 |
|
|
|
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Inspired by the "math related image" thread.
Sphere-6-5: Most vertices have 6 edges, but the red ones have 5. I think
this is a standard Geodesic Dome.
Sphere-6-4: Most vertices have 6 edges, but the red ones have 4.
Sphere-4-3: Most vertices have 4 edges, but the red ones have 3.
Sphere-6-3: Most vertices have 6 edges, but the red ones have 3.
Post a reply to this message
Attachments:
Download 'Sphere-4-3.jpg' (138 KB)
Download 'Sphere-6-3.jpg' (120 KB)
Download 'Sphere-6-4.jpg' (133 KB)
Download 'Sphere-6-5.jpg' (127 KB)
Preview of image 'Sphere-4-3.jpg'
Preview of image 'Sphere-6-3.jpg'
Preview of image 'Sphere-6-4.jpg'
Preview of image 'Sphere-6-5.jpg'
|
|
| |
| |
|
|
|
|
| |
| |
|
|
-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1
Mike Williams wrote:
> Inspired by the "math related image" thread.
>
> Sphere-6-5: Most vertices have 6 edges, but the red ones have 5. I think
> this is a standard Geodesic Dome.
If you are, at any times, on USA-administered territory, you are in
trouble. There is a patent on it! (just ask the golf-ball makers about
it...)
Have a nice sentence...
-----BEGIN PGP SIGNATURE-----
Version: GnuPG v1.4.0 (MingW32)
Comment: Using GnuPG with Thunderbird - http://enigmail.mozdev.org
iD8DBQFCSUwBs/YJ43cSjHIRAoPsAKDP/+kQJTYVdLT6MCRv1YlXMOCqcwCgpMKZ
6RMqcHIFY5cww86tx6/Db14=
=iVm8
-----END PGP SIGNATURE-----
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
So, what you basicly are saying to Mike is that
he's not allowed to render pictures of golfballs
or geodomes?
I honestly hope that was some kind of bad joke..
"Le Forgeron" <jgr### [at] free fr> skrev i meddelandet
news:42494c01$1@news.povray.org...
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> Mike Williams wrote:
>> Inspired by the "math related image" thread.
>>
>> Sphere-6-5: Most vertices have 6 edges, but the red ones have 5. I think
>> this is a standard Geodesic Dome.
>
> If you are, at any times, on USA-administered territory, you are in
> trouble. There is a patent on it! (just ask the golf-ball makers about
> it...)
>
> Have a nice sentence...
>
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v1.4.0 (MingW32)
> Comment: Using GnuPG with Thunderbird - http://enigmail.mozdev.org
>
> iD8DBQFCSUwBs/YJ43cSjHIRAoPsAKDP/+kQJTYVdLT6MCRv1YlXMOCqcwCgpMKZ
> 6RMqcHIFY5cww86tx6/Db14=
> =iVm8
> -----END PGP SIGNATURE-----
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Wasn't it Le Forgeron who wrote:
>Hash: SHA1
>
>Mike Williams wrote:
>> Inspired by the "math related image" thread.
>>
>> Sphere-6-5: Most vertices have 6 edges, but the red ones have 5. I think
>> this is a standard Geodesic Dome.
>
>If you are, at any times, on USA-administered territory, you are in
>trouble. There is a patent on it! (just ask the golf-ball makers about
>it...)
I thought US patents only lasted 20 years. The geodesic dome itself was
patented 51 years ago by Buckmister Fuller, so it might be out of patent
by now. I guess that the geodesic geometry patented in 1974 by Shoji
Sadao is not quite the same thing (otherwise it wouldn't have been an
original invention) but that might be out of patent too.
A method for laying out a 60-face geodesic pattern of dimples on a golf
ball was patented in 1996 by Robert Thurman, but since my image has more
than 90 faces (I think I have 768), and I'm not making golf balls, I'd
probably be OK. His patent also included balls with more dimples, but
that was achieved by having more than one dimple per face.
--
Mike Williams
Gentleman of Leisure
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Mike Williams wrote:
> A method for laying out a 60-face geodesic pattern of dimples on a golf
> ball was patented in 1996 by Robert Thurman, but since my image has more
> than 90 faces (I think I have 768), and I'm not making golf balls, I'd
> probably be OK. His patent also included balls with more dimples, but
> that was achieved by having more than one dimple per face.
That raises an interesting question, what if a patented method for
laying out dimples on a golf ball were used in a scene file, to create
an accurate representation of the geometry of a golf ball. Would that be
considered patent infringement?
--
~Mike
Things! Billions of them!
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Mike Raiford <mra### [at] hotmailcom> wrote:
>
> That raises an interesting question, what if a patented method for
> laying out dimples on a golf ball were used in a scene file, to create
> an accurate representation of the geometry of a golf ball. Would that be
> considered patent infringement?
>
> --
> ~Mike
>
> Things! Billions of them!
Patent - A government grant giving the right to exclude others from making,
using or selling an invention.
Patent infringement - Making, using or selling an invention on which a
patent is in force without the inventor's permission.
In the case of the golfball and most other things, I don't think rendering
would qualify it for infringement since I believe most patents are written
to involve the creation/application of physical objects/processes. There
are cases where algorithms/code are patented I believe, but I think for the
most part, no one really cares unless you are try to make money off of it,
somehow decreasing the money they make off of it, or going around claiming
it's your idea.
But then again what do I know, I'm an engineer, not a laywer.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Mike Williams wrote:
> Inspired by the "math related image" thread.
>
> Sphere-6-5: Most vertices have 6 edges, but the red ones have 5. I think
> this is a standard Geodesic Dome.
>
> Sphere-6-4: Most vertices have 6 edges, but the red ones have 4.
>
> Sphere-4-3: Most vertices have 4 edges, but the red ones have 3.
>
> Sphere-6-3: Most vertices have 6 edges, but the red ones have 3.
>
>
>
>
Very nice! How are you generating the vertices? From a data file, or
from an algorithm? Same question for edges, for that matter....
Dave Matthews
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Wasn't it Dave Matthews who wrote:
>Mike Williams wrote:
>> Inspired by the "math related image" thread.
>>
>> Sphere-6-5: Most vertices have 6 edges, but the red ones have 5. I think
>> this is a standard Geodesic Dome.
>>
>> Sphere-6-4: Most vertices have 6 edges, but the red ones have 4.
>>
>> Sphere-4-3: Most vertices have 4 edges, but the red ones have 3.
>>
>> Sphere-6-3: Most vertices have 6 edges, but the red ones have 3.
>>
>>
>>
>>
>Very nice! How are you generating the vertices? From a data file, or
>from an algorithm? Same question for edges, for that matter....
I'm actually generating the faces (by simple recursive subdivision).
I then draw cylinders along the edges of each face, and spheres at the
corners. That actually means that each visible sphere is really as many
as six coincident POV spheres, but the scene renders fast enough that
I've not bothered removing the duplication.
--
Mike Williams
Gentleman of Leisure
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
"Mike Williams" <nos### [at] econymdemoncouk> wrote in message
news:42494252@news.povray.org...
> Inspired by the "math related image" thread.
>
> Sphere-6-5: Most vertices have 6 edges, but the red ones have 5. I think
> this is a standard Geodesic Dome.
>
> Sphere-6-4: Most vertices have 6 edges, but the red ones have 4.
>
> Sphere-4-3: Most vertices have 4 edges, but the red ones have 3.
>
> Sphere-6-3: Most vertices have 6 edges, but the red ones have 3.
Nice pictures! I like (from an aesthetic point of view) the cube
subdivision one the best.
Recursive subdivision of the regular tetrahedron (each triangle into
4 new triangles all with vertices on the circumscribing sphere) results
(at stage 3 IIRC) in a non-convex polyhedron with triangular faces.
This surprised me when I first realized it 10 years or so ago.
No such problems with the octahedron or icosahedron.
Jim Buddenhagen
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
