B样条基转换矩阵的解析表示和计算公式  

THE ANALYTIC REPRESENTATION AND COMPUTATIONAL FORMULAS TO THE TRANSFORMATION MATRIX OF B-SPLINE BASES

作　　者：潘日晶[1] 

机构地区：[1]福建师范大学数学与计算机科学学院,福州350007

出　　处：《应用数学学报》2005年第3期441-452,共12页Acta Mathematicae Applicatae Sinica

基　　金：福建省自然科学基金(A0210016);福建省教育厅B类科研基金(JB01114)资助项目

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.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.

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 

分 类 号：O144[理学—数学] TH122[理学—基础数学]