| B样条基转换矩阵的解析表示和计算公式 |
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| 引用本文： | 潘日晶. B样条基转换矩阵的解析表示和计算公式[J]. 应用数学学报, 2005, 28(3): 441-452 |
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| 作者姓名： | 潘日晶 |
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| 作者单位： | 福建师范大学数学与计算机科学学院,福州,350007 |
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| 基金项目： | 福建省自然科学基金（A0210016）和福建省教育厅B类科研基金（JC01114）资助项目 |
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| 摘 要： | 摘要B样条基的转换矩阵具有重要的理论和应用意义。本文研究其最基本的问题：存在性条件、解析表示和计算方法，利用差商展开系数得到了上述问题的有关结果，本文的结果为CAGD中B样条曲线的节点插入、节点删除、升阶、降阶、分割、组合等重要技术提供了一个统一的数学背景和实现方法。
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| 关 键 词： | B样条 基底 转换矩阵 解析表示 计算公式 B样条基 存在性条件 B样条曲线 计算方法 展开系数 |
| 收稿时间： | 2003-04-02 |
| 修稿时间： | 2003-04-02 |
THE ANALYTIC REPRESENTATION AND COMPUTATIONAL FORMULAS TO THE TRANSFORMATION MATRIX OF B-SPLINE BASES |
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| PAN RIJING. THE ANALYTIC REPRESENTATION AND COMPUTATIONAL FORMULAS TO THE TRANSFORMATION MATRIX OF B-SPLINE BASES[J]. Acta Mathematicae Applicatae Sinica, 2005, 28(3): 441-452 |
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| Authors: | PAN RIJING |
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| Abstract: | The transformation matrix of B-spline bases is significant both in theory and application. In this paper, the essential problems about the transformation matrix of B-spline bases-the conditions of existence, the analytic representation and the computational formulas of the transformation matrix are studied, and the results in those aspects are given. In CAGD, those results provide a uniform mathematical background and easily realized approach for the basic operations of B-spline curves including knot insertion, degree elevation, subdivision, composition etc. |
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| Keywords: | B-spline base transformation matrix analytic representation computational formula |
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