If the two points you select on the sphere are poles of eachother (ie, their distance through the sphere is equal to the sphere's diameter, then you need to hav

If the two points you select on the sphere are poles of eachother (ie, their distance through the sphere is equal to the sphere's diameter, then you need to have an infinite distance from the sphere. What you're looking for is a triangle between the two points and a third point forming your observer. The two points are visible at the same time if the derivative of the sphere's surface and the side of the triangle between a point form a positive angle (the derivative intersects the triangle at a point other than the points). So the question then becomes "if the two points are poles, what does that mean"; easy, if the two points are poles and they're only visible if the surface derivative is within the triangle, the angle between the observer, the point and the other point must be 90°. This must hold for both points as the solution is symmetric. However, there is no well defined triangle that has two angles of 90° inside. So the solution is "doesn't work" (or possibly infinite distance).