Linear Independence of T-Spline Blending Functions

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.