Unified and extended form of three types of splines

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:216

Article

Wang, Guozhao ; Fang, Mei'e

关键词: UE-splines;    frequency sequence;    composed splines;    polynomial splines;    trigonometric splines;    hyperbolic splines;    modelling;   

DOI  :  10.1016/j.cam.2007.05.031

来源: Elsevier

【 摘 要 】

The three types refer to polynomial, trigonometric and hyperbolic splines. In this pap er, we unify and extend them by a new kind of spline (UE-spline for short) defined over the space {cos wt, sin wt, 1, t, ..., t(l), ...}, where l is an arbitrary nonnegative integer. omega is a frequency sequence {omega(i) = root alpha(i)}(-infinity)(+infinity), alpha(i) is an element of R. Existing splines, such as usual polynomial B-splines, CB-splines, HB-splines, NUAT splines, AH splines, FB-splines and the third form FB-splines etc., are all special cases of UE-splines. UE-splines inherit most properties of usual polynomial B-splines and enjoy some other advantageous properties for modelling. They can exactly represent classical conics, the catenary, the helix, and even the eight curve, a kind of snake-like curves etc. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free