[R] Quadrat counting with spatstat

[AMFTom]

I have photographs of plots that look like so:

http://r.789695.n4.nabble.com/file/n4631960/Untitled.jpg 

I need to divide it up so each circle has an equal area surrounding it. So
into 20 equal segments, each of which contains a circle. Quadratcount is not
sufficient because if I divide it up into 36 equal quadrats, some quadrats
do not contain one of the circles. 

I'm not even sure how to do it mathematically, let alone using R.  

Can anyone help?

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