空间三次曲线的最佳双圆弧逼近和误差估计

Approximation of space cubic curve with optimal bi-arc spline and estimation of the error

三次曲线的双圆弧逼近在船体数学放样中占有十分重要的地位。利用局部的旋转坐标系 ,给出了过空间两点、两切线的三次曲线方程 ,采用相邻圆弧所在平面的夹角最小与相邻圆弧的曲率半径尽可能接近的方法得到最佳的双圆弧 ,并用法

The approximation of space cubic curve with bi-arc spline played an important role in mathematics ship-lofting. The rotation of local coordinate system was used. A space cubic curve equation was given tluough two points and two tangents. The minimum angle of intersection and the minimum radius deviation of curvature about consecutive circular arc were solved .An optimal bi\|arc spline was obtained. The error was estimated between space cubic curve and optimal bi\|arc spline using normal error function.