Here is a convex object and an origin point outside it.

is an arbitrary point in the boundary. Find the farthest point on the boundary along the vector . Name the farthest point .

We get a new vector to find the farthest point on the boundary along the direction . The point is added to the simple vertices set = {, }.

Connect points and , find the closet point on the line segment to the origin O. Find the farthest point on the boundary with direction . The point is added to the simple vertices set = {, , }.

Find the closest point on the triangle (, , ). We can find the farthest point on the boundary along direction . Now we focus on the new convex hull = <, , >.

The length of the W triangle will become smaller as we continue these steps. For convex faceted objects, the closest point will be found in a finite number of steps.