Degree elevation of unified and extended spline curves

作者：Duan, Xiao-juan^*; Wang, Guo-zhao

来源：Journal of Zhejiang University-Science C(Computers and Electronics), 2014, 15(12): 1098-1105.

DOI：10.1631/jzus.C1400076

• Degree elevation
• Unified and extended splines (UE-splines)
• Bi-order UE-splines
• Corner cutting
• Geometric explanation

Unified and extended splines (UE-splines), which unify and extend polynomial, trigonometric, and hyperbolic B-splines, inherit most properties of B-splines and have some advantages over B-splines. The interest of this paper is the degree elevation algorithm of UE-spline curves and its geometric meaning. Our main idea is to elevate the degree of UE-spline curves one knot interval by one knot interval. First, we construct a new class of basis functions, called bi-order UE-spline basis functions which are defined by the integral definition of splines. Then some important properties of bi-order UE-splines are given, especially for the transformation formulae of the basis functions before and after inserting a knot into the knot vector. Finally, we prove that the degree elevation of UE-spline curves can be interpreted as a process of corner cutting on the control polygons, just as in the manner of B-splines. This degree elevation algorithm possesses strong geometric intuition.

• 出版日期2014-12
• 单位浙江大学