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Consider a cone with height H and radius of base circle R. Take a point on the circular edge of the cone and make that the center of another circle of radius r whose normal points at the apex of the cylinder. Rotate this circle around the axis of the cone to create a surface. Given an angle theta for the circle of radius R, and an angle phi for the circle of radius r, you get a point on the surface. I believe a point on the surface can correspond to multiple theta/phi solutions (not sure though).

I'd like to learn more about this type of surface. In particular, among other things, I'd like to be able to:

- Find the closest point on the surface to a given point P, and find the solution(s) of theta/phi that correspond to this point.

- Find the point(s) on the surface a given distance from a point P, and find the solutions(s) of theta/phi that correspond to this point.

I'm trying to attach a prismatic joint to the smaller circle connected to a fixed point P, and find a path that causes the largest change of theta + phi as the joint is extended.

Would appreciate pointers - thanks in advance!

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# Help with a special kind of Torus

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