The model shows the penetration of two right circular cylinders. One of the cylinders can be pulled out. Therefore the curve of intersection can be seen clearly. In this model both cylinders have a common tangential plane; the curve of intersection has one double point.

Circular cylinders are surfaces of the second order. If two surfaces of the second order intersect, generally an intersection curve of the fourth order is generated. This can have a maximum of one double point. If two double points occur, the curve collapses into two (flat) curves of the second order. This phenomenon can be observed at cross vaults. There the involved circular cylinders have the same diameter, the axes intersects each other and the segment curves are ellipses.