4 . the local interpolation methodd above are extended from order 4 to the case of arbitrary order , the existence for singular piecewise function of arbitrary order is proved , and a unite interpolation formula for odd and even - order is given , which develop and perfect the nuat b - spline curve and surface interpolation methods 4 .将四阶混合插值法推广到任意阶情形,给出任意阶奇异分段函数存在性的证明,并得到了奇数阶和偶数阶样条奇异混合插值公式的统一表达式,发展和完善了nuatb样条插值方法和奇异混合思想