Numpy matrix combination

Question

I have a rotation matrix and translation vector as corresponding numpy objects. What is the best way to combine them into a 4x4 transform matrix? Are there any functions which allow to avoid dummy element-wise copying?

Answer 1

There are many ways to do this; here are two.

You can create an empty 4x4 array. Then the rotation matrix and the translation vector can each be copied into the 4x4 transform matrix with slice assignment. For example, R and t are the rotation matrix and translation vector, respectively.

In [23]: R
Out[23]: 
array([[ 0.51456517, -0.25333656,  0.81917231],
       [ 0.16196059,  0.96687621,  0.19727939],
       [-0.8420163 ,  0.03116053,  0.53855136]])

In [24]: t
Out[24]: array([ 1. ,  2. ,  0.5])

Create an empty 4x4 array M, and fill it with R and t.

In [25]: M = np.empty((4, 4))

In [26]: M[:3, :3] = R

In [27]: M[:3, 3] = t

In [28]: M[3, :] = [0, 0, 0, 1]

In [29]: M
Out[29]: 
array([[ 0.51456517, -0.25333656,  0.81917231,  1.        ],
       [ 0.16196059,  0.96687621,  0.19727939,  2.        ],
       [-0.8420163 ,  0.03116053,  0.53855136,  0.5       ],
       [ 0.        ,  0.        ,  0.        ,  1.        ]])

Or you can assemble the transform matrix with functions such as numpy.hstack and numpy.vstack:

In [30]: M = np.vstack((np.hstack((R, t[:, None])), [0, 0, 0 ,1]))

In [31]: M
Out[31]: 
array([[ 0.51456517, -0.25333656,  0.81917231,  1.        ],
       [ 0.16196059,  0.96687621,  0.19727939,  2.        ],
       [-0.8420163 ,  0.03116053,  0.53855136,  0.5       ],
       [ 0.        ,  0.        ,  0.        ,  1.        ]])

Note that t[:, None] (which could also be spelled t[:, np.newaxis] or t.reshape(-1, 1)) creates a 2-d view of t with shape (3, 1). This makes the shape compatible with M in the call to np.hstack.

In [55]: t[:, None]
Out[55]: 
array([[ 1. ],
       [ 2. ],
       [ 0.5]])