Is there a simple algorithm for calculating the maximum inscribed circle into a convex polygon?

Question

I found some solutions, but they\'re too messy.

Answer 1

Summary: It is not trivial. So it is very unlikely that it will not get messy. But there are some lecture slides which you may find useful.

Source: http://www.eggheadcafe.com/software/aspnet/30304481/finding-the-maximum-inscribed-circle-in-c.aspx

Your problem is not trivial, and there is no C# code that does this straight out of the box. You will have to write your own. I found the problem intriguing, and did some research, so here are a few clues that may help.

First, here's an answer in "plain English" from mathforum.org:

http://mathforum.org/library/drmath/view/67030.html

The answer references Voronoi Diagrams as a methodology for making the process more efficient. In researching Voronoi diagrams, in conjunction with the "maximum empty circle" problem (same problem, different name), I came across this informative paper:

http://www.cosy.sbg.ac.at/~held/teaching/compgeo/slides/vd_slides.pdf

It was written by Martin Held, a Computational Geometry professor at the University of Salzberg in Austria. Further investigation of Dr. Held's writings yielded a couple of good articles:

http://www.cosy.sbg.ac.at/~held/projects/vroni/vroni.html http://www.cosy.sbg.ac.at/~held/projects/triang/triang.html

Further research into Vornoi Diagrams yielded the following site:

http://www.voronoi.com/

This site has lots of information, code in various languages, and links to other resources.

Finally, here is the URL to the Mathematics and Computational Sciences Division of the National Institute of Standards and Technology (U.S.), a wealth of information and links regarding mathematics of all sorts:

http://math.nist.gov/mcsd/

-- HTH,

Kevin Spencer Microsoft MVP