For a game I am thinking about making I would need to know how to project points from a differentiable bounded 3-manifold to a Euclidean plane (the computer screen). The manifold would be made from a 3-dimensional space with two balls cut out of it and a hypercylinder glued onto it at the holes created. The result, hopefully, would be similar to the game Portal. I only have a cursory knowledge of topology, so I do not know how to do such a projection or where to look to find out. An explanation of how or where to look for one would be a great help to me.