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I believe you can do the following: To rotate a point <Quoted Image Removed> by an angle <Quoted Image Removed> about an axis aligned with a vector <Quoted Image Removed> but passing through point <Quoted Image Removed>, first subtract <Quoted Image Removed> from your point <Quoted Image Removed> to move the axis so that it passes through the origin, then do the quaternion <Quoted Image Removed> step with <Quoted Image Removed> as usual, and then finally add <Quoted Image Removed> back in again to move everything back where it should be.