椭球曲面的拟合

Fitting of Ellipsoidal Surface

为测定空间一任意放置的椭球形状设备的变形,可根据由全站仪采集到的设备表面离散点的坐标,来求得椭球体的空间位置和大小.讲述了通用二次曲面拟合的误差方程和法方程的组成,介绍了运用Jacobi变换方法来处理系数相关性问题和法方程的求解,还介绍了将通用系数形式转化为标准椭球方程的方法,从而求得观测坐标系与椭球主轴坐标系之间的关系,最后求得椭球在空间的位置、方向和大小,以及椭球体的形变值.

In order to get the distortion of ellipsoidal equipment in space, we can fit the ellipsoidal surface by using coordinates of points spreading around it. In this paper we describe how to form observation equations and normal equations when fitting general conicoid. Jacobi transformation is used to find correlations among coefficients and to solve normal equation. Then we introduce a method to transform general conicoid to formal ellipsoidal equation. The location, direction and size of ellipsoid are obtained. The distance between observed points and the fitted surface is just the distortion of the equipment.