常见两曲面立体相贯线的讨论Discussion on the intersecting line of two surfaces

一、相贯的特殊情况 Special case of intersecting

    特殊情况下，相贯线可能是直线、圆或其它平面曲线：两柱轴线平行或两锥共顶时，相贯线为直线；两回转面共轴线时相贯线是垂直于轴线的圆，此圆在与轴线平行的投影面上的投影是直线。

     In special cases, the intersecting line may be a straight line, circle or other plane curve: when the axes of two columns are parallel or the two cones share the top, the intersecting line is a straight line;When two rotating surfaces are coaxial, the intersecting line is a circle perpendicular to the axis, and the projection of this circle on the projection plane parallel to the axis is a straight line.

     特殊情况下，相贯线可能是直线、圆或其它平面曲线：当两个二次回转面轴线相交且外切于同一球时，相贯线为两条平面曲线(多为椭圆)，这两条平面曲线都通过两个重切点（公切球与两回转面切线的交点，图中的点K），而且在与两轴线平行的投影面上的投影为直线。

       Curve under special circumstances, may be a straight line, round, or other plane curve: when two quadratic surface of revolution axis intersection and cut in the same ball, interfingering lines for two plane curve (mostly elliptic), the two plane curve with two heavy tangent point (and cut the ball with two rotary surface tangent intersection point, the point in the graph K), but with two parallel to the axis of the projection plane is a straight line.

二、相贯线的变化趋势The changing trend of intersecting line

     1.当相交两立体的形状、位置不变，而大小变化时，相贯线会发生变化。当直立圆柱直径小于水平圆柱时，前者全部贯穿后者，相贯线为上下两条；当两圆柱直径相等时，相贯线为两个椭圆；当直立圆柱直径大于水平圆柱时，后者全部贯穿前者，相贯线为左右两条。

     When the shape and position of the intersecting two solids remain unchanged, but the size changes, the intersecting line will change. When the diameter of vertical cylinder is smaller than that of horizontal cylinder, the former runs through the latter, and the intersecting line is up and down. When the diameters of two cylinders are equal, the intersecting lines are two ellipses. When the diameter of the vertical cylinder is larger than that of the horizontal cylinder, the latter runs through the former and the intersecting lines are left and right.

    2.若两立体形状、大小不变，而相对位置改变时，相贯线同样发生变化。

     If the shape and size of two solids remain the same, but the relative position changes, the intersecting line also changes.