| 基于离散曲率的三次均匀B样条的局部光顺算法 |
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| 引用本文： | 喻德生,程程. 基于离散曲率的三次均匀B样条的局部光顺算法[J]. 浙江大学学报(理学版), 2011, 38(5): 511-517. DOI: 10.3785/j.issn.1008-9497.2011.05.007 |
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| 作者姓名： | 喻德生 程程 |
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| 作者单位： | 南昌航空大学数学与信息科学学院,江西南昌,330063 |
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| 基金项目： | 江西省教育厅科技计划项目(GJJ10524); 江西省教改课题(Jxjg-07-7-9) |
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| 摘 要： | 在研究B样条曲线节点的曲率和对应控制点的离散曲率之间关系的基础上,引入了一种新的离散曲率——第二离散曲率的概念,得出了三次均匀B样条曲线节点的曲率和对应控制点的第二离散曲率成正比的结论,并给出了基于第二离散曲率三次均匀B样条曲线的光顺算法.该算法通过直接调整控制点的第二离散曲率进行曲线的光顺,从而使光顺过程更为简洁、更具几何直观性.算例表明,该算法具有较好的光顺效果.
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| 关 键 词： | 离散曲率 差分 光顺 三次均匀B样条 |
On local fairing algorithm for cubic B-spline with discrete curvature |
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| YU De-sheng,CHENG Cheng. On local fairing algorithm for cubic B-spline with discrete curvature[J]. Journal of Zhejiang University(Sciences Edition), 2011, 38(5): 511-517. DOI: 10.3785/j.issn.1008-9497.2011.05.007 |
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| Authors: | YU De-sheng CHENG Cheng |
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| Affiliation: | YU De-sheng,CHENG Cheng(College of Mathematics and Information Sciences,Nanchang Hangkong University,Nanchang 330063,China) |
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| Abstract: | On the basis of investigating the relationship between the curvature of B-spline curves and the discrete curvature of its corresponding control points,a new conception of discrete curvature,the second discrete curvature is introduced.It is obtained that the curvature of cubic uniform B-spline curve at its joining points is proportional to the second discrete curvature of the corresponding control points.The fairing algorithm for cubic uniform B-spline based on the second discrete curvature is given.With thi... |
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| Keywords: | discrete curvature differential fairing cubic uniform B-spline |
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