Chinese Journal of Computers   Full Text
Title	Degree Elevation of Algebraic Hyperbolic B-spline Curves and Corner Cutting Based on Bi-order Spline
Authors	ZHANG BoWANG Guo-Zhao
Address	(Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou310027)
Year	2008
Issue	No.6(1056—1062)
Abstract &   Background	Abstract The authors consider the degree elevation of algebraic hyperbolic(AH) B-spline curves and prove that the degree elevation of AH B-spline curves can be interpreted as corner cutting process in theory. A new class of basis functions, to be called bi-order algebraic hyperbolic B-spline basis functions, is constructed and discussed by the integral definition of spline. This class of basis functions has bi-order property and the transforming formulae between AH B-spline and bi-order AH B-spline lead to the corner cutting for degree elevation of AH B-spline curves. Keywords bi-order spline; algebraic hyperbolic B-spline; degree elevation; corner cutting Background This research is supported by the National Natural Science Foundation of China (10371110, 60473130) and the National Basic Research Program(973 Program) of China(2004CB318000). It is well known that the degree elevation of Bézier curves is corner cutting. The authors consider the degree elevation of algebraic hyperbolic B-spline curves. There are several methods that have been proposed in the literatures for the degree elevation of B-spline curves, and these methods can also be used in the degree elevation of the algebraic hyperbolic B-spline curves. However none of them can be interpreted as corner cutting. In this paper, the authors construct a new class of basis functions called bi-order algebraic hyperbolic B-spline basis functions. By using these new basis functions, the corner cutting algorithm for the degree elevation of algebraic hyperbolic B-spline curves can be achieved.