Rational biquartic interpolating surface based on function values

Abstract

In this paper a bivariate rational biquartic interpolating spline based on function values with two parameters is constructed , and this spline is with biquartic numerator and bilinear denominator. The interpolating function has a simple and explicit mathematical representation, which is convenient both in practical application and in theoretical study. The interpolating surface is C 1 in the interpolating region when one of the parameters satisfies a simple condition. The interpolating surface can be modified by selecting suitable parameters under the condition that the interpolating data are not changed. It is proved that the values of the interpolating function in the interpolating region are bounded no matter what the parameters might be; this is called the bounded property of the interpolation. The approximation expressions of the interpolation are derived:they do not depend on the parameters. © 2008 Springer-Verlag Berlin Heidelberg.