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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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Attachments:
Download 'si_grid.jpg' (41 KB)
Preview of image 'si_grid.jpg'
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Attachments:
Download 'si_menger.jpg' (112 KB)
Preview of image 'si_menger.jpg'
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Attachments:
Download 'si_sierpinski.jpg' (83 KB)
Preview of image 'si_sierpinski.jpg'
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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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