三维空间中圆锥、圆柱和平面交线的绘制

The Intersections of Cylinder, Circular Cone with Arbitrary Plane in 3D Space

在三维空间中,要绘出任意圆锥、圆柱和任意平面的交线,一般先选取适当坐标系,得到交线的标准型方程,绘出后,再经过一组坐标变换,显示在当前屏幕上。本文通过分析圆柱、圆锥和平面的几何关系,推导出它们的交线的显式表示,从而给出在三维空间中直接绘制这类交线的方法。

In three-dimension space, the intersections of cylinder, circular cone with arbitrary plane are quadratic curves. The general method to draw the curves is that first the standard equations of the intersections are obtained, then display them on the screen through a series of transforms. In this paper, through analyzing the relations of cylinder, circular cone with arbitrary plane, the explicit expressions of the intersections are obtained, thus the intersection curves can be drawn simply in original 3D space without any transformations.