How to calculate all 24 rotations of 3d array?

Question

I have a 3d numpy array describing a polycube (imagine a 3d tetris piece). How can I calculate all 24 rotations?

Numpy\'s array manipulation routines includes a rot90 me

Answer 1

I encountered a similar problem when trying to randomly rotate a 3D one hot encoded numpy array, just before feeding into my neural network. I will demonstrate here for a 3D array, but this also works with a 4th dimension (when using OHE).

>>> m = np.reshape(np.arange(8),(2,2,2))
>>> m
array([[[0, 1],
        [2, 3]],

       [[4, 5],
        [6, 7]]])

Next we rotate the array 3 times, each time in a different direction. Repeat 24,000 times to see distribution (expecting 1000 counts for each unique rotation):

>>> rot_list = []
>>> for _ in range(24000):
        a = np.rot90(m,np.random.randint(0,4),axes=(0,np.random.randint(1,3)))
        b = np.rot90(a,np.random.randint(0,4),axes=(np.random.randint(1,3),0))
        c = np.rot90(b,np.random.randint(0,4),axes=(1,2)) # or axes=(2,1)
        rot_list.append(c)
>>> unique_rotation_matrices, counts = np.unique(np.asarray(rot_list),axis=0, return_counts=True)
>>> len(unique_rotation_matrices)
24

So we see we get all the 24 possible rotations. Let's look at their distribution:

>>> counts
[1062  946  917  982 1096  978 1153  936  939  907 1183  932  958  932 1122
  926 1115  954  933  932 1135  924 1138  900]

Distribution looks quite even, but rerunning this a number of times reveals it is slightly biased.