I know some algorithms which compute the convex hull in a continuous space. Are there efficient algorithms to compute it in a discrete domain?
For example in 3D discrete space, given the blue points, we want the convex hull including the green points. This fugure's points are plotted on the plane $v_1 + v_2 + v_3 = 7$. So, it's a pseudo 3D, e.g., green ones are $(2, 4, 1)$ and $(3, 1, 3)$.