Question

How can I modify/rotate an axis angle from world coords to object coords?

See below:

void RotateMatrix4(float *m, float angle, float *axis);
//This function rotates a matrix in object space

void RotateLocal(float angle, float *axis) {
    RotateMatrix4(m, angle, axis)
}

void RotateGlobal(float angle, float *axis) {
    //Do something to axis here
    RotateMatrix4(m, angle, axis)
}

Answer 1

You found the answer yourself – that is simply a multiplication between a tranformation matrix and a vector – you are simply transforming the axis vector into object coords.

Look at Transformation Matrix for more information on Transformation matrices.

(I would comment on your answer – but my rank is not yet high enough…)