On linear independence of T-spline blending functions

Authors:
Xin Li;Jianmin Zheng;Thomas W. Sederberg;Thomas J. R. Hughes;Michael A. Scott
Affiliations:
University of Science and Technology of China, Hefei, Anhui, PR China;School of Computer Engineering, Nanyang Technological University, Singapore;Computer Science Department, Brigham Young University, United States;ICES, University of Texas at Austin, United States;ICES, University of Texas at Austin, United States
Venue:
Computer Aided Geometric Design
Year:
2012

Citing 4
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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.