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copied!<p>I spent the other day trying to find the exact same thing for an animation editor; here is how I did it:</p> <ol> <li>Take the axis you want to find the rotation around, and find an orthogonal vector to it.</li> <li>Rotate this new vector using your quaternion.</li> <li>Project this rotated vector onto the plane the normal of which is your axis</li> <li><p>The acos of the dot product of this projected vector and the original orthogonal is your angle.</p> <pre><code>public static float FindQuaternionTwist(Quaternion q, Vector3 axis) { axis.Normalize(); // Get the plane the axis is a normal of Vector3 orthonormal1, orthonormal2; ExMath.FindOrthonormals(axis, out orthonormal1, out orthonormal2); Vector3 transformed = Vector3.Transform(orthonormal1, q); // Project transformed vector onto plane Vector3 flattened = transformed - (Vector3.Dot(transformed, axis) * axis); flattened.Normalize(); // Get angle between original vector and projected transform to get angle around normal float a = (float)Math.Acos((double)Vector3.Dot(orthonormal1, flattened)); return a; } </code></pre></li> </ol> <p>Here is the code to find the orthonormals however you can probably do much better if you only want the one for the above method:</p> <pre><code>private static Matrix OrthoX = Matrix.CreateRotationX(MathHelper.ToRadians(90)); private static Matrix OrthoY = Matrix.CreateRotationY(MathHelper.ToRadians(90)); public static void FindOrthonormals(Vector3 normal, out Vector3 orthonormal1, out Vector3 orthonormal2) { Vector3 w = Vector3.Transform(normal, OrthoX); float dot = Vector3.Dot(normal, w); if (Math.Abs(dot) > 0.6) { w = Vector3.Transform(normal, OrthoY); } w.Normalize(); orthonormal1 = Vector3.Cross(normal, w); orthonormal1.Normalize(); orthonormal2 = Vector3.Cross(normal, orthonormal1); orthonormal2.Normalize(); } </code></pre> <p>Though the above works you may find it doesn't behave as you'd expect. For example, if your quaternion rotates a vector 90 deg. around X and 90 deg. around Y you'll find if you decompose the rotation around Z it will be 90 deg. as well. If you imagine a vector making these rotations then this makes perfect sense but depending on your application it may not be desired behaviour. For my application - constraining skeleton joints - I ended up with a hybrid system. Matrices/Quats used throughout but when it came to the method to constrain the joints I used euler angles internally, decomposing the rotation quat to rotations around X, Y, Z each time. </p> <p>Good luck, Hope that helped.</p>

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