def vignettingEq(xxx_todo_changeme, f=<NUM_LIT:100>, alpha=<NUM_LIT:0>, Xi=<NUM_LIT:0>, tau=<NUM_LIT:0>, cx=<NUM_LIT:50>, cy=<NUM_LIT:50>):
(x, y) = xxx_todo_changeme<EOL>dist = ((x - cx)**<NUM_LIT:2> + (y - cy)**<NUM_LIT:2>)**<NUM_LIT:0.5><EOL>A = old_div(<NUM_LIT:1.0>, (<NUM_LIT:1> + (old_div(dist, f))**<NUM_LIT:2>)**<NUM_LIT:2>)<EOL>G = (<NUM_LIT:1> - alpha * dist)<EOL>T = np.cos(tau) * (<NUM_LIT:1> + (old_div(np.tan(tau), f))<EOL>* (x * np.sin(Xi) - y * np.cos(Xi)))**<NUM_LIT:3><EOL>return A * G * T<EOL>
Vignetting equation using the KARL-WEISS-MODEL
see http://research.microsoft.com/en-us/people/stevelin/vignetting.pdf

f - focal length
alpha - coefficient in the geometric vignetting factor
Xi - tilt factor of a planar scene
tau - rotation angle of a planar scene
cx - image center, x
cy - image center, y