We closed this forum 18 June 2010. It has served us well since 2005 as the ALPHA forum did before it from 2002 to 2005. New discussions are ongoing at the new URL http://forum.processing.org. You'll need to sign up and get a new user account. We're sorry about that inconvenience, but we think it's better in the long run. The content on this forum will remain online.
Index › Programming Questions & Help › Programs › Circle, around circumference packing.
‹ Previous Topic | Next Topic ›
Page Index Toggle Pages: 1
Circle, around circumference packing. (Read 1571 times)
RickiG
Circle, around circumference packing.
Jul 14th, 2009, 7:34am  
Hi

I read a paper on some circle packing algorithms. I wanted to try and
pack circles around the circumference of a larger circle.

So if I have a circle with radius = 50, I would like to place x number of circles with radius = r around the first circle, all these circles with their center on the circumference of the original circle.

Hmm would be a bit simpler to explain with a pen and paper:)

like this one, but without the outer circle and inner circle and with a circle drawn through the center of all the circles.
The circle I wish to pack the smaller circles around is not in this illustration.
...

Hope someone one can point me in the direction of the math involved, I can't think of it.

Cheers
Back to top
 
Regards Ricki
 
gll
Re: Circle, around circumference packing.
Reply #1 - Jul 14th, 2009, 7:42am  
http://en.wikipedia.org/wiki/Sphere_packing
http://en.wikipedia.org/wiki/Circle_packing_theorem

In your drawing, you don't have homogenous circles, but when you explain it, they seems homogenous (radius = r). Do you want sames radius circles?

http://www.cricketschirping.com/processing/CirclePacking1/
http://www.math.utk.edu/~kens/
Back to top
 
LaBelle / ANAR.ch / LaBelle.spaceKIT.ca
WWW  
gll
Re: Circle, around circumference packing.
Reply #2 - Jul 14th, 2009, 9:33am  
If you are looking for regular (homogenous) circles, then the problem is easy. The circles are distributed around a regular hexagon plus one circle in the middle. You'll have 6 circles (or 7 if the center circle is counted). This is not what you have in your drawing.

The hexagon radius is

Code:
hr = R - r
hr = 2*r
r = R/3


hr = hexagonRadius
R  = containningCircle
r  = circleRadius


http://upload.wikimedia.org/wikipedia/commons/0/0a/Empilement_compact_plan.svg
Back to top
 
LaBelle / ANAR.ch / LaBelle.spaceKIT.ca
WWW  
Page Index Toggle Pages: 1
‹ Previous Topic | Next Topic ›