The Minimal enclosing circle algorithm finds the smallest circle that contains all given points.
Found the following 2 pages that had a nlogn and a n^2 algorithm.
http://www.cs.brown.edu/people/tor/java/mec/ O(nLogN)
http://www.personal.kent.edu/~rmuhamma/Compgeometry/MyCG/CG-Applets/Center/centercli.htm linear time
Why is such an algorithm important?
For graphics and games (collision detection).
Bomb damage assesment (minimum size of bomb to take out a set of targets)
I don't know if engravers or the like ever blog here but if they do they might be interested in free western clipart.
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