Let's say I have a cube map that has a resolution of 256x256 for each face and I want to generate mip maps for it using a box filter.
It's tempting to just mip each face individually, cutting the resolution of each face in half for each mip, by averaging each 2x2 group of pixels.
Doing this, information never crosses the boundary of a cube map face though, which feels like it might be incorrect.
What is the correct way to generate mips for a cube map?