I have four cones. The angle of each cones is 140 degree. I need to project it onto a sphere(place it ) such that, the cones cover the maximum area with minimum overlap. I initially thought that placing each cone at 90 degree would be sufficient. But this does not look to be the case. I was thinking maybe a teatrahedron, but I still dont know how to do it in terms of equations. Also, the radius of the sphere is mportant. So I guess I need an answer in terms of r, so I can plot a graph of the radius vs the angle covered to identify the optimal point. But I do not know how to proceed. Could someone please give me some pointers?

I cannot look at it in terms of volume only. The volume of a cone depends only on radius, height. Where should I factor the angle in? THe question is where on the sphere should the center of these cones be placed?

  • $\begingroup$ Your description is very unclear. Cones are infinite in extent. What do you mean by "project it onto a sphere"? What sort of projection are we talking about? In what way does a cone "cover" an area? What sort of "equations" are you after? How is the radius important? Any concepts I can put together for this look exactly the same for any value of $r$. What does volume have to do with it? you were talking about area earlier, not volume. Just on general principles of symmetry, the tetrahedral arrangement is sure to be the answer. $\endgroup$ – Paul Sinclair Jan 22 '16 at 4:46
  • $\begingroup$ @PaulSinclair, what i am trying to say is that if I have some camera lenses with a fixed FOV, then at exactly what angle do I have to place tthem on a sphere to get maximum overlap as well as field of view. IS there any equation you can point me to? $\endgroup$ – red car Jan 22 '16 at 12:46

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