The Analysis of T-spline Blending Functions Linear Independence

Abstract

In 2003, Sederberg and Zheng proposed T-splines which belongs non-uniform rational B-splines with T-knot. Compared to B-splines, T-splines have more advantages especially in the surface merging, local refinement, and data compression. The T-spline blending function plays an important role in the T-spline surface modeling. In this paper we give an equivalent condition of the open question that whether T-spline blending functions are linearly independent. According to the equivalent condition the paper presents an algorithm to determine whether T-spline blending functions are linearly independent or not. Finally, we give a sufficient condition of the linear independence, and by using the sufficient condition it can be easily to determine the linear independence of some T-spline blending functions. Several examples are given to illustrate the feasibility and effectiveness of this approach.

Keywords:

• T-spline
• linear independence
• surface modeling