Article ID Journal Published Year Pages File Type
4642344 Journal of Computational and Applied Mathematics 2008 11 Pages PDF
Abstract

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 {cosωt,sinωt,1,t,…,tl,…}{cosωt,sinωt,1,t,…,tl,…}, where l   is an arbitrary nonnegative integer. ωω is a frequency sequence {ωi=αi}-∞+∞,αi∈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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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