三维曲面的几何展开

GEOMETRIC APPROACH OF 3D SURFACE DEVELOPMENT

本文提出了一种三维曲面展开的新方法．三维曲面一般可分为平面、直纹面和复杂曲面，复杂曲面先分割为若干个条状区域，每一区域用一直纹面逼近，再将直纹面进行三角网格分割．本文的方法定义了两个精度：面积精度δａ和长度精度δｌ．δａ用来计算三角网格分割所需的最少三角平面数目．δｌ用来保证三维曲面边界弧长的逼近精度．本算法在ＣＡＴＩＡ软件环境下测试，表明达到了高精度．

A new method of developing 3D surfaces is presented in this paper.Complex surfaces are further classified into ruled surfaces and non-ruled-complexsurfaces. For the ruled surfaces, a plate pattern is obtained by triangulating the surfaces into planar triangles, and rotating them into a plane. The non-ruled-complex-surfaces are subdivided into several regions and each region is approximated with a ruled surface. The algorithm is based on two accuracy criteria: the area accuracy δa and the length accuracy δl.δa is used to calculate the minimal number of approximating facets, while δ, controls the maximal tolerance between the surface boundary and its flattened form. The given method is evaluated on the platform ofCATIA software and shows high accuracy of pattern development.