Abstract: In general situations, there will be two spatial intersection curves generated when a cylinder
and a cone are intersected with each other. This paper analyzes the various cases of the intersection
curves and their special point locations when the axes of the cylinder and the cone are obliquely or
perpendicularly intersected. If the intersecting curves are separated as two branches on the left and right,
the distribution equation of the innermost points on the two intersection curves is obtained through
theoretical analysis. The paper also analyzes the exact geometric conditions for classifying the four
forms of the intersection curves and their corresponding cylinder radius distributions. The auxiliary
sphere radius corresponding to the inner most point is also obtained. Finally, a graphical method of
locating all the special points on the intersection curve is proposed in the paper.

Key words: descriptive geometry, intersection curve of a cylinder and a cone, oblique intersection;
analytical proof, graphical method