[R] circle fill problem

[Ray Brownrigg]

I suspect the number is:
trunc((x + 3*r)/(2*r)) * trunc((y + 3*r)/(2*r)) + trunc((x +
    2*r)/(2*r)) * trunc((y + 2*r)/(2*r))
where x and y are the dimensions of the rectangle and r is the radius of the 
circle.

I have some code which graphs the overlapping circles if you want visually to 
check the algorithm (but although it is only a page, I won't post it here).

HTH
Ray Brownrigg

On Thursday 08 February 2007 22:39, MINI GHOSH wrote:
> Dear Ingmar and Robin,
>
> Thanks for you suggestions. I will see to it.
>
> Regards,
> Mini
>
> --- Ingmar Visser <i.visser at uva.nl> wrote:
> > Robin & Mini,
> > For those interested, googling for the 'orange
> > packing problem' as it
> > is known, or more officially the sphere packing
> > problems gives you
> > quite a few hits on these and similar problems.
> > So at least the 3-d case the problem has been solved
> > (I imagine the
> > problem is easier in 2-d ...)
> > hth, Ingmar
> >
> > On 8 Feb 2007, at 09:52, Robin Hankin wrote:
> > > Mini
> > >
> > > This is a hard problem in general.
> > >
> > > Recreational mathematics has wrestled with
> > > this and similar problems over the years; the
> > > general field is the "set cover problem" but
> > > in your case the sets are uncountably infinite
> > > (and there are uncountably many of them).
> > >
> > > I would be surprised if your problem were not NP
> >
> > complete.
> >
> > > HTH
> > >
> > >
> > > Robin
> > >
> > > On 8 Feb 2007, at 05:15, MINI GHOSH wrote:
> > >> Dear R user,
> > >>
> > >> I want to know is there a way to find the minimum
> > >> number of circles (of given radius) required to
> >
> > fill a
> >
> > >> given area (say rectangular) where overlapping of
> > >> circles is allowed.
> > >>
> > >> Thanks,
> > >> Regards,
> > >> Mini Ghosh
> > >>
> > >> ______________________________________________
> > >> R-help at stat.math.ethz.ch mailing list
> > >> https://stat.ethz.ch/mailman/listinfo/r-help
> > >> PLEASE do read the posting guide
> >
> > http://www.R-project.org/posting-
> >
> > >> guide.html
> > >> and provide commented, minimal, self-contained,
> >
> > reproducible code.
> >
> > > --
> > > Robin Hankin
> > > Uncertainty Analyst
> > > National Oceanography Centre, Southampton
> > > European Way, Southampton SO14 3ZH, UK
> > >   tel  023-8059-7743
> > >
> > > ______________________________________________
> > > R-help at stat.math.ethz.ch mailing list
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide
> >
> > http://www.R-project.org/posting-
> >
> > > guide.html
> > > and provide commented, minimal, self-contained,
> >
> > reproducible code.
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html and provide commented, minimal,
> self-contained, reproducible code.