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Unified and extended form of three types of splines

✍ Scribed by Guozhao Wang; Mei’e Fang

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
275 KB
Volume
216
Category
Article
ISSN
0377-0427

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✦ Synopsis

The three types refer to polynomial, trigonometric and hyperbolic splines. In this paper, we unify and extend them by a new kind of spline (UE-spline for short) defined over the space {cos t, sin t, 1, t, . . . , t l , . . .}, where l is an arbitrary nonnegative integer. is a frequency sequence

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.

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