| Uniform trigonometric polynomial B-spline curves |
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| 作者姓名： | 吕勇刚 汪国昭 杨勋年 |
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| 作者单位： | LU Yonggang WANG Guozhao & YANG XunnianInstitute of Computer Graphics and Image Processing，Department of Mathematics，Zhejiang University，Hangzhou 310027，China |
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| 基金项目： | This work was partially supported by the National Natural Science Foundation of China (Grant No. 19971079)，and Foundation of State Key Basic Research 973 Development Programming Item (Grant No. G1998030600). |
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| 摘 要： | This paper presents a new kind of uniform spline curve, named trigonometric polynomial B-splines, over space Ω = span{sini,cost, tk-3,tk-4, …,t, 1} 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.
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| 收稿时间： | 10 December 2001 |
Uniform trigonometric polynomial B-spline curves |
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| Lü Yonggang , Wang Guozhao and Yang Xunnian.Uniform trigonometric polynomial B-spline curves[J].Science in China(Information Sciences),2002,45(5):335-343. |
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| Authors: | Lü Yonggang Wang Guozhao and Yang Xunnian |
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| Affiliation: | Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University,Hangzhou 310027, China |
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| Abstract: | This paper presents a new kind of uniform spline curve, named trigonometric polynomial B-splines, over spaceΩ = span{sint, cost,t
k−3,t
k−4, …,t, 1} of whichk 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. |
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| Keywords: | C-curves uniform B-splines C-B-splines trigonometric polynomial B-splines |
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