In the projection of a sphere, each point on the disc except the circumference represents two points. One is a point on the upper hemisphere and the other is a point on the lower hemisphere. Likewise, each point in the glome except the surface represents two points. One is a point in the negative hemiglome and the other is a point in the positive hemiglome.
The two hemiglomes are separate spaces though they are represented by one globe in a three-dimensional space. This is the same as if the disc in the projection of a sphere represents two hemispheres.
Going straight on a sphere is transformed to following an ellipse on a plane in the projection of a sphere. And the movement from one hemisphere to another is represented by the contact between the ellipse and the circumference of the disc. |