Turned out deriving a formula for calculating normals from each of my tetrahedral interpolation formulae was easy. The calculation is a quite a bit simpler than for trilinear interpolation. So here's a screenshot, showing how the world is now entirely made up of flat surfaces. It's not that much faster, so either I need to work on it a bit or it wasn't really worth it. But I should at least look at the milliseconds (not framerate) before I decide.