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Author Topic: Polyhedrons, many many polyhedrons...  (Read 11514 times)
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DarkBeam
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Posts: 1666


The spaghetti formula coder


« on: January 22, 2012, 10:08:52 AM »

Uh, I am having a trip on Wiki, if you want to get lost into 3D space you can have a look here;

Polyhedron theory
List of uniform polyhedra
Johnson solids (not uniform)
List of Wenninger polyhedron models
Catalan solids

Probably there are many more but I can't tell embarrass
The sad notice; very few solids have the coordinates shown, so you cannot replicate them in your fave 3D/fractal application. undecided
Like a ... 4D8 Puzzle wink

Get inspired cheesy

« Last Edit: January 22, 2012, 10:19:19 AM by DarkBeam » Logged

Formulas are never too much (?)

knighty
Fractal Bachius
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Posts: 570


« Reply #1 on: January 22, 2012, 12:30:51 PM »

Many of these polyhedrons can be rendered with DE using the fold and cut method. smiley
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DarkBeam
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Posts: 1666


The spaghetti formula coder


« Reply #2 on: January 22, 2012, 12:40:13 PM »

Many of these polyhedrons can be rendered with DE using the fold and cut method. smiley

Your technique is tricky ... Never understood it after all smiley

And at high iterations it tends to disappear smiley
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knighty
Fractal Bachius
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Posts: 570


« Reply #3 on: January 22, 2012, 12:57:58 PM »

No, it's quite simple... Humm... that means that I'll have to give a better explanation! embarrass
Forget about the iterations. The process is simple:
given the point p:
- Fold: apply some folding operations: p1:=Folds(p); (planar as I did or if you like, spherical ones).
- Cut: return the distance to some object: DE=distanceFunction(p1); (I simply used a plane but any shape will do the job)

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DarkBeam
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Posts: 1666


The spaghetti formula coder


« Reply #4 on: January 22, 2012, 01:00:40 PM »

Thanks, I have the full frag formula too! wink
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Formulas are never too much (?)

blob
Strange Attractor
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Posts: 253



« Reply #5 on: January 22, 2012, 01:02:35 PM »

Cool free polyhedra software for more inspiration:

http://sourceforge.net/projects/antiprism/
http://bulatov.org/polyhedra/stellation_applet/stellation_010914.zip
http://sourceforge.net/projects/gsolaar/

 afro
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DarkBeam
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Posts: 1666


The spaghetti formula coder


« Reply #6 on: January 22, 2012, 01:22:20 PM »


Wow ty, AntiPrism does not work, which app should I run? They just crash! cry
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blob
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« Reply #7 on: January 22, 2012, 01:50:14 PM »

Wow ty, AntiPrism does not work, which app should I run? They just crash! cry

They all run fine here, perhaps you must put them in lower OS compatibilty mode if you use Vista/7.

I am far from knowing antprism well but I know how to generate most of the included polyhedron models, I've attached a few batch files for model generation and for viewing them drag the generated off files onto antiview.exe. The off generated by Antiprism 0.19.2 appear to be viewable by 3D apps who support the OFF format whereas those generated by Antiprism 0.20.pre18 seem to be openable only with antiview.

There is an antiprism website outside of sourceforge with plenty of examples of use but many pages appear to be down since a while unfortunately. Perhaps the wayback machine has them.

http://www.antiprism.com/

* batch files 4 antiprism.zip (3.61 KB - downloaded 148 times.)
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Adrian
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« Reply #8 on: January 23, 2012, 04:02:16 PM »

Hi

I am the author of the Antiprism project and happened to notice this thread in the site logs.

The Antiprism site was unfortunately offline for three weeks because of problems with the hosting/domainregistering comany. I was able to bring it back online again yesterday

   http://www.antiprism.com

I am not sure what the problem is with the OFF files produced by the Windows binaries in 0.20pre18. The OFF output should be text files in all cases.

A problem that sometimes arises is that unix and msdos use different line terminators for text files, and not all programs that read OFF will necesarily handle both formats. However, I have just checked the 0.19.2 and 0.20pre18 Windows binaries on XP and they both produced OFF files with msdos-style line termination.

If, for some reason, the problem is due to line termination there are various utilities that will switch between formats, say,

   http://www.sg-chem.net/u2win/

I made a 0.20pre19 snapshot a couple of days ago using a new method of creating the Windows package. It may have had some effect on the OFF file incompatibility and/or the difficulties of running the Windows programs

   http://tech.groups.yahoo.com/group/antiprism/message/6275

In general, I recommend using a 0.20 prerelease (if possible) rather than the old 0.19.2. The prerelease is easier to use and has a lot more features. There are some example commands for the prerelease here

   http://www.antiprism.com/ex_album/

Adrian.
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blob
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« Reply #9 on: January 23, 2012, 05:19:43 PM »

Hello, I think the OFF issue has nothing to do with the text file format as both appear to be valid windows text files.

What is certain though is that the content of files appears to be different from version 0.19 to version 0.20 for the same object and Meshman, Meshlab, Wings3D and Remesh all fail to open 0.20 files when they open 0.19 ones just fine.

However I have now found out that both OpenFlipper and OpenCTM can open 0.20 files so that issue isn't an issue anymore as far as I am concerned since I can convert them to other formats with those now.

Nice to see you popping around here.

Cheers.
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Adrian
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« Reply #10 on: January 23, 2012, 05:52:59 PM »

Thanks for the further information. I have a copy of meshlab and from a quick test it appears to have trouble reading an OFF file that contains colour data.

Most of the named polyhedra in Antiprism 0.20pre include colour data, but there are also uncoloured versions (starting with 'std_') of some of the common ones

    http://www.antiprism.com/ex_album/590_std_polyhedra/

It is also possible to strip an OFF file down to just the geometry (remove colours and faces with fewer than 3 vertices) with the 0.20pre command 'off_util -g'.

Adrian.

P.S. In case it is useful, I wrote a very basic command line program that will convert the geometry in an OFF file to 3ds format, which some modelling programs can read

   http://groups.google.com/group/geodesichelp/browse_thread/thread/30dc7ee504b4e238/18b8b9f4f2920a8d
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blob
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Posts: 253



« Reply #11 on: January 23, 2012, 06:28:22 PM »

Using the -g argument the 0.20 generated files are now compatible with all the apps I mentioned, thanks for the heads up, I can definitively put version 0.19 to rest now.

I have grabbed the converter also, might come in handy, thanks.
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DarkBeam
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Posts: 1666


The spaghetti formula coder


« Reply #12 on: January 26, 2012, 09:17:25 AM »

Hey hello grin

Is there a chance of getting the 3D cartesian coordinates of vertex of some simple polys? wink Luca
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Adrian
Guest
« Reply #13 on: January 26, 2012, 03:25:08 PM »

Hi Luca

If you just want coordinates (rather than expressions for coordinates) you can copy the coordinates from an OFF model into a file using the Antiprism off2crds program like this

   off2crds std_cube > std_cube.txt

The file std_cube_coords.txt contains

1 1 1
1 1 -1
1 -1 1
1 -1 -1
-1 1 1
-1 1 -1
-1 -1 1
-1 -1 -1

The "standard" polyhedron collection includes common polyhedra using well-known "nice" coordinates

   http://www.antiprism.com/ex_album/590_std_polyhedra/

Pyramids, prisms, etc. models made of regular polygons are here

   http://www.antiprism.com/ex_album/560_polygons/

Adrian.

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Adrian
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« Reply #14 on: January 26, 2012, 08:27:30 PM »

I noticed a mismatch of file names in my message. If the command is

   off2crds std_cube > std_cube.txt

Then the coordinates are in std_cube.txt !

Adrian.
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