Before revision: Let P be a set of n points in the plane and _{\theta}(P), has minimum (or maximum) area in optimal O(n\log n) time and O(n) space, improving the previous O(n^2) bound.
After revision: Let P be a set of n points in the plane and 0,2\pi) for which the rectilinear convex hull of P, denoted by \mathcal{RH_{\theta}(P), has minimum (or maximum) area in optimal O(n\log n) time and O(n) space, improving the previous O(n^2) bound.