| 引用本文: | 王兴波,石金龙,卢世荣.囿于控制多边形的NURBS拐点分析与控制.[J].国防科技大学学报,2004,26(5):79-84.[点击复制] |
| WANG Xingbo,SHI Jinlong,LU Shirong.Analysis and Control of Inflection Points on NURBS Curves via Control-polygon[J].Journal of National University of Defense Technology,2004,26(5):79-84[点击复制] |
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| 囿于控制多边形的NURBS拐点分析与控制 |
| 王兴波1, 石金龙1, 卢世荣2 |
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(1.国防科技大学 机电工程与自动化学院，湖南 长沙 410073;2.国防科技大学 理学院，湖南 长沙 410073)
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| 摘要: |
| 从变形的观点出发，首先研究了一般平面参数曲线变形过程中产生拐点的充分必要条件以及判定拐点的一个泛函方程。在此基础上，给出了研究非凸控制多边形NURBS曲线拐点的方法，特别研究了正则单拐、双拐多边形NURBS曲线拐点的分布问题，得到了分析与控制相应曲线拐点的条件和判据。本文的结果可应用于调节与控制曲线形状的算法设计，也可指导CAD造型工程师的交互设计。 |
| 关键词: 拐点 参数曲线 形状控制 算法设计 |
| DOI： |
| 投稿日期：2004-04-02 |
| 基金项目:国家自然科学基金资助项目(50175106)；广东省自然科学基金资助项目(04021250) |
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| Analysis and Control of Inflection Points on NURBS Curves via Control-polygon |
| WANG Xingbo1, SHI Jinlong1, LU Shirong2 |
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(1.College of Mechatronics Engineering and Automation, National Univ. of Defense Technology, Changsha 410073, China;2.College of Science, National Univof Defense Technology, Changsha 410073, China)
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| Abstract: |
| This paper first makes a study of the shape variation laws of generic planar parametric curves by means of geometry deformation, obtains a necessary and sufficient condition for a curve's occurring inflection points and a functional equation to determine the inflection points on the deforming curves. Then based on the results, the paper puts forward a method to study the inflection points on NURBS of non-convex control polygon, particularly makes an investigation on the distribution of inflection points on the curve whose control polygon is regular and with one to two inflection points, and gains several conditions and criterions for analysis and manipulation of the respected NURBS curves. The results are useful for the algorithm-design and shape-control in CAD modeling. |
| Keywords: inflection point parametric curve shape control algorithm design |
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