Blending between right circular cylinders with parabolic cyclides

There are right circular cylinders touching a parabolic cyclide along a curve, and all the cylinders have the same point of contact with the cyclide. So a pair of cylinders with a point of contact are blended by a parabolic cyclide. In this paper, a method for blending between a pair of right circular cylinders with a parabolic cyclide is presented. A blend with a parabolic cyclide is a kind of variable-radius rolling-ball blend. The contour lines of the blending surface are central conics.