ewh. There is no need for apology. I very much enjoy this kind of discussions and benefit from it in educating my self. I think we need at least four points. 3 points to define a circle and 1 point to hold the part axialy. I think if we have 4 special points we can seat a cylinder on it so that it touches all four point and stays in space (fully constrained). A special case can explain this a little better. Suppose we have three points in a plane (every three point make a plane) called point A, B, and C. Now if we connect A to B and B to C and draw a line perpendicular to AB that passes through the middle of AB and another line perpendicular to BC that passes through the center of BC, the intersection of these two latter line will be the center of a circle that passes through A, B and C. So holds a plane of cylinder Now another point not on this same plane but on the surface of the cylinder can hold and constrain the cylinder. Stated differently, 3 points not only define a plane but can be used to define a circle in that plane. No another point out side that plane is needed to stablish the axis (from that point perpendicular to the plane). The problem is that only in this special case, where 4 points is enough, we are using the concept of a line perpendicular to a plane. If we add another point so that points 4 and 5 define an axis then our probem is solved. So 5 points are needed. But then how we define those 5 points on a cylindrical surface.
One answer might be we define three point on the surface to define the circle. Now that we have the circle, it's center is established, the two other point, again on the surface of the cylinder. define the direction. But then this define an axis and a plane all we need is another point for clocking to have a cylindrical datum frame! So do we need six points
I think I am confused a little and I have to go. I hope we can continue this discussion later.