Just a style/judgment thing.

I think this is

np.dot(v, [[[1, 0], [1, 1]], [[0, 0], [1, 1]]]

or alternatively, just don't bother with dot products at all

s = np.sin(phi)
c = np.cos(phi)
X = [[s, s+c], [0, c]]

(either fully vectorize the thing, or don't vectorize it at all.)

I've chosen this notation intentionally to illustrate the projection of the corners on v.

The upper does not produce the same result (I assume it's some axis ordering, but didn't investigate). The lower does work, but obscures what the calculation actually does.

Ah, I didn't see it as a projection; indeed, that makes things clearer.

Just passing the angle (in degrees or in radians, up to you) seems simpler (in particular to explain)?

It would be the angle only for square images. In general, it's a (nonlinear monotoneous) parametrization of the angle due to the distortion. I did not bother to untangle the transformation from extent; and I didn't want to raise false expectations.

If you want to make real angles work, you are welcome to provide a PR. OTOH, maybe one does not want real angles - probably depends on the application. 0.5 is now always a gradient along the diagonal of the image.

Good point, let's just leave it as it is.