Extracting Yaw from a Quaternion

math xna quaternions
Venatu picture Venatu · Apr 25, 2011 · Viewed 45.3k times · Source

I have a rotation quaternion and want to extract the angle of rotation about the Up axis (the yaw). I am using XNA and as far as I can tell there is no inbuilt function for this. What is the best way to do this?

Thanks for any help, Venatu

Answer

JCooper picture JCooper · Apr 25, 2011

The quaternion representation of rotation is a variation on axis and angle. So if you rotate by r radians around axis x, y, z, then your quaternion q is:

q[0] = cos(r/2);
q[1] = sin(r/2)*x;
q[2] = sin(r/2)*y;
q[3] = sin(r/2)*z;

If you want to create a quaternion that only rotates around the y axis, you zero out the x and z axes and then re-normalize the quaternion:

q[1] = 0;
q[3] = 0;
double mag = sqrt(q[0]*q[0] + q[2]*q[2]);
q[0] /= mag;
q[2] /= mag;

If you want the resulting angle:

double ang = 2*acos(q[0]);

This assumes that the quaternion representation is stored: w,x,y,z. If both q[0] and q[2] are zero, or close to it, the resulting quaternion should just be {1,0,0,0}.

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