How to implement camera pan like in 3dsMax?

What are the necessary maths to achieve the camera panning effect that's used in 3ds max?

In 3ds max the distance between the cursor and the mesh will always remain the same throughout the entire movement (mouse_down+mouse_motion+mouse_up).

My naive and failed attempt has been trying to move the camera on the plane XY by using dt (frame time) multiplied by some hardcoded constant and the result is really ugly and uintuitive.

The code I've got so far is:

def glut_mouse(self, button, state, x, y):
    self.last_mouse_pos = vec2(x, y)
    self.mouse_down_pos = vec2(x, y)

def glut_motion(self, x, y):
    pos = vec2(x, y)
    move = self.last_mouse_pos - pos
    self.last_mouse_pos = pos
    self.pan(move)

def pan(self, delta):
    forward = vec3.normalize(self.target - self.eye)
    right = vec3.normalize(vec3.cross(forward, self.up))
    up = vec3.normalize(vec3.cross(forward, right))

    if delta.x:
        right = right*delta.x
    if delta.y:
        up = up*delta.y

    self.eye+=(right+up)
    self.target+=(right+up)

Could you explain how the maths of camera panning in 3dsmax work?

EDIT:

My question has already been answered initially by @Rabbid76 but there's still one case where his algorithm won't work properly. It doesn't handle properly the case where you panning is started from empty space (said otherwise, when depth buffer value takes the far value=1.0). In 3dsmax camera panning is handled correctly in all situations, no matter which value of the depth buffer.

from How to implement camera pan like in 3dsMax?