Taking the average (a + b / v2) and detail (a - b/ v2)
amounts to rotating the pair of samples 45deg, so I
'rotate' about concentric squares instead of actually
rotating by staying on the same circle. Equivalently,
it's the conjugate of a 45deg rotation by a purely
radial transformation that takes every circle to a square
centered at the origin. Some care had to be taken at
the edge cases, though.