用换面法求解直线与椭圆球面的交点

Seeking the Intersection of a Line and an Ellipsoidal Surface with the Projection Plane Transforming Method

求解直线与椭圆球面交点的方法一般采用辅助平面法求截交线 ,这条截交线的非积聚性投影往往为椭圆曲线 .这种方法求解繁琐 ,而且精度低 .采用换面法求解直线与椭圆球面的交点 ,关键在于确定被改换投影面的位置 ,使截交线在投影面上的投影为圆 .此法使作图大大简化 ,而且精度极大提高 .

To seek the intresection of a line and an ellipsoidal surface, an ordinary way is to use the auxiliary plane method to seek out the intersectional trajectory whose unconvergency projection is usually an ellipse curve. This method is very complex and the accuracy is very poor. A new method——“projection plane transforming method”, is the key to ascertain the position of the transformed projection plane which makes the projection of the intersectional trajectory be a circle. With this method the process of drawing graph is greatly simplified, and the accuracy is improved.