Calculate axis of rotation

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If you have a single relative transform then copy-paste this rotation_from_matrix function to the Python console, and then to get rotation axis from a transform node you can run this:

transformNode = getNode('Transform')  # replace 'Transform' with the actual name of your transform node
import numpy as np
import math
transformMatrix = arrayFromTransformMatrix(transformNode)
angle, axisDirection, axisPosition = rotation_from_matrix(transformMatrix)

# Display rotation axis
rotationAxisMarkupsNode = slicer.mrmlScene.AddNewNodeByClass("vtkMRMLMarkupsLineNode", "RotationAxis")
rotationAxisMarkupsNode.AddControlPoint(vtk.vtkVector3d(axisPosition[:3]-50*axisDirection))
rotationAxisMarkupsNode.AddControlPoint(vtk.vtkVector3d(axisPosition[:3]+50*axisDirection))

Getting rotation axis from a single relative transform is probably not very robust or accurate. It would be better to compute an “average” axis from multiple transforms, similarly how Pivot calibration module in SlicerIGT extension does it (see a recent discussion about the algorithm that the module uses here).

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