一种直纹渐变曲面展开的通用算法

根据微分几何的定理，对直纹渐变曲面的形成进行了分析，为了实现直纹渐变曲面的自动展开，又对曲面上的扭曲四边形的组成元素进行分析，利用曲线的参数方程，给出了计算扭曲四边形的展开元素长度的具体方法。为了实现直纹渐变曲面自动展开的算法，采用局部坐标系平移和旋转的方法，可方便地进行展开元素长度及求交点的计算，这一算法适合于一切用解析式表示的曲线形成的直纹渐变曲面的自动展开。最后，通过两个直纹渐变曲面自动展开的实例，说明自动展开通用算法的过程，并给出了相应的展开图。

A universal algorithm for development of straight grained transition curved surfaces

The formation of straight grained transition curved surfaces is analyzed based on the theorem of differential geometry. For realization of the automatic development of the straight grained transition curved surface, an analysis is made of the components of distorted quadrangles on the curve surface, and a specific method is given to calculate the length of developed components of the quadrangles by use of the curve parameter equation. An algorithm for automatic development of straight grained transition curved surface is realized by adoption of the local coordinate translation and rotation, which make it easy to calculate the length of the developed components and derive the intersection points. The algorithm is suitable for the automatic development of the transition curved surface formed of curves expressed by arbitrary analytical functions. Finally, the process of the algorithm is demonstrated by two cases, and corresponding figures of curve surface development are also given.