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Hi!
Here are some sphere inversions I've done recently, of course inspired
by what scam [1] and Paul Bourke [2] did. I've used isosurfaces, meshes
and sphere sweeps, depending on the original geometry. Aside from the 3
I'm posting here, there are some more on [3], including my version of
the "RSOCP of sphere inversion", the Truchet tiling :)
Comments welcome!
[1]http://news.povray.org/web.447c45efc019fdb45c947f990%40news.povray.org
[2]http://local.wasp.uwa.edu.au/~pbourke/surfaces_curves/truchet/
[3]http://www.torfbold.com/external/si.html
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Download 'si_grid.jpg' (41 KB)
Preview of image 'si_grid.jpg'
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Download 'si_menger.jpg' (112 KB)
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Download 'si_sierpinski.jpg' (83 KB)
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Florian Brucker wrote:
>
> ------------------------------------------------------------------------
>
Wow! I have always disliked Menger Sponge renders,... until now. Superb!
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...now in the name of God do you "invert" a sphere?
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Orchid XP v3 <voi### [at] dev null> wrote:
> ...now in the name of God do you "invert" a sphere?
Roll over Pluto! Good boy.
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#2 of 3 makes me somehow want to see a fly-through :)
Florian Brucker <tor### [at] torfboldcom> wrote:
>
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"Charles C" <nomail@nomail> wrote in message
news:web.45d612ceb46ebe1a7d5894630@news.povray.org...
> #2 of 3 makes me somehow want to see a fly-through :)
>
or pour water through it
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OOH! I like these. I think my favorites are the grid (#1) and the toruses
(#4 on the site).
Orchid XP v3: As I recall, a spherical inversion is not actually inverting
the *sphere*, as it is reflecting points across the surface of a sphere.
It's easier to imagine in two dimensions (see Escher); but the idea is that
for any point outside the sphere, there is a corresponding point inside the
circle. The closer to the surface of the sphere on the outside, the closer
tot eh surface of the sphere on the inside. The further away (i.e. closer
to infinite distance) the closer you get to the center of the sphere. So
infinite space is represented inside a finite volume --- so number one, if
you un-inverted it (same as re-inverting) would --- correct me if I'm wrong
--- be a rectangular grid stretching across all of space. The others
actually began with objects inside the spherical radius, so they end up
outside the sphere, and as none of the affected points were at the center
of the circle, there are no infinites involved.
A funny idea I just had --- a spherical inversion of a sufficiently small
concentric sphere (that started on the inside) would contain any given
point outside. So you could be outside the original, and inside the
inversion --- but still only see one side of the sphere. I think that means
that infinity only has one side ;)
Sam Bleckley
http://enso.freeshell.org/
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Hi Florian, these are very nice, well done! Glad to see I wasn't the only
one mesmerized by these objects.
You've inspired me to have another look at these things, so I'll try and
come up with something interesting to post.
By the way, if anyone is interested in the code I used to generate my
version Florian referenced above, it's available here:
http://news.povray.org/web.447d804452ae62aa5c947f990%40news.povray.org
Cheers,
Sam (aka scam)
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Florian Brucker wrote:
> Hi!
>
> Here are some sphere inversions I've done recently, of course inspired
> by what scam [1] and Paul Bourke [2] did. I've used isosurfaces, meshes
> and sphere sweeps, depending on the original geometry. Aside from the 3
> I'm posting here, there are some more on [3], including my version of
> the "RSOCP of sphere inversion", the Truchet tiling :)
>
> Comments welcome!
...
Here's two similar ones:
http://home.online.no/~t-o-k/POV-Ray_Images/Isosurface_Sphere_Inversion.jpg
http://home.online.no/~t-o-k/POV-Ray_Images/Isosurface_Circle_Inversion.jpg
-But I like your texture and light setting better !
--
Tor Olav
http://subcube.net
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So... is that something like taking the reciprocol of a complex number?
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Orchid XP v3 <voi### [at] devnull> wrote:
> So... is that something like taking the reciprocol of a complex number?
Here's a good introduction in 2D:
http://mathworld.wolfram.com/Inversion.html
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>> So... is that something like taking the reciprocol of a complex number?
>
> Here's a good introduction in 2D:
> http://mathworld.wolfram.com/Inversion.html
http://mathworld.wolfram.com/Reciprocal.html
Seems to indicate that the reciprocal of a complex number is indeed an
inversion with respect to the unit circle in the complex plane.
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Florian Brucker wrote:
> Hi Tor!
>
> Tor Olav Kristensen wrote:
>> Here's two similar ones:
> Ah, I've seen them before, but I forgot about them! The geometry is
> nice, what's the original structure?
It's a "straight" version of the isosurface used in this image:
http://hof.povray.org/Isosurface-Cubic_Space_Division.html
That structure looks similar to the one in the image in this post:
http://news.povray.org/3A21093C.4D45881A%40online.no
"Cubic Sphere Inversion" (21 Jan. 2004 to p.b.i.)
--
Tor Olav
http://subcube.net
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Florian Brucker wrote:
> The water would be the ultimate render time killer, I guess.
Transparency, ior and radiosity -compilation is also pretty good one ;).
--
Eero "Aero" Ahonen
http://www.zbxt.net
aer### [at] removethiszbxtnetinvalid
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Florian Brucker wrote:
>
> ------------------------------------------------------------------------
>
nice. this is quite pleasing to the eye
bob
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Florian Brucker wrote:
> Eero Ahonen wrote:
>> Florian Brucker wrote:
>>> The water would be the ultimate render time killer, I guess.
>> Transparency, ior and radiosity -compilation is also pretty good one ;).
>
> Yep, but that's you Aero, nobody else is that crazy :P
>
But hey, craziness is my trademark in such things. May I show the
textured versions of your inversions (well, I only have Torinet so far,
but I _will_ trace more:) here?
BTW, I'm still tracing my CGSphere draft's next version, THIS is getting
a bit too slow to get something done...
232:09:11 Rendering line 116 of 768, 4896 supersamples, 22577 rad. samples
--
Eero "Aero" Ahonen
http://www.zbxt.net
aer### [at] removethiszbxtnetinvalid
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Florian Brucker wrote:
>
> Sure, show it! It's always interesting to see what different people make
> out of the same underlying concept :)
>
Great :). Here's the red and transparent version of Torinet...
--
Eero "Aero" Ahonen
http://www.zbxt.net
aer### [at] removethiszbxtnetinvalid
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