On linear independence of T-spline blending functions

Authors

Xin Li, University of Science and Technology of China
Jianmin Zheng, School of Computer Science and Engineering
Thomas W. Sederberg, Brigham Young University
Thomas J.R. Hughes, The University of Texas at Austin
Michael A. Scott, The University of Texas at Austin

Document Type

Article

Publication Date

1-1-2012

Abstract

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. © 2011 Elsevier B.V. All rights reserved.

Publication Source (Journal or Book title)

Computer Aided Geometric Design

First Page

63

Last Page

76

Recommended Citation

Li, X., Zheng, J., Sederberg, T., Hughes, T., & Scott, M. (2012). On linear independence of T-spline blending functions. Computer Aided Geometric Design, 29 (1), 63-76. https://doi.org/10.1016/j.cagd.2011.08.005