5.12. Multidimensional arrays

In the previous section, we learned how to access one element of a one-dimensional array using indexing, and how to access multiple elements of a one-dimensional array using slicing and filtering. We will now generalize this to multidimensional arrays. Throughout this tutorial, we will use these two sample arrays:

Sample array #1: Trajectory of a marker during three samples

The position of a marker is expressed by three coordinates (x, y, z), usually followed by a constant value of 1. A trajectory is expressed as a series of positions. Therefore, we express the trajectory of a marker using:

• Axis 0: sample

• Axis 1: coordinate

import numpy as np

position = np.array(
    [
        [0.497, 0.973, 0.010, 1.0],
        [0.528, 0.973, 0.017, 1.0],
        [0.589, 0.970, 0.025, 1.0],
    ]
)

position

array([[0.497, 0.973, 0.01 , 1.   ],
       [0.528, 0.973, 0.017, 1.   ],
       [0.589, 0.97 , 0.025, 1.   ]])

Sample array #2: Series of segment orientation during two samples

The orientation of a segment is expressed as a 4x4 homogeneous matrix. Therefore, we can express a series of orientations using:

• Axis 0: sample

• Axis 1: line of the homogeneous transform matrix

• Axis 2: column of the homogeneous transform matrix

orientation = np.array(
    [
        [
            [1.0, 0.0, 0.0, 0.0],
            [0.0, 1.0, 0.0, 0.0],
            [0.0, 0.0, 1.0, 0.0],
            [0.0, 0.0, 0.0, 1.0],
        ],
        [
            [1.0, 0.000, 0.000, 0.0],
            [0.0, 0.999, -0.017, 0.0],
            [0.0, 0.017, 0.999, 0.0],
            [0.0, 0.000, 0.000, 1.0],
        ],
    ]
)

orientation

array([[[ 1.   ,  0.   ,  0.   ,  0.   ],
        [ 0.   ,  1.   ,  0.   ,  0.   ],
        [ 0.   ,  0.   ,  1.   ,  0.   ],
        [ 0.   ,  0.   ,  0.   ,  1.   ]],

       [[ 1.   ,  0.   ,  0.   ,  0.   ],
        [ 0.   ,  0.999, -0.017,  0.   ],
        [ 0.   ,  0.017,  0.999,  0.   ],
        [ 0.   ,  0.   ,  0.   ,  1.   ]]])