Changing XYZ order when converting Euler-angles to quaternions

Question

I'm using the following code to produce a quaternion from XYZ Euler-Angles in radians:

c1 = Math.cos( x / 2 )
c2 = Math.cos( y / 2 )
c3 = Math.cos( z / 2 )

s1 = Math.sin( x / 2 )
s2 = Math.sin( y / 2 )
s3 = Math.sin( z / 2 )

quaternion = [
              c1 * c2 * c3 - s1 * s2 * s3,
              s1 * c2 * c3 + c1 * s2 * s3,
              c1 * s2 * c3 - s1 * c2 * s3,
              c1 * c2 * s3 + s1 * s2 * c3,
             ]

from: http://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToQuaternion/index.htm

This produces a quaternion that first rotates around the z, then y, then finally the x-axis - Z-Y-X. Is it possible to alter this formula so that it rotates around the axes in a different order? What I'm looking for is the opposite, so X-Y-Z.

You can create 3 quaternions for rotations around single axis, and compose them by multiplication any way you need. — minorlogic
– minorlogic, Commented Apr 25, 2018 at 6:42
Yeah that's definitely the most versatile way and is how i'm working atm. Just looking for a more preferment method. — treeseal7
– treeseal7, Commented Apr 25, 2018 at 11:39

treeseal7 · Accepted Answer · 2018-04-25 11:44:45Z

4

If anyone's interested...

Yes you can, turns out on this occasion I just needed to swap the plus and minus signs around to get an X-Y-Z order (traditionally written ZYX). Like so...

       [
        c1 * c2 * c3 + s1 * s2 * s3,
        s1 * c2 * c3 - c1 * s2 * s3,
        c1 * s2 * c3 + s1 * c2 * s3,
        c1 * c2 * s3 - s1 * s2 * c3
        ]

Three.js has a full list of the different formulas for various xyz orders - in the function THREE.Quaternion.setFromEuler

https://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToQuaternion/steps/index.htm

edited Apr 25, 2018 at 11:44

answered Apr 24, 2018 at 23:35

treeseal7

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