How to isolate the x and z components of a quaternion rotation?

Question

I can't comment other posts yet. ShawnFeatherly in this post wrote:

Here's a way to get the local rotation of just the y-axis. This function can be modified to get the x or z-axis.

/// <summary> isolate the y-Component of a rotation </summary>
private Quaternion yRotation(Quaternion q)
{
    float theta = Mathf.Atan2(q.y, q.w);

    // quaternion representing rotation about the y axis
    return new Quaternion(0, Mathf.Sin(theta), 0, Mathf.Cos(theta));
}

It works for me! But how can I change this to get xRotation and zRotation? My quaternion representation is (x, y, z, w). Thanks!

Answer 1

As far as I know you can do the same with the other components:

float theta_y = Mathf.Atan2(q.y, q.w);

Quaternion yRotation = Quaternion(0, Mathf.Sin(theta_y), 0, Mathf.Cos(theta_y));

float theta_x = Mathf.Atan2(q.x, q.w);

Quaternion xRotation = Quaternion(Mathf.Sin(theta_x), 0, 0, Mathf.Cos(theta_x));

float theta_z = Mathf.Atan2(q.z, q.w);

Quaternion zRotation = Quaternion(0, 0, Mathf.Sin(theta_z), Mathf.Cos(theta_z));