近似可展曲面的构造及应用  

CONSTRUCTION AND APPLICATION OF APPROXIMATE DEVELOPABLE SURFACES

作　　者：李亮[1] 邓建松[1] 

机构地区：[1]中国科学技术大学数学系,合肥230026

出　　处：《高等学校计算数学学报》2006年第4期374-384,共11页Numerical Mathematics A Journal of Chinese Universities

基　　金："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

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.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.

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 

分 类 号：O186.1[理学—数学]