# Why does Graham Scan not extend to three dimensions?

The Graham scan algorithm computes the convex hull of a finite sets of points. It works only in the plane but is also fast (time $O(n \log n)$).

An old exam question asks, why does the algorithm not extend for three dimensional space? I just can't find an answer; it seems to me as if it should work.

• Sorting the points according to a pivot should not be a problem.
• Detecting a Left/Right turn (or measering the inner angle) neither.

Then what is the problem when we try to extend the algorithm to three dimensions?

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