"Snap to angle" view

I am not sure of the right term, it makes my searches fruitless. I would like to make a shader that snap the viewing angle to certain increments, but I am not sure where to start.

The goal would be to have the camera see the model from only 4 angles, or 8, etc. Something that would be more akin to dynamic billboarding.

Yes, this is for yet another retro-fps. Right now the has 4 directions for most sprites, but not all, and sticking to raster sprites limits what I wanna do. I could have all the sprites redone, or just try to fake it, and faking it sounds more fun, but the POC I made is all in code, and I *know* it can be done in a shader, just not how. I would prefer to spend the art budget on low-resolution looking textures on a mobile model, rendered at angles.

 

"Doom sprite" is a common way to refer to it.