Quote Originally Posted by BigEars View Post
I may have a method which I have yet to test. Find the smallest rectangle which will enclose all the points and calculate its centre. That will be the centre of the circle with a radius of half the length of the diagonal. Thinking about this really cocked up my pistol session this afternoon.
Easy to say but is no simpler to actually do. Simples if the rectangle is confined to one orientation, however this will not be the smallest rectangle of the many possible orientations of the rectangle. The problem is essentially the same for any enclosure with a form which can be mathematically defined. Lots of work been done on these kind of problems and no linear solution (one which follows a direct mathematical path to the solution, or in computing terms one which can produce a solution in a predictable time for an arbitrary number of points) has been found so far - all solutions found so far are iterative (progressively refine successive guesses).

But there just might be an elegant approach which does yield the smallest enclosure with no iterations

Also does "smallest rectangle" cover the smallest area or have the smallest perimeter?