Journal of Applied Mathematics
Volume 2012 (2012), Article ID 624978, 11 pages
http://dx.doi.org/10.1155/2012/624978
Research Article

Nonnegativity Preserving Interpolation by 𝐶 1 Bivariate Rational Spline Surface

Xingxuan Peng, Zhihong Li, and Qian Sun

School of Mathematics, Liaoning Normal University, Dalian 116029, China

Received 7 January 2012; Accepted 8 February 2012

Academic Editor: Kai Diethelm

Copyright © 2012 Xingxuan Peng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the nonnegativity preserving interpolation of data on rectangular grids. The function is a kind of bivariate rational interpolation spline with parameters, which is 𝐶 1 in the whole interpolation region. Sufficient conditions are derived on coefficients in the rational spline to ensure that the surfaces are always nonnegative if the original data are nonnegative. The gradients at the data sites are modified if necessary to ensure that the nonnegativity conditions are fulfilled. Some numerical examples are illustrated in the end of this paper.