title: Solve for Rotation Angle About Arbitrary Axis
body: <p>I'm working on an embedded system which has been tasked with an interesting problem. It knows the initial location of three points on a sphere. After the sphere rotates, it knows the distance by which these points have changed. This should be solvable to two solutions, and I have a method formed to eliminate one of them. From this I've been tasked with solving the current orientation of the sphere.</p>
  
  <p>I've done enough analysis to know that it is theoretically possible to solve this out, but I don't know if there's an established method to do this analytically. </p>