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Largest Inscribed Circle in a Closed Polygon

Posted on 2004-04-12
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Last Modified: 2007-12-19
Hi Experts,

Given a set of points that form a closed polygon, how do I determine the largest inscribed rectangle of that polygon?

I've seen examples online for how to determine the inscribed rectangle of a circle or triangle, but I'm

dealing with shapes that aren't necessarily circles or triangles. Is this even possible?

Thanks!

-Me
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Question by:CPOsosky
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3 Comments
 
LVL 27

Expert Comment

by:aburr
ID: 10807451
Your title asks for a circle, your body asks for a rectangle.
-
I think the question as asked will be impossible to answer in general with a finite number of words. The first problem is to draw the polygon. The answer will depend on the order in which the points are connected.
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Author Comment

by:CPOsosky
ID: 10807735
Sorry. Typo in the title.

I'm looking for the largest inscribed RECTANGLE of a polygon.

Here's an example:

Given points A, B, C, D, E

Drawing order goes from

A to B
B to C
C to D
D to E
E to A

The points can have varying distances between them.

Line segments only intersect at the end points.

-Me












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LVL 45

Accepted Solution

by:
sunnycoder earned 250 total points
ID: 10810586
this is a special case for largest empty rectangle algorithms ... It is still an active research topic

http://portal.acm.org/citation.cfm?id=41988&dl=ACM&coll=portal
http://portal.acm.org/citation.cfm?id=767364&dl=ACM&coll=portal

I had worked on largest empty isothetic rectangles but not on largest empty rectangles ... but it is possible and the above links have the algorithms too ... I think you will have to register to view the paper
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