Well, okay, yeah a game which used orthographic projection would be very odd indeed. I suppose my post is exactly about the differences between orthographic and perspective projection when considering points at infinity. Perspective permits points at infinity being presented, which could be vanishing points (such processes seem to neglect a nice curvature in the lens for ease of drawing).

The way your flat monitor distorts your round game camera lens, your round eyes distort straight lines. That's why road lines converge in the horizon.

The thing that's weird about orthographic projection is in how it deals with points at infinity, mathematically speaking. If you're standing inside of a finite sphere, then everything makes sense: your Tait Bryan coordinates for your flat lens are in 1-1 correspondance with points on the sphere.

If you try to take the limit of this sphere as the radius goes to infinity, **** gets weird really ****ing fast. The property above I mentioned is one. You'd think your vision could converge toward any point at infinity on the infinity sphere by tracing a radius out. But unless your eye is at the exact center, the angle you need to look directly at that pointliterally doesn't exist. So while every Tait Bryan angle you can look at has stuff in it, there is a huge amount of that infinity sphere you just plain cannot see using real-valued angles.

What's weirder? Move a step in any direction, apply the same argument above. You can't see any point you could in the previous spot. If you tried to trace that line with your eyes, you'd converge back to the line you're at parallel to the previous line, which looks in a different spot. Basically, while you can indeed see points in every direction, what you see is precisely none of it (in the measure 0 sense).

Thismightbe a way of cutting up S^2 into nonmeasurable sets. Nor am I sure such an object can exist or be well-defined, it may violate some other property I haven't considered. Assuming you can have a sphere with infinite radius, whatever properties it may have are seriously weird.