T样条调配函数线性无关性的判定算法

摘要

Aimed at the open question whether T-spline blending functions are linear independence or not, this paper proposes a linear independence determining algorithm for T-spline blending functions. First, based on the property of T-spline blending functions, by converting T-splines to B-splines, this paper gives a proof of the necessary and sufficient condition for the linear independence of T-spline blending functions. The sufficient condition for the linear independence of T-spline blending functions has been also proved, which makes us easier to determine the linear independence of some special cases. Then combined two conditions mentioned above, an algorithm for determining the linear independence of T-spline blending functions has been given. Some examples are given to verify the effectiveness of the algorithm.%针对T样条调配函数的公开问题——T样条曲面表达式中的调配函数是否具有线性无关性,提出一种T样条调配函数线性无关性的验证算法.首先分析了T样条调配函数的数学性质,给出T样条调配函数线性无关的充要条件和充分条件,通过充分条件可以较容易地对一些特殊的T样条调配函数的线性无关性进行判定；然后结合充要条件和充分条件给出一种T样条调配函数线性无关性的验证算法.最后通过实例验证了该算法的有效性.文中结果对于开展T样条造型算法方面的研究有重要意义.