【摘要】 针对曲线与曲面拟合问题 ,研究多结点样条插值方法。这类方法具有基数型、显式计算 (无须求解方程组 )及局部性等优点。主要的新结果是 :对多结点样条基本函数的构造给出了新的表述 ;提出一类新的不带移动的混合型多结点样条基本函数 ;基于多尺度分析的思想 ,给出了一种自适应的细化算法 ,它对消减采样数据的相关性是简便有效的。更多还原

【Abstract】 This paper is aimed at fitting curves and surfaces, investigating many knot spline interpolation schemes. This kind of schemes has advantages such as cardinal type, explicit calculation(no need to solve system of equations) and localization. New results are: present new expression for the basic function of many knot spline interpolation; produce a new kind of hybrid basic function of many knot spline interpolation without shift; based on the thought of multi scale analysis, present a self fitting refinement algorithm that is simple and efficacious for reduces dependence of the sampling data.更多还原