4, when P is exterior to the rectangle AMBN, where [absolute value of PO] means the classical 2D-distance between the point P and O, and similarly for [absolute value of P'O] and [absolute value of PP'].
= - max d (point O, point M on the frontier of AMBN. (6)
In this case, we extend the line OP to intersect the frontier of the rectangle AMBN. P' is closer to P than P", therefore we consider P'.
a) (x, y) [member of] Int(AMBN) if [rho] [(x, y),AMBN] < 0, where Int (AMBN) means interior of AMBN;
b) (x, y) [member of] Fr(AMBN) if [rho] [(x, y), AMBN] = 0, where Fr (AMBN) means frontier of AMBN;
c) (x, y) [not member of] AMBN if [rho] [(x, y), AMBN] > 0.
Let [A.sub.0][M.sub.0][B.sub.0][N.sub.0] and AMBN be two rectangles whose sides are parallel to the axes of the Cartesian system of coordinates, such that they have no common end points, and [A.sub.0][M.sub.0] [B.sub.0][N.sub.0] [subset] AMBN.
d) If (x, y) [member of] Fr (AMBN), then [K.sub.2D(x,y)] = 0;
e) If (x, y) [not member of] AMBN, then K2D(x, y) < 0.