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Better description for Andrew's algorithm

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Antti H S Laaksonen 2017-02-24 00:52:49 +02:00
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@ -396,21 +396,20 @@ an easy way to
construct the convex hull for a set of points construct the convex hull for a set of points
in $O(n \log n)$ time. in $O(n \log n)$ time.
The algorithm constructs the convex hull The algorithm constructs the convex hull
in two steps: in two parts:
first the upper hull and then the lower hull. first the upper hull and then the lower hull.
Both steps are similar, so we can focus on Both parts are similar, so we can focus on
constructing the upper hull. constructing the upper hull.
We sort the points primarily according to First, we sort the points primarily according to
x coordinates and secondarily according to y coordinates. x coordinates and secondarily according to y coordinates.
After this, we go through the points and always After this, we go through the points and
add the new point to the hull. add each point to the hull.
After adding a point we check using cross products Always after adding a point to the hull,
whether the tree last point in the hull turn left. we make sure that the last line segment
If this holds, we remove the middle point from the hull. in the hull does not turn left.
After this we keep checking the three last points As long as this holds, we repeatedly remove the
and removing points, until the three last points second last point from the hull.
do not turn left.
The following pictures show how The following pictures show how
Andrew's algorithm works: Andrew's algorithm works: