I have a bunch of points in a 3D coordinate system that approximates a circle. I'm able to find the best-fitting plane of the points, and then find a 2D coordinate system in that plane, using the answer for this question: 2D Coordinates of Projection of 3D Vector onto 2D Plane
When I have the new 2D coordinate system e'1, e'2 (can also be described in 3D by just adding the normalvector of the plane as a Z-axis), I'm able to find the best-fitting-circle to the points. This gives me a correct radius, and a circle center point. Now I would like to plot this circle in the original 3D coordinate system. How can I translate the circle center point that is now described in e'1, e'2-coordinates, back to x, y, z-coordinates?
I've tried with rotation matrixes but no luck