| 近似可展曲面的构造及应用 |
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| 引用本文： | 李亮,邓建松. 近似可展曲面的构造及应用[J]. 高等学校计算数学学报, 2006, 28(4): 374-384 |
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| 作者姓名： | 李亮 邓建松 |
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| 作者单位： | 中国科学技术大学数学系,合肥,230026 |
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| 基金项目： | “973”项目(2004CB318000)，国家杰出青年基金(60225002)，国家自然科学基金(10201030与60473132)，教育部高校青年教师奖励计划，教育部留学回国人员科研启动基金的资助 |
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| 摘 要： | 1引言经典微分几何中Gauss曲率为零的曲面称为可展曲面,它是一种特殊的直纹面．可展曲面有且只有三种,即锥面、柱面和切线面,它对于自由曲面造型具有重要的意义．例如,如果物体外壳是可展曲面,那么它可以没有形变地展开到平面上,从而可以用平板材料无形变地设计出来．这一性质对于造船业、航空业中的外形设计具有重要的意义．关于可展曲面的微分几何性质,可以在任何一本微分几何教材中找到,例如[3]．可展曲面可以说是微分几何中比较简单的一类曲面,但是在计算机辅助几何设计(CAGD)和计算机图形学中至今还不存在简单有效的设计方法．在[1,2,5]以及它们的参考文献中
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| 关 键 词： | 可展曲面 Gauss曲率 应用 构造 自由曲面造型 外形设计 微分几何 直纹面 |
| 收稿时间： | 2004-11-28 |
| 修稿时间： | 2004-11-28 |
CONSTRUCTION AND APPLICATION OF APPROXIMATE DEVELOPABLE SURFACES |
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| Li Liang,Deng Jiansong. CONSTRUCTION AND APPLICATION OF APPROXIMATE DEVELOPABLE SURFACES[J]. Numerical Mathematics A Journal of Chinese Universities, 2006, 28(4): 374-384 |
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| Authors: | Li Liang Deng Jiansong |
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| Affiliation: | Dept. of Math., University of Science and Technology of China, Hefei 230026 |
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| Abstract: | Developable surfaces have wide applications in free form surface modeling. In the three dimensional space, there is not always a regular developable surface that interpolates a given boundary which is an arbitrary piecewise closed curve. In this paper, we discuss how to construct an approximate developable surfaces interpolating a closed curve. We construct a surface, in tensor-product polynomial surface space, which minimizes the Gaussian curvature of the surface in some sense, where the nonlinear optimization problem is solved by trust region algorithm and quasi Newton method in optimization theory. The result is applied, as an application, into texture mapping in computer graphics, and a method is proposed to decrease the distortion. |
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| Keywords: | tensor-product polynomial surfaces developable surfaces texture mapping nonlinear optimization. |
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