OpenGL make camera to rotate around object - c

Question

I am having trouble to make the camera rotate around my object. I am going to try to express myself as good as i can.
The objective is that when i load a new object and select it, (selecting it means that _selected_object points to the new object), the active camera points only to the center of the object(when analisis mode is activated), so the rotations and translation( translations just in the Z axis) are made around this object.
This is what i am trying right now:
_selected_camera->at.x=_selected_object->mtptr->M[3];
_selected_camera->at.y=_selected_object->mtptr->M[7];
_selected_camera->at.z=_selected_object->mtptr->M[11];
This code happens when the analisis mode (camera pointing and moving towards object) is activated. But when i move the object, the camera points nowhere or where it was initially pointing.
at.x from selected camera is the point towards the camera is looking. mtptr is the 4x4 matrix position of the object (in which object transformations are made), where last column has the center of the object.

Answer 1

If you're using legacy OpenGL, use gluLookAt.
Otherwise (pseudo code):
mat4 lookAt(vec3 eye, vec3 target, vec3 up)
{
//calculate axes based on the provided parameters
//cross product gives us the perpendicular vector
vec3 z = eye - target;
vec3 x = cross(up, z);
vec3 y = cross(z, x);
//normalize to make unit vectors
normalize(x);
normalize(y);
normalize(z);
//translation vector
//based on the angle between the eye vector (camera position) and the axes
//hint: angle = dot(a, b) -> see: https://en.wikipedia.org/wiki/Dot_product
vec3 t = {
-dot(eye, x),
-dot(eye, y),
-dot(eye, z)
};
return { //a combined scale, skew, rotation and translation matrix
x[0], x[1], x[2], t[0],
y[0], y[1], y[2], t[1],
z[0], z[1], z[2], t[2],
0, 0, 0, 1
};
}
Multiply the resulting (view) matrix with a projection matrix (ortho, perspective).