Distance from each unit-norm direction vector to its x-axis neighbor.
dx = [
np.sqrt(np.sum((v[:-1, :, :] - v[1:, :, :])**2, -1)) for v in directions
]
dx = [np.concatenate([v, v[-2:-1, :]], 0) for v in dx]
# Cut the distance in half, and then round it out so that it's
# halfway between inscribed by / circumscribed about the pixel.
radii = [v[..., None] * 2 / np.sqrt(12) for v in dx]`
`