dot product of two quaternion rotations

Question

I understand that the dot (or inner) product of two quaternions is the angle between the rotations (including the axis-rotation). This makes the dot product equal to the angle between two points on the quaternion hypersphere.
I can not, however, find how to actually compute the dot product.

Any help would be appreciated!

current code:

public static float dot(Quaternion left, Quaternion right){
    float angle;

    //compute

    return angle;
}

Defined are Quaternion.w, Quaternion.x, Quaternion.y, and Quaternion.z.

Note: It can be assumed that the quaternions are normalised.

Answer 1

The dot product for quaternions is simply the standard Euclidean dot product in 4D:

dot = left.x * right.x + left.y * right.y + left.z * right.z + left.w * right.w

Then the angle your are looking for is the arccos of the dot product (note that the dot product is not the angle): acos(dot).

However, if you are looking for the relative rotation between two quaternions, say from q1 to q2, you should compute the relative quaternion q = q1^-1 * q2 and then find the rotation associated withq.