 |
|
|
|
|
|
| |
| |
|
|
|
|
| |
| |
|
|
A while back I stumbled across these links for that great 3D puzzle, the
Soma Cube.
http://www.fam-bundgaard.dk/SOMA/SOMA.HTM
and
http://basden.net/somacube/
The Soma cube was invented by Danish physicist Piet Hein in the early 1930s,
while doodling at a lecture given by Heisenberg. The Soma cube pieces
consist of all the nonconvex polycubes of degree 4 or less. These pieces
can be assembled into a 3x3x3 cube in 240 different ways, not counting
rotations or reflections. (This was proved by John Conway, inventor of
Life).
I've played with this puzzle for over thirty years, but I never thought of
modelling it in POV before. The first link above has many hundreds of
patterns available, using a fairly simple notation. So I wrote an awk
script or two to extract the patterns from a webpage & to translate the
data into POV include files.
Source code (POV and AWK) available if anyone's interested. Of course, I'm
not going to upload hundreds of converted patterns here!
Here are the basic Soma pieces, using Conways standard colours.
Post a reply to this message
Attachments:
Download 'somab2s.jpg' (47 KB)
Preview of image 'somab2s.jpg'
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Here's a small 'menagerie' of a few Soma cubes creatures, plus the 3x3x3
cube itself, and a water trough.
Post a reply to this message
Attachments:
Download 'somaf0s.jpg' (77 KB)
Preview of image 'somaf0s.jpg'
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Here's a dog, which actually stands up when constructed in non-virtual
reality.
The Soma cube is a good way to sharpen your ability to think in 3
dimensions; a skill all POV users need. :)
Post a reply to this message
Attachments:
Download 'somai3s.jpg' (85 KB)
Preview of image 'somai3s.jpg'
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Here are a couple of Soma pieces done in a metallic texture. It was done in
POV 3.6, using Jaime's pHDRI macro, and a 'light dome' built using Pose
Ray. The dome contains 159 light sources (some shadowless). They are all
simple lights; I'm afraid of what area lights would do to the render time.
I'm still very new to this light-probe stuff. It takes a lot of time on this
old 566MHz machine, but the results are compelling.
This image uses focal_blur, rather than anti-aliasing, with a little bit of
post-process smoothing. I've also adjusted the gamma a little so the image
isn't too bright on the majority of monitors, but it may require further
adjustments.
Post a reply to this message
Attachments:
Download 'somal6s.jpg' (89 KB)
Preview of image 'somal6s.jpg'
|
|
| |
| |
|
|
|
|
| |
| |
|
|
This reminds me of a similar puzzle that I saw solved a while back - a 5x5x5
cube made from similar arrangements of smaller cubes, although not a
complete set. I sketched the solution and raytraced it with wackily
textured pieces:
http://www.infradead.org/~wmp/gallery4/puzzle.jpg
http://www.infradead.org/~wmp/gallery4/puzzle2.jpg
There's a couple of coincident surface problems in these images, but they're
not too serious!
Bill
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
PM 2Ring wrote:
> The Soma cube was invented by Danish physicist Piet Hein in the early 1930s,
> while doodling at a lecture given by Heisenberg.
He probably accomplished more during that lecture than anyone else who
attended it.
Regards,
John
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
"Bill Pragnell" <bil### [at] hotmail com> wrote:
> This reminds me of a similar puzzle that I saw solved a while back - a 5x5x5
> cube made from similar arrangements of smaller cubes, although not a
> complete set. I sketched the solution and raytraced it with wackily
> textured pieces:
>
> http://www.infradead.org/~wmp/gallery4/puzzle.jpg
> http://www.infradead.org/~wmp/gallery4/puzzle2.jpg
Interesting! Those textures sure are wacky, alright!
> There's a couple of coincident surface problems in these images, but they're
> not too serious!
I didn't notice them. Nice rounding on your polycubes, BTW.
I was going to modify the rounding algorithm I used on the polyominos I
posted a while ago, but it looked like too much work, modifying a 2D
algorithm to work in 3D. Besides, I wanted to keep the individual cubes
visible in the Soma cube pieces, so I'm just using a superellipsoid.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
John VanSickle <evi### [at] hotmailcom> wrote:
> PM 2Ring wrote:
>
> > The Soma cube was invented by Danish physicist Piet Hein in the early 1930s,
> > while doodling at a lecture given by Heisenberg.
>
> He probably accomplished more during that lecture than anyone else who
> attended it.
Maybe, but I'm uncertain. :)
He must've had brilliant powers of 3D visualization to realize the Soma
pieces could fit together to make a cube, just from a few sketches.
Here's a stereo pair. Change the file extension to .jps to view with
DepthCharge or with the Andreas Petersik's Stereoscope Applet.
Post a reply to this message
Attachments:
Download 'somaj0s.jpg' (57 KB)
Preview of image 'somaj0s.jpg'
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Hi,
I like these Soma cubes! Could you send me the source files, or better
still perhaps you could post them to p.b.s-f
Thanks in advance
Reuben
reu### [at] pslconnectcom
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Reuben Pearse <reu### [at] pslconnectcom> wrote:
> I like these Soma cubes!
Thanks for your interest, Reuben.
> Could you send me the source files, or better
> still perhaps you could post them to p.b.s-f
Sure. I'll post a basic main scene file, an include file of the basic Soma
pieces, and an include file of 25 assorted shapes in p.t.s-f. That's the
text group, not the bin group (I've had problems with zip files & the Web
interface in the past).
The utilities to convert patterns from HTML or plain text to POV arrays
require Unix/Linux. Are they any use to you?
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
