On 5/29/24 06:54, Bald Eagle wrote:
> You can invert anything, even whole patterns, like so:

Thanks for posting more detailed code. I played a little - and it's cool 
- though the results kinda twist my head around at times. :-)

Attached is a slice of a sphere to the -z side of the x,y plane where 
the radius of a f_sphere() is getting 'inverted / chopped' with your 
'Checker_Inv()' (I also clamped the maximum Inversion() value to 15). 
The sides sliced at the inversions don't render cleanly with the 
isosurface, but we still end up with an interesting looking shape.

A little surprised it worked as well as it did...

Bill P.

FYI. I did get a few divisions by zero from Inversion() until I added 
some off grid, anti-directional, numerical fuzz to CenterX, CenterY and 
CenterZ. This might be due how my yuqk AA works compared to the 
officially released AA.

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Attachments:
Download 'tmp2.png' (105 KB)

Preview of image 'tmp2.png'

So that's very cool, and I wondered what it would look like if rendered as a
whole sphere, maybe with a glass texture and some sort of variation of the color
- perhaps determined by the Manhattan distance from the center.

I just used a quick, textured box, and the larger the inversion circle, the
smaller / more compact the pattern.   Patterns jump out at different scales.

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Attachments:
Download 'invertedpatternsphere.png' (262 KB)

Preview of image 'invertedpatternsphere.png'

Ever inspired by the talented Francesco De Comite, I made a 3D version as a
little doodle.

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Attachments:
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Preview of image '3dpappuschain.png'

On 12/06/2024 03:03, Bald Eagle wrote:
> Ever inspired by the talented Francesco De Comite, I made a 3D version as a
> little doodle.
> 

You have contaminated me ;)





-- 
Kurtz le pirate
Compagnie de la Banquise

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Attachments:
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Preview of image 'papus3.png'

kurtz le pirate <kur### [at] gmailcom> wrote:
> On 12/06/2024 03:03, Bald Eagle wrote:
> > Ever inspired by the talented Francesco De Comite, I made a 3D version as a
> > little doodle.
> >
>
> You have contaminated me ;)

You spelled "inspired" wrong.   :P

That's a beauty.
I'll bet that would amazing done in glass with caustics.
Or as stone spheres in a field of grass.

I still need to work out some good code for an Appolonian gasket.
(Unless you beat me to it  ;)  )

- BW

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"Bald Eagle" <cre### [at] netscapenet> wrote:

> I'll bet that would amazing done in glass with caustics.

Check out:

https://www.dumas.io/limset3d/

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On 12/06/2024 17:52, Bald Eagle wrote:
> I still need to work out some good code for an Appolonian gasket.
> (Unless you beat me to it  ;)  )



I'm working on it too.

wip here : <http://louisbel.free.fr/scenes/scene038.shtml>
(in french for the moment)





-- 
Kurtz le pirate
Compagnie de la Banquise

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On 12/06/2024 17:52, Bald Eagle wrote:

> That's a beauty.
Thanks

> I'll bet that would amazing done in glass with caustics.

Hum.. hum... lot of work.
I have to think about it

> Or as stone spheres in a field of grass.

Easier and faster. First test attached.
Does it match your idea ?


Note :
- Random textures from "stones.inc" without optimization
- Makegrass macro from Gilles Tran


-- 
Kurtz le pirate
Compagnie de la Banquise

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Attachments:
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Preview of image 'papus_grass.jpg'

hi,

kurtz le pirate <kur### [at] gmailcom> wrote:
> ...
> wip here : {...}

the "l'image en noir et blanc" does it for me, v nice.


regards, jr.

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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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