1. The line AB is the axis of the cylinder. Then AB is perpendicular to the plane which contains the base circle of the cylinder. The equation of this plane is:
where is the staionary vector of the point A and (x, y, z) are the coordinates of any point in the plane.
2. The point C is placed on the circle line around A with radius d in the above mentioned plane.
3. The point D has the staionary vector
4. What you need is the equation of a circle in 3-D in relation to the "tilt" of AB.