def _norm_grid(A: Affine, tol=1e-8) -> Union[F4, F6]:
"""Compute normalised grid.
Different grids related via whole pixel translation will have the same
normalised grid.
Scale and Translation only
--------------------------
Normalised grid is defined by:
sx, sy, tx, ty
Where sx, sy is resolution (CRS units per pixel)
and (tx, ty) is sub-pixel translation in (-0.5, 0.5)
Order is: subpix translate -> scale
General Case
------------
Normalised grid is defined by:
sx, sy, tx, ty, ca, w
Order is: subpix translate -> scale -> rotate+shear
WARNING: general case is not currently implemented
"""
R, W, S = decompose_rws(A)
(ca, _, tx, _, _, ty, *_) = R
(_, w, *_) = W
(sx, _, _, _, sy, *_) = S
is_st = abs(ca - 1) < tol and abs(w) < tol
if is_st:
# No rotation no shear -- commonest case
# sx, sy, tx, ty fully defines the grid
# Tw*S*Xp == S*Tp*Xp
#
# Here `p` is Pixel, `w` is World
# convert from: <Scale pixels to World, then translate>
# into : <Translate pixels then scale to World>
tx_p, ty_p = tx / sx, ty / sy
# Remove whole pixel translation to normalise grid
_, (tx_p, ty_p) = split_translation((tx_p, ty_p))
return (maybe_int(sx, tol), maybe_int(sy, tol), maybe_zero(tx_p, tol),
maybe_zero(ty_p, tol))
else:
raise NotImplementedError('TODO: rotated grids')
def run_test(a, scale, shear=0, translation=(0, 0), tol=1e-8):
A = mkA(a, scale=scale, shear=shear, translation=translation)
R, W, S = decompose_rws(A)
assert get_diff(A, R * W * S) < tol
assert get_diff(S, mkA(0, scale)) < tol
assert get_diff(R, mkA(a, translation=translation)) < tol