# Convex hull in a discrete space

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 $$(3, 1, 3)$$.

• Neither of those green points looks to me like it is inside the convex hull -- neither is a convex combination of the blue points. What is your definition of "convex" here? – j_random_hacker Sep 23 at 19:39
• You are right that blue points are not convex here. We want to look for the green points to fill the hollow, which is the definition of the convex I though. – Smith Sep 25 at 15:18