Don't always want to average over the whole area. Sometimes rectangles or parallograms. Triangles should be close to equilateral. With quads, the artifacts look like the imperfections you have in walls and floors anyway. Once we have a big planar shape, we need to mesh it.
Simple way is to just triangulate it with long skinny tris.
Good thing for rectangular stuff is to turn it into quads. Then triangularize the quads in some smart way, maybe. If a block is sitting on the floor, remove the block's shape from the floor object since you're gonna have a discontinuity there. Preprocess to find these discontinuity events. Just chop it up.