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Uniform trigonometric polynomial B-spline curves. (English) Zbl 1185.41008
Summary: This paper presents a new kind of uniform spline curve, named trigonometric polynomial B-splines, over space ${\Omega }=\text{span}\left\{\text{sin}\phantom{\rule{4.pt}{0ex}}t,\text{cost},{t}^{k-3},{t}^{k-4},\cdots ,t,1\right\}$ of which $k$ is an arbitrary integer larger than or equal to 3. We show that trigonometric polynomial B-spline curves have many similar properties to traditional B-splines. Based on the explicit representation of the curve we have also presented the subdivision formulae for this new kind of curve. Since the new spline can include both polynomial curves and trigonometric curves as special cases without rational form, it can be used as an efficient new model for geometric design in the fields of CAD/CAM.
##### MSC:
 41A15 Spline approximation 42A10 Trigonometric approximation
##### References:
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