| 插值细分曲线有理参数点的精确求值 |
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| 引用本文： | 刘秀平,李宝军,苏志勋,郁博文.插值细分曲线有理参数点的精确求值[J].计算数学,2009,31(3):253-260. |
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| 作者姓名： | 刘秀平 李宝军 苏志勋 郁博文 |
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| 作者单位： | 大连理工大学应用数学系,辽宁大连,116024 |
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| 基金项目： | 国家自然科学基金，国家教育部新世纪优秀人才支持计划 |
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| 摘 要： | 本文提出了求值插值细分曲线上任意有理参数的算法.通过构造与细分格式相关的矩阵,m进制分解给定有理数以及特征分解循环节对应算子乘积,计算得到控制顶点权值,实现对称型静态均匀插值细分曲线的求值.本文给出了四点细分和四点Ternary细分曲线的求值实例.算法可以推广到求值其他非多项式细分格式中.
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| 关 键 词： | 插值细分格式 矩阵乘积 参数分解 尺度方程 特征分解 |
| 收稿时间： | 2008-01-02 |
EXACT EVALUATION OF THE INTERPOLATORY SUBDIVISION CURVES AT RATIONAL PARAMETER VALUES |
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| Liu Xiuping,Li Baojun,Su Zhixun,Yu Bowen.EXACT EVALUATION OF THE INTERPOLATORY SUBDIVISION CURVES AT RATIONAL PARAMETER VALUES[J].Mathematica Numerica Sinica,2009,31(3):253-260. |
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| Authors: | Liu Xiuping Li Baojun Su Zhixun Yu Bowen |
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| Institution: | Applied Mathematics, Dalian University of Technology, Dalian 116024, Liaoning, China |
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| Abstract: | An algorithm for exact evaluation of interpolatory subdivision curves at arbitrary rational points is proposed. The algorithm is designed based on the parametric m-ary expansion and construction of associated matrix sequence. The weights of the control points on the initial polygon can be obtained, through computation by multiplying the finite matrix sequence corresponding to the expansion sequence and eigen decomposition of the contraction operator related to the period of rational numbers. Two examples of evaluation of four-point subdivision scheme and four-point ternary one are given. The algorithm proposed in this paper can be generalized to evaluation of other non-polynomial subdivision schemes.
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