When viewing an ambiguous object from two different angles, the shape of the object appears to change. When you see an object, your eyes capture the 3D object as a 2D projection. It can be thought of like a camera taking a picture of a room and returning a 2D image. Our brains then extrapolate from the 2D visual stimuli to let us understand 3D space, that is, perceive depth. Ambiguous objects exploit this by projecting a different shape onto a plane from different angles. Simply, a projection of a 3D object is to move all points by a normal vector to the plane until all points of the object lie on the plane, like flattening the object. So, we want to find a 3D curve which when projected onto a plane at two different angles, the projections will be different.

Theoretically, the angles can be selected at will, but for the purposes of a 3D object which appears differently in its reflection, we want to use an angle of 45 degrees or Pi/4 radians. The reflection of the object shows the other side of the object at roughly 45 degrees as well. Viewing the object from a further distance will improve the effect of the illusion since the slight difference in angle becomes inconsequential to the viewer. A "view from infinity" refers to this, in which a slight difference in location on the object accounts for only a slight change in angle of view when the viewer is far away. It can be thought of like how shooting a bullet at a very small angle off center can result in the bullet hitting far off target. This choice of angle lets us take a point on the object, say