| 周期B样条基转换矩阵的表示和计算 |
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| 引用本文： | 潘日晶,姚志强,刘晓芬.周期B样条基转换矩阵的表示和计算[J].应用数学学报,2012,35(2):263-282. |
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| 作者姓名： | 潘日晶 姚志强 刘晓芬 |
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| 作者单位： | 1. 福建师范大学数学与计算机科学学院,福州350007;福建师范大学网络安全与密码技术重点实验室,福州350007
2. 福建师范大学软件学院,福州350007;福建师范大学网络安全与密码技术重点实验室,福州350007 |
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| 基金项目： | 国家自然科学基金(No.60673014);福建省自然科学基金(No.2010J01318)的资助项目 |
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| 摘 要： | 周期B样条基以一种简洁的形式表示闭B样条曲线.周期B样条基转换矩阵为闭B样条曲线及相关曲面的不同表示间的转换提供了一个数学模型.本文给出了周期B样条基转换矩阵的存在性条件,给出并证明了周期B样条基转换矩阵的一个简单的递归表示式.在此基础上,本文进一步给出了周期B样条基转换矩阵的计算公式和高效算法.周期B样条基转换矩阵为闭B样条曲线的节点插入、升阶、节点删除和降阶等基本运算提供了一个统一而简单的解决方法,本文给出了一些应用例子.
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| 关 键 词： | B样条基 转换矩阵 闭B样条曲线 递归表示 周期性 |
Representation and Computation of the Transformation Matrices of Periodic B-spline Bases |
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| PAN RIJING
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YAO ZHIQING
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LIU XIAOFEN.Representation and Computation of the Transformation Matrices of Periodic B-spline Bases[J].Acta Mathematicae Applicatae Sinica,2012,35(2):263-282. |
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| Authors: | PAN RIJING YAO ZHIQING LIU XIAOFEN |
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| Institution: | (College of Mathematics and Computer Science,Fujian Normal University,Fuzhou 350007) (Key Lab of Network Security and Cryptology,Fujian Normal University,Fuzhou 350007) |
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| Abstract: | With periodic B-spline bases closed B-spline curves can be represented compactly. The transformation matrices of periodic B-spline bases provide a mathematical model for the conversion between different representations of closed B-pline curves and the relevant surfaces.In this paper,we first present the existence conditions of the transfor- mation matrices of periodic B-spline bases.Then we propose and demonstrate a simple recursive formula for the transformation matrices of periodic B-spline bases.Based on the recursive formula,we further develop an efficient algorithm for the computation of the transformation matrices of periodic B-spline bases.With the transformation matrices of periodic B-spline bases,we can establish a uniform scheme for the essential operations of closed B-spline curves and the relevant surfaces such as knot insertion,knot removal,degree elevation and degree reduction.Several examples for the applications of the transformation matrices of periodic B-spline bases are provided lastly. |
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| Keywords: | B-spline basis transformation matrix closed B-spline curve recursive representation periodicity |
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