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I will have access to vertices and normals at discrete points on the surface, but it will be expected that the number of these points will be different from cone to cone, and the cone orientation and position may be arbitrary.

I know that once I find the vertex of the cone I can project all the points I have to anunit sphere about the vertex. The normal to the circle that is transcribed projected on the sphere will give me the axis of the cone. But I need a way to determine the location of the vertex (which I may not have a point for)

Anyone have any suggestions? Thanks!