The thing you describe as "per-pixel optimizations" is exactly what a fragment shader is? You don't need "a polygon" per say, you can just run said code over ever pixel in the frame for each frame. This is how simple screenspace effects are implemented, compositing, HDR, etc.
Interesting. While I've played with ShaderToy a bit, I've not gotten such a thing to run locally. Maybe I should revisit this..
I guess all that I'd need would be in-memory buffer of my field, then a single function to copy the buffer (or section of the buffer if I want larger than screen fields) to the video buffer.
