Indeed, - it's a question of storage. If you imagine mipmaps being precalculated convolutions of the original texture map, then there are infinitely many such c

Indeed, - it's a question of storage. If you imagine mipmaps being precalculated convolutions of the original texture map, then there are infinitely many such convolutions that may be appropriate for some 3D view of that textured surface. On a related note, there is a technique called summed area tables, which allows for the rapid evaluation of the total value of all pixels in any axis aligned rectangle, with only a few additions and subtractions. AFAIK this never really caught on though, because it required the storage of much larger numbers than GPU textures could historically support.