High Quality Content by WIKIPEDIA articles! For objects lying in a plane (2-dimensional space), the separating axis theorem states that, given two convex shapes, there exists a line onto which their projections will be separate if and only if they are not intersecting. A line for which the objects have disjoint projections is called a separating axis. An equivalent way of stating the theorem is to say that two convex shapes in the plane are not intersecting if and only if a line can be placed with one shape to one side of the line and the other shape to the other side. Such a separating line will be perpendicular to a separating axis.