Convex Hull: the "Gift Wrap" algorithm
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The "gift wrap algorithm" has an acceptable efficiency, quadratic order, or O(N2). This means that the algorithm will run 100 times longer (in time) for ten times as many points.
Example: for the point set, find the lowest vertex (or, you could find the highest, rightmost, or leftmost). This vertex must be on the convex hull. Then, find the point which makes the smallest angle to the horizontal drawn through the lowest point, in a counterclockwise direction. This point must also be on the convex hull. Then, continue to find the point which makes the smallest angle with the preceding edge. Continue until you return to the lowest point. These edges constitute the convex hull. The algorithm is called the "gift wrap" algorithm because it resembles wrapping paper around an arbitrary collection of points, as if they were a strange-shaped package. Click the Download button at the right to download a zipped file of all movies on this page. |