Quote Originally Posted by Turnup View Post
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?
All good questions.
I was working using the edges of the target as traditional x and y axes. The size of the rectangle seems to be the same regardless of orientation. My refinment, after finding the centre of the rectangle is not to use the 0.5 diagonal as the radius, but the distance to the furthest point from my rectangle's centre.
However, man that is born of woman etc..

I'm not even sure knowing what the smallest circle is would be of any practical help to someone who shoots really well, or really badly,come to that.