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| Improved vector-valued Padé approximation and its application in offset approximation |
| ZHAO Hong-yan1,2,3, WANG Guo-jin1,2 |
(1.Department of Mathematics, Zhejiang University, Hangzhou 310027, China;
2.State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China;
3. College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, China) |
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Abstract A new approximation method of offset curve was proposed in order to effectively meet the representation and data exchange requirements of CAD/CAM system in industry. Based on the improvement on the traditional vector-Padé approximation, the new method can generate low-order offset approximation, which is in urgent need for industry designing, but cannot be implemented by the existing methods. In this sense, the method has strong applicability. Endpoints interpolation was also considered together with curve subdivision and series expansion at midpoint, which helped to generate rational approximation under user-specified precision. Lots of experiments illustrated the feasibility and effectiveness of the proposed method.
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Published: 16 January 2010
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向量Padé逼近的改进及其在等距逼近上的应用
为满足工业生产中CAD/CAM系统对等距曲线的表示和数据交换的特殊要求,提出一种可以产生任意次有理逼近的等距逼近新方法. 基于对传统的向量值Padé逼近方法的改进,提出向量类Padé逼近,可以实现以往各种有理等距逼近所不能执行、但为外形设计所迫切需要的低次逼近,因而应用价值显著.通过构造保端点插值的Padé逼近,综合运用曲线细分、中点展开构造等方法,可设计出任意次数的满足用户的特殊需要,达到预设精度的等距有理逼近. 大量实验表明,该算法简洁有效,适合于工程应用．
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