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September 13th, 2012, 03:15 PM  #1 
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0  Inscribing the largest possible oval within a polygon
It's been awhile since I've posted on here! Life has changed a lot, I've changed a lot, and I'm now working as an engineer. Anyway, I've got an interesting problem I am trying to solve. How do I inscribe the largest possible oval within any given irregular polygon (can be convex, concave, anything)? I am assuming here that the axis of this oval is at all times aligned with the axis of the Cartesian coordinate system upon which the polygon is drawn. I am primarily interested in where the center of this oval is. It would also be very useful if I could provide limits to the oval's widthtoheight ratio, so, for instance, I could specify that the algorithm only consider oval candidates whose widths were at least twice their heights but less than three times their heights, or something like that. Any ideas on where I should start trying to solve this problem? Is this way more insanely complicated that I think it is? 
September 14th, 2012, 08:37 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,885 Thanks: 1088 Math Focus: Elementary mathematics and beyond  Re: Inscribing the largest possible oval within a polygon
It seems that you mean "ellipse" where you say "oval". Is this so? Under what conditions do you consider the oval to be inscribed in the polygon? Of course, if tangency of the oval to all sides of the polygon is required then it may not be possible.


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