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Does anyone know of an equation to fill a 2d surface with circles?
Nekar
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On Thu, 15 Feb 2001 09:30:27 +0200, "Nekar Xenos" <vir### [at] icon coza>
wrote:
>Does anyone know of an equation to fill a 2d surface with circles?
It's been a long time, but try searching for "apolonian packing of
circles" at google or the like. You may have try try seaching on
variations on ap(p)ol(l)onian, I'm not sure of the spelling since it's
been 10 years or more since I messed with it. It got 'interesting'
trying to make a 3d version, but I never got it working right in 3d.
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Nekar Xenos wrote:
> Does anyone know of an equation to fill a 2d surface with circles?
I posted a macro that will fill any object with a 3d matrix of densely
packed spheres.
news://news.povray.org/3a4e9ea8%40news.povray.org
I've been trying a render to look at what this can do for just plain
circles, it's taking a long time.....
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Thanks.I think I'll have to get MegaPov 0.5 to see this. Haven't looked at
the code yet...
Nekar
Greg M. Johnson <gre### [at] my-dejanewscom> wrote in message
news:3A8C4561.B2AFC289@my-dejanews.com...
> Nekar Xenos wrote:
>
> > Does anyone know of an equation to fill a 2d surface with circles?
>
> I posted a macro that will fill any object with a 3d matrix of densely
> packed spheres.
> news://news.povray.org/3a4e9ea8%40news.povray.org
>
> I've been trying a render to look at what this can do for just plain
> circles, it's taking a long time.....
>
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On Thu, 15 Feb 2001 21:04:18 GMT, eso### [at] scacscdk (Erkki
>It's been a long time, but try searching for "apolonian packing of
>circles" at google or the like. You may have try try seaching on
>variations on ap(p)ol(l)onian, I'm not sure of the spelling since it's
>been 10 years or more since I messed with it. It got 'interesting'
>trying to make a 3d version, but I never got it working right in 3d.
Was it Marthin Gardner who had chosen a bachelor's thesis along the
lines of "Optimal Packing of Equisized Spheres In 27-Dimensional
Space"? It gets even odder... he provided diagrams :)
I am not sure if it was him. I know I read something along these lines
in one of his books, not sure which volume though :)
Peter Popov ICQ : 15002700
Personal e-mail : pet### [at] vipbg
TAG e-mail : pet### [at] tagpovrayorg
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On Fri, 16 Feb 2001 23:09:25 +0200, Peter Popov <pet### [at] vipbg> wrote:
>>It's been a long time, but try searching for "apolonian packing of
>>circles" at google or the like. You may have try try seaching on
>>variations on ap(p)ol(l)onian, I'm not sure of the spelling since it's
>
>Was it Marthin Gardner who had chosen a bachelor's thesis along the
>lines of "Optimal Packing of Equisized Spheres In 27-Dimensional
>Space"? It gets even odder... he provided diagrams :)
The appolonian packing of spheres isn't limited to equisized spheres
but adds smaller spheres in as many levels as levels as you have
patience for.
As for multi-dimensional math I remember some Linear Programming where
the solution plane is an n-1 dimensional plane intersecting the
n-dimensional variable space. The trick was finding the highest point
on that plane. At that time at had to run my models on a 4 MHz 8086
machine so big models took time. I rarely went above 20 dimensions but
they could take up to half an hour to solve (or infinity if there was
multiple solutions!). As I added more constraints the solution time
increased exponentially and when the models was getting complex enough
to be usefull they were too big to handle.
Erkki
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news:3a8db1bd.63582321@news.povray.org...
> On Fri, 16 Feb 2001 23:09:25 +0200, Peter Popov <pet### [at] vipbg> wrote:
> >>It's been a long time, but try searching for "apolonian packing of
> >>circles" at google or the like. You may have try try seaching on
> >>variations on ap(p)ol(l)onian, I'm not sure of the spelling since it's
> >
> >Was it Marthin Gardner who had chosen a bachelor's thesis along the
> >lines of "Optimal Packing of Equisized Spheres In 27-Dimensional
> >Space"? It gets even odder... he provided diagrams :)
>
> The appolonian packing of spheres isn't limited to equisized spheres
> but adds smaller spheres in as many levels as levels as you have
> patience for
This sounds like it could be what I'm looking for. Haven't had time to
search the net for it yet, though.
Nekar
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