关键词: 二元插值, 二元有理样条, 参数, 计算机辅助几何设计

Abstract: A bivariate rational interpolation spline with parameters was created in an earlier work which was based on function values only, and this spline is a rational one with biquartic numerator and biquadratic denominator. This paper discusses the spline’s boundary property, the approximation expression of the interpolation and the point control method of the interpolating surface. It is proved that the values of the interpolating function in the interpolation region are bounded no matter what the parameters might be, which is called the boundary property of the interpolation. Also, the approximation expression of the interpolation are derived, which does not depend on the parameters. More important is that the values of the interpolating function at any point in the interpolating region can be modified under the condition that the interpolating data are not changed by selecting the suitable parameters, so the interpolation surface can be modified for the given interpolation data when needed in practical design.

Key words: bivariate interpolation, bivariate rational spline, parameter, computer aided geometric design