Is 126 degrees right angle of view for horizontal axis? Then calculations show that sphere's size on screen differs twice depending on position on screen (distance to sphere is the same). My simple program confirms it. Maybe it is wrong way of projection?
images: straight view after moving camera
calculations: distance to screen 1, screen length 4, angle between extreme sphere's points = a sphere's size along x axis in first case: 2tg(a/2) in second case: 2-(2-tg(a)) / (1+2tg(a))
i tried to project points not on screen, but on sphere around viewer (using arctg)