number the elements in clockwise order from 1..n suppose n is 12 then start from a point here we start from the point 1 then we find the farthest point from it in O(n) suppose that's point 5 now if we want to find the farthest point from point 2 since we moved clockwise the farthest point must turn clockwise i.e. points 3 and 4 cannot be the farthest point from 2 since the farthest point must turn clockwise when we want to find the farthest point from point 5 the farthest point would be point 1 this means that when we want to find the farthest point from the next point we don't search the hole polygon it just can be incremented from the last result a few times i hope it's clear now
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