Asymmetric Projection Matrix

Question

I have a little "2 1/2-D" Engine I'm working on that targets multiple platforms, but currently I am upgrading my DirectX 11 version.

One of the things that is really important for my engine to do is to be able to adjust the horizon point so that the perspective below the horizon moves into the distance at a different angle than the perspective above the horizon.

In a normal 3D environment this would be typically accomplished by tilting the camera up above the horizon, however, in my engine, which makes heavy use of 2D sprites, tilting the camera in the traditional sense would also tilt the sprites... something I don't want to do (It ruins the 16-bit-arcade-style of the effect)

I had this working at one point by manually doing the perspective divide in the CPU using a center-point that was off-center, but I'd like to do this with a special projection matrix if possible. Right now I'm using a stock matrix that uses FOV, Near-Plane, and Far-Plane arguments.

Any ideas? Is this even possible with a matrix? Isn't the perpective divide automatic in the DX11 pipeline? How do I control when or how the perspective divide is performed? Am I correct in assuming that the perspective divide cannot be accomplished with a matrix alone? It requires each vertex to be manually divided by Z, correct?

Answer 1

What you are looking for is an off center perspective projection matrix, instead of a fov and aspect ratio, you provide left/right/top/bottom has tan(angle). The result is more or less the same as with a symmetric projection matrix with the addition of two extra non zero values.

You are right also, the GPU is hard wired to perform the w divide, and it is not a good idea to do it in the vertex shader, it will mess with perspective correction for the texture coordinates and clipping ( either not a big deal with the sprite special case ).

You can find an example of such a matrix here : https://msdn.microsoft.com/en-us/library/windows/desktop/bb205353(v=vs.85).aspx