Camera Rotation (for mouse look) with LookAt does not work as expected (Local/Global)

Question

My code for rotating my 3D fps camera isn't working as expected.
I expect that the X-axis does rotate with the Y-axis, but it ain't so.

I made some pictures to explain it better, I think its doing global rotation instead of local rotation.
But I searched in the internet and used code for local rotation and it was still the same result.

Image

1. Normal Position
2. Rotated on Y-Axis
3. Rotated on X-Axis (how it is)
4. Rotated on X-Axis (how it should be)

And this is my rotating code: X-Axis

float sx = sinf(x);
float cx = cosf(x);

up.y = up.y*cx - up.z*sx;
up.z = up.y*sx + up.z*cx;

center.y = center.y*cx - center.z*sx;
center.z = center.y*sx + center.z*cx;

Y-Axis

Math::Vector3f f = Normalise(center - eye);

float sy = sinf(y);
float cy = cosf(y);

center.z = eye.z + f.z*cy - f.x*sy;
center.x = eye.x + f.z*sy + f.x*cy;

It doesn't matter with which order I rotate, still the same.

Answer 1

Hmm, when you update a point, e.g. your center, you destroy the information! Here's a snippet to illustrate my point:

 NewCenter.y = center.y * cx - center.z * sx;
 NewCenter.z = center.y * sx + center.z * cx;
 center = NewCenter;

The problem is that in your first snippet, the center.y component got "dirty" before it could be used in your center.z computation. It's simple matrix-vector multiplication.

UPDATE

If one wishes to devise a transformation chain in which the x axis moves together with the y axis, then this is achievable through the following set of transformations:

If the point to be transformed is (x,y,z), then it has to undergo a series of frame transformations: from F2 to F1 you have a rotation against the x by an angle alpha, then from F1 to F0 = world system, you have a rotation against the y axis by an angle beta. Chaining the transforms together, you should get the final position of your point in the world system.

You can see it as a double rotation joint system, the camera being attached to the x axis, which is in term attached to the y joint.