By: Peter (tomservo2007)  20070628 07:57

I copied and pasted the code on the page: https://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToAngle/index.htm to convert euler angles to axisangle. I edited the code to compile on my laptop However, once I started using it, I noticed it did not give the same answers as the java applet calculator for eulertoaxisangle. Specifically, there are minus signs on some of the axis coordinates and sometimes the angle is about twice what it should be. Is there a problem with that code that anybody else has found? 
Thanks
for letting me know about this, If there is a discrepancy between the
java applet calculator and the code on the eulertoaxisangle page, my
number one suspect would be the applet calculator. I think this is used
less than the code on the main page and therefore less well tested.
Since the applet calculator works in a different way it could be
faulty. I'll have a look at it. Martin 
martinbaker)  20070703 07:09
By: Martin Baker ( 
Peter, I found a bug in the applet which I think would have caused the discrepancy that you saw. I've uploaded a new version and tested it as much as I can but I would appreciate any feedback about whether this fixes the problem. Cheers, Martin 
nhughes)  20070703 20:45
By: nhughes ( 
Gentlemen, I fail to see why there is extended discussion on converting a set of Euler angles to an axis/angle representation. The conversion is trivial. The conversion process is as follows: 1) form three quaternions, one for each of the three Euler angles, being cognizant of the rotations and their order. For example, if the rotation sequence is 313, the three quaternions would be Q1 = 0 0 sin(ang1/2) cos(ang1/2) Q2 = sin(ang2/2) 0 0 cos(ang2/2) Q3 = 0 0 sin(ang3/2) cos(ang3/2) and so on for any of the twelve Euler rotation sequences. 2) perform the quaternion multiplication Qt = Q1 * Q2 * Q3 and normalize 3) the axis is the three vector elements, normalized (the first three elements, if you're using the scalar last convention, the second through fourth elements, if you're using the scalar first convention) 4) the angle is the inverse cosine of the scalar component (the component not used in step three). Quaternion mathematics is not difficult! In the next few months, I hope to complete a paper on my process for converting a quaternion to Euler angles for any rotation sequence (finding the time is the problem; I have a number of higher priority tasks ahead of this one). After I've published it, I will share it with you and any other interested parties. Noel Hughes 