基于矩形网格追踪法的曲面主曲率等值线生成算法*

针对自由曲面在展开平面上的主曲率等值线生成问题，提出一种基于矩形网格追踪算法的等值线生成算法。利用面积坐标方法将曲面上的点及其极值曲率映射到优化展开平面上，在展开平面上采用遍历法得出等值点序列；利用矩形网格追踪法将等值点序列划分为连续无交叉的开等值线或连续封闭的闭等值线。最后以直纹面、锥形面和自由曲面为算例分别对算法进行计算验证，并与线性插值三角网格法进行对比。计算结果表明，基于矩形网格追踪的等值线生成算法具有计算速度快、精度高的特点。

Generating algorithm of principle curvature isolines of free surface based on rectangle mesh tracking

This paper proposed a generation algorithm for principle curvature isolines of free surface based on rectangle mesh tracking method. First, mapped points on the surface and the corresponding curvatures to optimal development plane. Then gained the point sequences of equivalent curvatures by traversing method on the development plane. Partitioned the point sequences to continuing no-cross open or closed isolines. Finally, tested and verified the algorithm with examples of ruled surface, cone-shaped face and free surface, and compared with triangulation linear interpolation method. The results show that the generation algorithm is more efficient and accurate.