In this work, by combining a class of local support and infinitely differentiable functions together with the sinc function, we construct a new class of univariate blending functions with three local shape parameters α_i, β_i, and λ_i. The new blending functions have the properties of \(C^{\infty }\) smoothness, compact support, and partition of unity. The shape parameter α_i has tension property, and β_i can adjust the support of the blending functions. With λ_i, the given blending functions can be used to interpolate sets of points partly or entirely without solving a linear system of equations. Some simple conditions for the blending functions possessing nonnegativity and/or linear independence are developed. Based on the new univariate blending functions, tensor product blending functions and local tensor product blending functions are also developed.

在这项工作中，通过与sinc函数结合在一起的一类的本地支持和无限可微函数，我们构建了一类新的单变量混合函数具有三个局部形状参数α_我，β_我，和λ_我。新的混合函数具有\（C ^ {\ infty} \）平滑度，紧凑的支持和统一分区的属性。形状参数α_我有张力性质，和β_我可以调整的混合功能的支持。随着λ_我，给定的混合函数可用于部分或全部内插点集，而无需求解线性方程组。为具有非负性和/或线性独立性的混合函数开发了一些简单条件。基于新的单变量混合函数，还开发了张量积混合函数和局部张量积混合函数。