On linear independence of T-spline blending functions

This paper shows that, for any given T-spline, the linear independence of its blending functions can be determined by computing the nullity of the T-spline-to-NURBS transform matrix. The paper analyzes the class of T-splines for which no perpendicular T-node extensions intersect, and shows that the blending functions for any such T-spline are linearly independent.

► This paper shows that linear independence of any T-spline can be determined by computing the nullity of the T-spline-to-NURBS transform matrix. ► T-spline linear independence is a function both of the control mesh topology and the knot values. ► The paper proposes a class of T-splines called analysis-suitable T-splines for which no perpendicular T-junction extensions intersect, and shows that all such T-splines are linearly independent.