| 摘要: |
| 构造了一系列次数为n且带有参数k(2(≤)k(≤)「n/2」+1)的新的广义Ball基,作为Wang-Ball基(k=2)到Said-Ball基(k=「n/2」+1)的过渡,并给出新基的一些性质.接着,由新基定义出新的广义Ball曲线,给出曲线的递归求值、升阶和降阶逼近算法.最后,提出相应的三角基,并给出三角曲面的递归求值和升阶算法. |
| 关键词: Ball基 Said-Ball基 Wang-Ball基 Berastein基 Bézier曲线 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant No.60473130(国家自然科学基金);the National Grand Fundamental Research 973 Program of China under Grant No.2004CB318000(国家重点基础研究发展规划(973)) |
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| Extension of the Ball Basis |
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SHEN Wan-Qiang,WANG Guo-Zhao
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| Abstract: |
| A new series of the generalized Ball basises of degree-n with parameter k(2≤k≤「n/2」+1) are constructed as the transition from Wang-Ball basis (k=2) to Said-Ball basis (k=n/2+n), and some properties of them are given. Then, the new generalized Ball curves are based on these new basises and the algorithms for recursive evaluation, degree-elevation, and degree-reduction are introduced. Finally, the corresponding trigonal Ball basises are shown and the algorithms for the recursive evaluation and degree-elevation of trigonal Ball surfaces are given. |
| Key words: Ball basis Said-Ball basis Wang-Ball basis Bernstein basis Bézier curve |
