一类改进的插值基函数

A Kind of Interpolating Basis Functions with Improved Properties

为了构造具有良好性质的插值基函数用来构造插值曲线与曲面,引入一类具有精确的局部支撑和无穷次可微的函数;将其与sinc函数结合并优化,构造一类相似于插值细分基函数的新基函数,这类新基函数保持了以往基函数的良好性质,并具有以往基函数所不具有的精确局部支撑性的优点.实例结果表明,文中构造的新基函数有很好的效果;与传统的Akima方法相比,所构造的曲线总体上具有较好的光顺性.

The main purpose of this work is to develop a kind of interpolating basis functions with good properties for constructing interpolatory curves and surfaces. We first introduce a new class of c？functions with local support. Combined with the sinc function with parameter optimization, we obtain a new kind of interpolating basis functions with similar properties to that of interpolatory subdivision basis functions. Compared with other similar basis functions in the literature, the new basis functions possess exact local support property. The curve example constructed using the new basis shows better visual effect compared with the well-known Akima＇s method, while other examples constructed by using the new basis exhibit similar visual effect compared with other similar basis functions in the literature.