| 论区间B样条曲线的升阶与割角的关系 |
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| 引用本文： | 魏永伟,汪国昭.论区间B样条曲线的升阶与割角的关系[J].计算机辅助设计与图形学学报,2010,22(2). |
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| 作者姓名： | 魏永伟 汪国昭 |
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| 作者单位： | 1. 浙江大学数学系计算机图象图形研究所,杭州,310027;上海海事大学应用数学系,上海,201306
2. 浙江大学数学系计算机图象图形研究所,杭州,310027 |
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| 基金项目： | 国家自然科学基金(60773179);;国家“九七三”重点基础研究发展计划项目(2004CB318000) |
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| 摘 要： | 为了解决区间B样条曲线的升阶理论问题,提出区间控制多边形概念,利用双次B样条基函数证明了区间B样条曲线具有升阶性质;并阐明了区间B样条曲线的升阶就是对其控制多边形的割角过程.最后证明了当升阶次数趋于无穷时,区间B样条曲线的控制多边形收敛到该曲线.
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| 关 键 词： | 区间B样条曲线 区间控制多边形 双次B样条基函数 升阶 割角 |
The Degree Elevation of Interval B-Spline Curves and Corner Cutting |
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| Wei Yongwei,Wang Guozhao.The Degree Elevation of Interval B-Spline Curves and Corner Cutting[J].Journal of Computer-Aided Design & Computer Graphics,2010,22(2). |
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| Authors: | Wei Yongwei Wang Guozhao |
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| Affiliation: | Institute of Computer Graphic and Image Processing/a>;Department of Mathematics/a>;Zhejiang University/a>;Hangzhou 310027;Department of Applied Mathematics/a>;Shanghai Maritime University/a>;Shanghai 201306 |
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| Abstract: | This paper investigates degree elevation of interval B-spline.Based on the concept of interval control polygon,we prove that interval B-spline curves hold the degree elevation property by using bi-degree B-spline basis functions.Further,we show that the degree elevation of interval B-spline curves is equivalent to corner cutting of control polygons.Finally,it's proved that the control polygon sequence by degree elevation will converge to the interval B-spline curve. |
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| Keywords: | interval B-spline curves interval control polygon bi-degree B-spline basis functions degree elevation corner cutting |
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