Maximal-Orthogonal Convex Hull (or Maximal-Rectilinear Convex Hull) In my research, I have come across a this paper from the Computational Geometry field and I am not able to understand the concept of Maximal-Rectilinear Convex Hull of a given point set in plane. In the attached image![image]( I have tried to explain my problem. Edit 1 : In sketch 4 of attached image, note that the set contains the inside of the rectangle as well and not just the periphery. Appreciate any help in clearing my confusion.

The maximal orthogonal convex hull is what is left of the plane when you take away all set-free quadrants, that is basically the intersection of the sets 1,2,3 below plus cutting off the rest outside the rectangle (I have shown only three the most important quadrants on the pictures as the others cannot penetrate in the rectangle, so they make the obvious cut - the same as half-planes). The intersection then is precisely the set drawn on the figure 3 above. In your answer it looks like you are taking away half-planes (less freedom) instead of the quadrants, that's why you get it different. By the way, the inside part of your rectangle seems to be empty. If so, how did you cut it off?![Set 1](

![Set 2](

![Set 3](