The editorial mentions that we should binary search for the intersection of the line with the convex hull. I am wondering why binary search is used here instead of ternary search.

In the diagram above, the points in the hull begin and end as non-optimal, and the best intersection (line with the least non-negative slope) will lie somewhere in the middle. So, we should be able to ternary search for that intersection.

I guess I can see how binary search might be used (binary searching on slopes and checking for intersection with the hull) but wouldnâ€™t ternary search on the hull make our lives much easier?

I might be missing something obvious, so any help would be greatly appreciated!