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5.56.1  Recognize an isometry: isom

isom takes as argument the matrix of a linear function in dimension 2 or 3.
isom returns:

Input:

isom([[0,0,1],[0,1,0],[1,0,0]])

Output:

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

which means that this isometry is a 3-d symmetry with respect to the plane xz = 0.
Input:

isom(sqrt(2)/2*[[1,-1],[1,1]])

Output:

[pi/4,1]

Hence, this isometry is a 2-d rotation of angle π/4.
Input:

isom([[0,0,1],[0,1,0],[0,0,1]])

Output:

[0]

therefore this transformation is not an isometry.


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