Convert Quaternion representing rotation from one coordinate system to another

system quaternions coordinate
Craig Delancy picture Craig Delancy · Sep 16, 2013 · Viewed 10.4k times · Source

I am getting a quaternion from sensor data that is in the coordinate system Y=up, X=right, and Z= backwards.Mine is X=forward, Y=right, Z=up.

So OX=Y, OY=Z and OZ=-X.

I have a function that can convert quaternions into 4by4 matrices, but no idea where to go from here. Any help would be greatly appreciated.

Answer

mkimball picture mkimball · Sep 16, 2013

Quaternions in the form of [X, Y, Z, W] are equivalent to axis-angle rotations where W is dependent only on the angle of rotation (but not the axis) and X, Y, Z are the axis of rotation multiplied by sin(Angle/2). Since X, Y, Z have this property, you can just swap and negate them as you would to convert a 3D coordinate between. To convert from your sensor's coordinate system to yours, you can simply do this:

MyQuat.X = -SensorQuat.Z
MyQuat.Y = SensorQuat.X
MyQuat.Z = SensorQuat.Y
MyQuat.W = SensorQuat.W

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