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| Distorting method for cubic NURBS based on weights |
| LUO Yong-Jun, YE Bang-Yan |
| School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China |
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Abstract The general law of the impact of changes in one weight or two neighboring weights on the shape of NURBS curve was summarized as well as the law of determining weights according to the shape of NURBS curve. Based on the existing research achievements, the characteristics of distorting the NUBRS curve to random directions by weights were discovered and proved. Furthermore, the calculation method of the corresponding weights or two neighboring weights according to the changes of the feature points on the revised cubic NUBRS curve was proposed too. In the situation of distorting cubic NURBS at the direction of non-controlling point, firstly, the ratio of the new curve's two neighboring weights was obtained by directly searching method, and then the weights were determined according to the weight calculation formula. Finally, examples were used to demonstrate that the proposed method agree with the reality well.
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Published: 28 December 2009
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基于权因子的三次NURBS曲线推拉方法
总结了更改1个或2个相邻权因子对NURBS曲线形状影响的一般规律,及根据新NURBS曲线形状来确定权因子的计算公式.在对前人研究成果的深入分析下,笔者发现并证明了通过权因子来使三次NURBS曲线朝任意方向推拉的有关性质,并提出根据修改后的三次NURBS曲线特征点的变化来推算相应1个或2个相邻权因子的计算方法.在针对指向非控制点方向的三次NURBS曲线推拉中,采用直接搜索法得出新曲线相邻两权因子的比值后根据权因子计算公式确定权因子.最后通过实例分析证明了所提出的方法与计算公式与实际相符.
关键词：
非均匀有理B样条,
权因子,
基函数,
曲线推拉变形
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