| 引用本文: | 方逵,朱国庆.C2有理插值样条曲线曲面.[J].国防科技大学学报,1996,18(3):147-151.[点击复制] |
| Fang Kui,Zhu Guoqing.C2 Rational Biquitic Interpolation Surface[J].Journal of National University of Defense Technology,1996,18(3):147-151[点击复制] |
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| C2有理插值样条曲线曲面 |
| 方逵, 朱国庆 |
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(国防科技大学 系统工程与数学系 湖南 长沙 410073)
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| 摘要: |
| 首先提出一组基函数向量，它具有以下特定的性质:BB(O)T=(0.0,1.0,0.0,0.0), BB(1)T=(0.0,0.0,1.0,0.0)
BB′(O)T=(-0.5,0.0,0.5,0.0)， BB′(1)T=(0.0,-0.5,0.0,0.5) BB"(O)T=(1.0,-2.0,1.0,0.0)
BB"(1)T=(0.0,1.0,-2.0,1.0)。进而研究了以此函数向量的张量积形式定义的有理样条曲面，并得以下结论: (1)插值性；(2) C2 连续性； (3) 局部性和可调性。文中还分析了“权”的作用，并指出它与三次B-样条的类似性。 |
| 关键词: 有理样条曲线，有理样条曲面，插值曲线曲面 |
| DOI： |
| 投稿日期：1996-01-09 |
| 基金项目:CAD/CG 国家重点实验室资助项目 |
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| C2 Rational Biquitic Interpolation Surface |
| Fang Kui, Zhu Guoqing |
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(Department of Systems Engineering and Mathematics，NUDT，Changsha，410073)
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| Abstract: |
| We first present a vector of function basis BB(t)that satisfied BB(O)T=(0.0,1.0,0.0,0.0),BB(1)T=(0.0,0.0,1.0,0.0)
BB′(O)T=(-0.5,0.0,0.5,0.0)，BB′(1)T=(0.0,-0.5,0.0,0.5)BB"(O)T=(1.0,-2.0,1.0,0.0)，BB"(1)T=(0.0,1.0,-2.0,1.0)Secondly we discuss the rational surface defined in tension-product form using above function vector BB (t). The interpolation surface implies the following results: (1)The surface interpolates control points; (2) It is second order parametrically continuous;(3) It is local and can be adjusted by weights. The effect of weights is also analysed and has similar result as bicubic rational B-spline surface. |
| Keywords: rational spline curve,rational spline surface,interpolation curve surface |
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