Interpolation Poisedness of NUAHT B-spline Basis

摘要

In this paper, a geometrical approach is proposed to prove the interpolation poisedness theorem of NUAHT B-spline basis. The poisedness of interpolation problem for univariate spline spaces means that for a sequence of given m points in the domain of spline spaces and arbitrary m real numbers, if there exist only one spline basis function can interpolate these numbers. Schoenberg-Whitney theorem provided a judging criteria for B-spline bases to determine if the set of interpolation points is poisedness. However, there is no corresponding theorem in the NUAHT B-spline bases space, which plays an important role in engineer design. Our work make complement to the NUAHT B-spline basis theory. In our approach, knot inserted algorithm is applied, combined with coefficient variation of NUAHT B-spline function, leading to an approach intuitively and geometrically.