目的 构造一类新的基于函数值与偏导数值的加权有理插值样条曲面,讨论该样条曲面的相关性质并分析曲面的局部约束控制。方法 一方面,先从x方向构造有理三次插值样条,再从y方向构造二元有理插值样条曲面;另一方面,按相反次序构造另一个二元有理插值样条曲面;最后将两种插值曲面加权得到一类新的有理插值样条曲面。结果 讨论插值曲面的性质,包括基函数、边界性质、积分加权系数的性质以及误差估计。通过选择合适的参数和加权系数,在不改变插值数据的前提下实现对插值区域内的局部约束控制。结论 实验结果表明,新的加权有理插值样条曲面具有良好的约束控制性质。

Objective This study presents a new weighted rational spline interpolation surface based on the values and partial derivatives of functions being interpolated and discusses its properties. The local constraint control of surfaces is parsed. Method On one hand, a rational cubic interpolation spline is constructed on the x-direction and a bivariate rational interpolation spline surface is constructed on the y-direction. On the other hand, another bivariate rational interpolation spline surface is obtained in the reverse order. Finally, a new weighted rational interpolation spline surface is generated by weighting two different interpolation surfaces. Result This study discusses several properties of the interpolating function, such as the bases of the interpolation, the bounded property, the properties of integral weighted coefficients, and the error between the interpolating function and the function being interpolated. By selecting suitable parameters and weight coefficients, the local constraint control in the interpolating region can be obtained without changing the interpolating data. Conclusion Experimental results illustrate that the new weighted rational interpolation spline surface possesses good constraint control properties.