关于旋转锥面与球面相交的研究(I)

用形数结合的方法对旋转锥面与球面相交进行研究．重点研究了交线的水平投影曲线，得出该曲线为著名的四次曲线——卵形线族的结论．通过对本曲线族的形状特征的详细研究得出如下结论：本曲线族中的每一条曲线都是由两支封闭的卵形成所组成，且其中的一支包围另一支；曲线的形状取决于方程式（ｘ２＋ｙ２－２ｒｘ＋ｐ）２－Ｌ２（ｘ２＋ｙ２）＝０中的参数ｐ、ｒ或Ｌ之值；当ｐ变化时，曲线形状由参数ｒ和Ｌ之值所确定；从而得出了本曲线的整个变化规律．交线的投影曲线方程直接为计算机快速绘制此类曲线提供了数学模型

THE STUDY ON THE INTERSECTION OF THE SPHERE CONE AND SPHERE (I)

The anthor have studied the intersection of sphere cone and sphere by the way of the combination of graph and digit,emphatically studied the horizontal projection curvc of the intcrsccting lincs,concludcd the curvc is the famous four-ordcr curvc egg-shaped curve family,Through the detailed study on the shape and character of the curve family,the anthor drawed the following conclusion:Every curve of the curve family is composed of two closing egg-shaped curvc and the one surrounds the another,the shape of the curve is determined by the value of the parameter p,r or L in the equation (x 2 y 2-2rx p) 2-L 2(x 2 y 2)=0. When p is changed,shapc of the curvc is determined by the valuc of paramcter r or L,then drawed the whole dhanging law of the curve family,the projection curve equation of the intersecting lines directly suply the mathimatical model for the computer drawing the curve family swiftly.