Challenging

Question

How can you rank the "circularity" of a polygon? Meaning that having many I wanted to calculate the most similar to a circle...
In general, how do I compare a polygon to another? I  have to assess the best site compatibility according to a building design (Comparing the area of the site, with the area of the building)
Thanks

GerryGabrisch · Answer

The metric you want is called the isoperimetric quotient.

http://mathforum.org/library/drmath/view/55406.html

DanLee · Answer

I don't have a solution or further suggestions at this point, but I am interested in knowing all the criteria in thinking of a new tool design, say Maximum Inscribing Geometry. I have seen a few similar posts on this subject. Anyone's input would be welcome!

NorbertHaug · Answer

The area ratio = polygonArea / minBoundingCircleArea. For example the value could be 0.7, 0.9, etc. If the polygon is close to the circle, then the area ratio will be close to 1.

The perimeter ratio = polygonShape_length / minBoundingCircleShape_length. For example the value could be 1.5, 2.8, etc. If the polygon is close to the circle, then the perimeter ratio will be close to 1. It is not enough to evaluate area only; you need to take into account both ratios.

For the second part, can you describe what the constraints are?

There are other design restrictions which deal with the proposed geometry of the site (geometry can consist of area, perimeter, width, length, etc).
What is the best site given the potential geometric restrictions?