POV-Ray : Newsgroups : povray.advanced-users : Pappus Chain : Re: Pappus Chain Server Time
18 Jul 2024 07:24:03 EDT (-0400)
  Re: Pappus Chain  
From: Bald Eagle
Date: 13 Jun 2024 13:25:00
Message: <web.666b2ad03bd24dfe57579a6b25979125@news.povray.org>
kurtz le pirate <kur### [at] gmailcom> wrote:

> I'm working on it too.
>
> wip here : <http://louisbel.free.fr/scenes/scene038.shtml>
> (in french for the moment)

Very nice.  Excellent work as always!
I see you've been going over the same references as I have.

I just started watching Daniel Schiffman's video this morning - I was hoping to
start writing some code based on it after work.

I'm still amazed that "Beyond the Descartes Circle Theorem" was only published
in 2001!  :O

I recall in one of the sites that I stumbled across, there was a method for
calculating how many circles there were for any given level of recursion.
That might be a nice addition to the debug stream, as well as warning/sanity
check before a render is attempted to be started with too high a level of
recursion for the system it's being run on.

It would also be nice to have a few ways to generate the output, so that the
gasket could be further used in a more complex scene.

1. Someone might want the tori to overlap such that the centers of their minor
radii are coincident/tangent, OR they might want the outside surfaces of the
tori to be tangent.

2. The coloration of each level of recursion ought to be able to be specified by
something like an array.  That way different textures and normals, etc can be
applied.  Also, it could then be rendered and subsequently used as a
heightfield.

3. There might be a desire to texture the circles based on their radius, or from
the distance from the center of the outer circle.

I've also found PDF and djvu copies of "Indra's Pearls" on the web, and they
have some very interesting algorithms to render a wide variety of variations on
this theme.

The authors even mention that some madman might be able to do this in Excel -
which is what I'm currently working on, since it's the only tool I have
available during the day.  :D

- BW


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