-1-0826 to observe and understand geophysical flows and coastal processes. The authors are grateful to Dallas Trinkle and MANGEN users for their ideas, remarks and tests of the tricubic interpolator. The HF radar data used in this paper was collected and processed by Jeffrey Paduan and Michael Cook (see Reference [11]).
Funders:
Funding AgencyGrant Number
Office of Naval ResearchN00014-01-1-0208
Office of Naval ResearchN00014-02-1-0826
Subject Keywords:tricubic; interpolation; computational dynamics
Record Number:CaltechAUTHORS:20100823-110032644
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100823-110032644
Official Citation:Lekien, F. and Marsden, J. (2005), Tricubic interpolation in three dimensions. International Journal for Numerical Methods in Engineering, 63: 455–471. doi: 10.1002/nme.1296
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19588
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:23 Aug 2010 20:00
Last Modified:26 Dec 2012 12:21

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