Read specific values from quaternion

Question

I want to read the following values from a Unity Quaternion https://docs.unity3d.com/ScriptReference/Quaternion.html

If x rotation (pitch) is 180 (alternatively 0)

If y rotation (roll) is 180 (alternatively 0)

What is the most performant formula to get the z rotation (yaw)?

I found this formula online to get z axis, is this the most performant? z = qz / sqrt(1-qw*qw) http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/

Answer 1

The formula I posted was a conversion from quaternion to angle and axis. What I needed was quaternion to euler angles. I realized I didn't need x and y angles anyway.

Found some code online and shaped it to suit my needs, this converts only the z angle to radians (1.3 ms 10K iterations)

public double GetZAngle(Quaternion q1)
{
    double sqw = q1.w * (double)q1.w;
    double sqx = q1.x * (double)q1.x;
    double sqy = q1.y * (double)q1.y;
    double sqz = q1.z * (double)q1.z;
    double unit = sqx + sqy + sqz + sqw; // If normalized is one, otherwise is correction factor
    double test = (double)q1.x * q1.y + (double)q1.z * q1.w;
    if (test > 0.499 * unit) // Singularity at north pole
        return Math.PI / 2;
    if (test < -0.499 * unit) // Singularity at south pole
        return -Math.PI / 2;
    return Math.Asin(2 * test / unit);
}

There is no clear pattern to just distinguish if the x and y angles were 0, but there is a code snippet here shows how to retrieve all of them in radians (2.14 ms 10K iterations (faster than Unity's 3 ms)) http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/