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| 实平面奇异代数曲线的全局B样条逼近 |
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方美娥1, 汪国昭1, 贺志民2
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1.浙江大学,数学系,计算机图像图形研究所,浙江,杭州,310027;2.浙江林学院,理学院,浙江,杭州,311300
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| 摘要: |
| 提出了一种用k次B样条曲线全局逼近实平面k次代数曲线的算法,每个连通部分用一条B样条曲线逼近.它适合于任意亏格的不可约的实平面代数曲线(包括含奇异点的曲线).这种逼近建立在所提出的代数曲线胀开采样的基础上,这种胀开采样算法从本质上解决了奇异点周围采样难的问题.实验结果表明,该方法的逼近精度高于已有算法. |
| 关键词: 实代数曲线 逼近 采样 奇异点 胀开 B样条 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant No.60473130(国家自然科学基金);the National Grand Fundamental Research 973 Program of China under Grant No.G2004CB318000(国家重点基础研究发展规划(973));the Foundation of the Department of Education of Zhejiang Province of China under Grant No.20060676(浙江省教育厅基金) |
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| Global B-Spline Approximations of Singular Real Algebraic Plane Curves |
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FANG Mei-E,WANG Guo-Zhao,HE Zhi-Min
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| Abstract: |
| This paper proposes an algorithm for globally approximating real algebraic plane curves of degree k with B-spline curves of the same degree. Each connected component is approximated with a B-spline curve. It is suitable for all irreducible real plane algebraic curves with arbitrary genus (including singular curves). This method is based on our blowup sampling method of algebraic curves, which solves the difficult problem of sampling around singular points in essence. The experimental results show that the algorithm achieves better accuracy than the existed methods. |
| Key words: real algebraic curve approximation sampling singular point blowup B-spline |
