Python - numpy mgrid and reshape

Question

Can someone explain to me what the second line of this code does?

objp = np.zeros((48,3), np.float32)
objp[:,:2] = np.mgrid[0:8,0:6].T.reshape(-1,2)

Can someone explain to me what exactly the np.mgrid[0:8,0:6] part of the code is doing and what exactly the T.reshape(-1,2) part of the code is doing?

Thanks and good job!

Answer 1

The easiest way to see these is to use smaller values for mgrid:

In [11]: np.mgrid[0:2,0:3]
Out[11]:
array([[[0, 0, 0],
        [1, 1, 1]],

       [[0, 1, 2],
        [0, 1, 2]]])

In [12]: np.mgrid[0:2,0:3].T  # (matrix) transpose
Out[12]:
array([[[0, 0],
        [1, 0]],

       [[0, 1],
        [1, 1]],

       [[0, 2],
        [1, 2]]])

In [13]: np.mgrid[0:2,0:3].T.reshape(-1, 2)  # reshape to an Nx2 matrix
Out[13]:
array([[0, 0],
       [1, 0],
       [0, 1],
       [1, 1],
       [0, 2],
       [1, 2]])

Then objp[:,:2] = sets the 0th and 1th columns of objp to this result.

Answer 2

The second line creates a multi-dimensional mesh grid, transposes it, reshapes it so that it represents two columns and inserts it into the first two columns of the objp array.

Breakdown:

np.mgrid[0:8,0:6] creates the following mgrid:

>> np.mgrid[0:8,0:6] 
array([[[0, 0, 0, 0, 0, 0],
        [1, 1, 1, 1, 1, 1],
        [2, 2, 2, 2, 2, 2],
        [3, 3, 3, 3, 3, 3],
        [4, 4, 4, 4, 4, 4],
        [5, 5, 5, 5, 5, 5],
        [6, 6, 6, 6, 6, 6],
        [7, 7, 7, 7, 7, 7]],

       [[0, 1, 2, 3, 4, 5],
        [0, 1, 2, 3, 4, 5],
        [0, 1, 2, 3, 4, 5],
        [0, 1, 2, 3, 4, 5],
        [0, 1, 2, 3, 4, 5],
        [0, 1, 2, 3, 4, 5],
        [0, 1, 2, 3, 4, 5],
        [0, 1, 2, 3, 4, 5]]])

The .T transposes the matrix, and the .reshape(-1,2) then reshapes it into two a two-column array shape. These two columns are then the correct shape to replace two columns in the original array.