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| 基于控制顶点偏移的等距曲线最优逼近 |
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刘利刚1, 王国瑾1
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浙江大学,CAD&CG国家重点实验室,浙江,杭州,310027,浙江大学,计算机图像图形研究所,浙江,杭州,310027
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| 摘要: |
| 利用最佳平方逼近的Legendre多项式来逼近基曲线的法矢曲线,计算出各控制顶点的偏移向量,由此产生偏移控制多边形来得到等距曲线的逼近曲线.通过与Tiller,Cobb,Coquillart和Elber等多种基于控制顶点偏移的等距逼近法的比较,表明此方法中曲线的离散次数和控制顶点数最少.此方法简单、直观,而且等距逼近曲线的表达式与原曲线具有相同形式,因而有很好的应用前景. |
| 关键词: 几何造型 等距曲线 曲线逼近 顶点偏移 Legendre多项式 |
| DOI： |
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| 基金项目:国家自然科学基金资助项目(60173034);国家重点基础研究发展规划973资助项目(G1998030600);浙江省自然科学基金资助项目(698025) |
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| Optimal Approximation to Curve Offset Based on Shifting Control Points |
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LIU Li-gang,WANG Guo-jin
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| Abstract: |
| In this paper, an approximation approach is presented for offsetting curve by approximating the normal curve of the base curve using Legendre least-square polynomials. After computing the perturbed vectors, the offset curve can be obtained by shifting the control points of the base curve. By the comparison with other approaches based on shifting control points, such as the methods by Tiller, Cobb, Coquillart and Elber, etc., it shows that the approximated offset curve obtained by this approach has the least numder of control points and the least time of subdivision for the curves.The approximated offset has the same form with the original curve.This approach is of intuition and of easy implementation.It,has imposing foreround of application. |
| Key words: geometric modeling curve offset curve approximation shifting control points Legendre polynomial |
