| 四点插值细分算法极限曲线曲面C2连续的充分必要条件 |
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| 引用本文： | 曹沅.四点插值细分算法极限曲线曲面C2连续的充分必要条件[J].计算机辅助设计与图形学学报,2003,15(8):961-966. |
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| 作者姓名： | 曹沅 |
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| 作者单位： | 复旦大学数学系,上海,200433 |
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| 基金项目： | 本课题得到国家自然科学基金(19971017)资助 . |
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| 摘 要： | 研究了四点插值细分算法的连续性．用若当标准形重新证明了Dyn的一个定理，从而得到了一个极限函数具有二阶导函数的充分必要条件及二阶导函数的解析表达式；并将结果推广到曲面的情形．
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| 关 键 词： | 四点插值细分算法 极限曲线曲面 C^2连续 CAGD CAD CAM 计算机辅助设计 |
| 修稿时间： | 2002年12月11 |
Necessary and Sufficient Conditions for the C2 Continuous Limit Curves and Surfaces of 4-Point Interpolatory Subdivision Scheme |
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| Cao Yuan.Necessary and Sufficient Conditions for the C2 Continuous Limit Curves and Surfaces of 4-Point Interpolatory Subdivision Scheme[J].Journal of Computer-Aided Design & Computer Graphics,2003,15(8):961-966. |
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| Authors: | Cao Yuan |
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| Abstract: | The continuity of 4 point interpolatory subdivision scheme was studied One of Dyn's theories was proved in a new way by using Jordan's normal form Necessary and sufficient conditions for the second derivative of limit function were obtained, and expression of second derivative was acquired as well The result was accordingly extended into the case of surfaces |
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| Keywords: | subdivision scheme limit curves and surfaces continuity necessary and sufficient condition |
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