when rendering the world why is common to render to a flat world texture instead of rendering to the surface of a sphere and then transforming it into a flat texture?
When rendering to the surface of a sphere you can increase the field of view more than pi/2
I just tried it and discovered that It will need lots of vertices to make it look good, it will need a vertex per pixel to make it look perfect.
That is actually called sphere mapping, which was commonly used in environment mapping in the old days. The reason not to do this is that you don't get an even distribution across the entire texture. In fact, if you use a full spherical project then you get a singularity at the point opposite of the projection (where the view wraps around the virtual sphere).
You can check out the environment mapping section of the D3D10 book linked in my signature for a comparison of sphere mapping, paraboloid mapping, and cube mapping if you are interested in learning more about it.
