I am attempting to find the angle between a detector and a source. Currently, I have a great many hollow cones with their points in the detector (essentially the origin) and the actual source somewhere on their edge (i.e. the distance and angle is not known, but it is known that the angle is some number of degrees off of such and such a direction). I am attempting to find a way to determine the true angle to the source, which should be the line upon which all of the cones intersect (though there is also some error in each of them). I should have thousands of such cones, so getting enough data shouldn't be a problem.
My thinking is that the ideal way to do this would be to project a sphere onto a grid such that it preserves area, draw a circle on it corresponding to the cone (I suppose that it wouldn't appear as a circle when on the flat map), and then find the point on the flat map with the most lines, but I cannot figure out how to do this. Any suggestions on how to do this, or alternatives, are greatly appreciated.
This is for compton imaging, if you care.