| 广义B样条曲线节点插入算法及其应用 |
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| 引用本文： | 张硕,孟宪瑞,李娜娜.广义B样条曲线节点插入算法及其应用[J].武汉理工大学学报,2010(2). |
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| 作者姓名： | 张硕 孟宪瑞 李娜娜 |
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| 作者单位： | 天津师范大学津沽学院;河北理工大学理学院;唐山学院; |
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| 基金项目： | 河北理工大学科学研究基金(z0819) |
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| 摘 要： | 通过研究二阶常系数微分算子的零空间及其初值问题解的唯一性,引入了广义B样条曲线的概念,给出了B样条曲线的一种统一表示形式,介绍了该样条的求值算法及节点插入算法,并以多项式B样条为例,将样条曲线的求值算法和节点插入算法推广到曲面。最后给出了相应算例。数值实验表明,求值算法和节点插入算法对样条曲线和样条曲面均准确、有效。利用广义B样条曲线在2个方向上取不同类型的样条曲线,构造了特殊曲面。
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| 关 键 词： | 广义B样条曲线 求值算法 节点插入算法 特殊曲面 |
Knot Insertion Algorithm of Generalized B-splines and Its Application |
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| ZHANG Shuo,MENG Xian-rui,LI Na-na.Knot Insertion Algorithm of Generalized B-splines and Its Application[J].Journal of Wuhan University of Technology,2010(2). |
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| Authors: | ZHANG Shuo MENG Xian-rui LI Na-na |
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| Affiliation: | ZHANG Shuo1,MENG Xian-rui2,LI Na-na3(1.Jingu College of Tianjin Normal University,Tianjin 300387,China,2.Institute of Science,Hebei Polytechnic University,Tangshan 063009,3.Tangshan College,Tangshan 063020,China) |
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| Abstract: | A new representation to B-splines and the concept of generalized B-spline are introduced in this paper by considering the null space of a second order constant coefficient differential operator and the unique solution to an initial-value problem.The evaluation algorithm and knot insertion algorithm for generalized Bsplines are also presented,and they are extended to surfaces by taking polynomial spline surface for example.At last,numerical examples show that the algorithms are valid to both curves and surfa... |
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| Keywords: | generalized B-splines curve evaluation algorithm knot insertion algorithm special surfaces |
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