I am attempting to implemented an FPS-style camera by updating three vectors: EYE, DIR, UP. These vectors are the same that are used by gluLookAt (since gluLookAt is specified by the position of the camera, the direction it is looking at, and an up vector).

I have already implemented the left-right and up-down strafing movements, but I'm having a lot of trouble understanding the math behind making the camera look-around while remaining stationary. In this case, the EYE vector remains the same, while I must update DIR and UP.

Below is the code I tried, but it doesn't seem to work properly. Any suggestions? Thanks.

void Transform::left(float degrees, vec3& dir, vec3& up) {
    vec3 axis;
    axis = glm::normalize(up);
    mat3 R = rotate(-degrees, axis);
    dir = R*dir;
    dir = R*up;
};

void Transform::up(float degrees, vec3& dir, vec3& up) {
    vec3 axis;
    axis=glm::normalize(glm::cross(dir,up));
    mat3 R = rotate(-degrees, axis);
    dir = R*dir-;
    up = R*up;
};