Alhazen Billiard problem in 3d

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I'm sure that everyone knows what the Alhazen's Billiard problem which is basically determining the point on the edge of a circular billiard table at which a cue ball at a given point must be aimed in order to canon off the edge of the table and hit another ball at a second given point. For my school project I wanted to extend this into a 3d context where the billiard table is spherical and the cue ball and the other ball is within the spherical space, and I am stuck on determining the point on the edge that the cue ball should hit. Does anyone have an idea of what to do?