First of all, I wish to thank Jaap for Jaap's Puzzle page and the Sphere-Symmetries Applet, wich have given me a lot.

I created a script-file for the Pov-Ray program, which can visualize Jaap's Sphere in other shapes.
The reason for me to do this was that I had a concept years ago to expand Jaap's Sphere. This concept included also, to illustrate the inner levels of puzzles, working with a set of hollow spheres. Strictly speaking it came to this concept, when I had taken apart my V-cube 7 for the first time, and I learned a few things about the construction principles of it, which really fascinated me. This concept included also to show the external representation of puzzles in other forms (i.e. non-spheres), and now I am glad to be a little bit closer to the latter.

What the script can do:

the script can take any configuration of Jaap's Sphere Applet, and show it in other outer shapes.
I decided to use cone-cuts (with the cone-cap (apex) at the origin), because they look equal on the Sphere-Applet and on the other shape's.

The advantage for using cone-cuts is, that the cuts on other shapes are similar to that of the sphere, i.e. it shows all Sphere-configurations exactly as on the Sphere. Even cuts are even easier to implement, but the size relation from the sphere to the shape must be more exact, and I wanted to show cone-cuts for getting them more familiar to others.

The usage of the script is convenient:
1. copy a configuration string from Jaap's Sphere Applet to the script
2. define the shape (to use) in the script
3. Hit the Run - Button in Pov-Ray.

if you want to try it, there is a bigger description in the attached *.zip file

Further examples (just to illustrate it a bit):
In case you want to try it: Version 02 with conical and planar cuts:New Version: Now planar and conical cuts can be mixed, and conical cuts can be defined more general, in freely moving the cone apex on the axle: edit: bug fixed (degenerate cone/cylinder error)
Thanks also to
-Pov-Ray (especially for the construction and render capabilities wich made it possible)
-Andreas Nortmann who encouraged me to post this

Jaap's Sphere is at http://www.jaapsch.net/puzzles/sphere.htm

and which took me no more than two minutes. I do not want to ask about the time you invested.

Great work.

Long live POV-RAY! Nice work....

Yeah, I started loving it when I got my splittings well for the first time. The first successful experiment was, when I splited a cube into two parts in subtracting a thin cuboid from it. The two parts can then be assigned to the cube again and when you do your next splitting, you can split 2 parts into 4 parts and so on. The simple statement is something like:

#declare Cube=difference {object{Cube} object{ThinCuboid}}

And the picture rendering of Pov-Ray is sooo professional

And thanks to everybody that is interested in this thread.

Stefan

Hi Stefan,

Thanks SOOO much for putting all of the work into this. It's fantastic. I'm very impressed you wrote the URL parameter parser in POV-Ray itself rather than writing an external program to parse and emit POV-Ray code. Your way is very simple and doesn't have any dependencies.

I barely know any POV-Ray but I'm learning here and there thanks to your code and some of Carl's.

If you haven't seen, I changed a few lines of your code to generate the images in this thread: viewtopic.php?f=9&t=24206

I have a few questions.

For each of the solids you've made, you instantiate the object with a "scale" factor. Each object has a different scale. What is this doing? Is it just a fudge to make them all look about the same size or is it needed for something beyond just aesthetics?

For the main camera, why are you looking very close to but not directly at the origin: <0.0, -0.01, 0.0> ?
Is this just to provide a tiny bit of depth instead of looking at the shape straight on?

I determined your long decimal expansion of the dwing constant is actually 2 * (sqrt(2) - 1) but where does this number come from? I haven't figure out where phi = 0.618034 but I assume it's the angle in some triangle where one of the sides of the triangle is of length dwing. I know dwing came from your cube wings code so is dwing just used for your shCW object?

I know it strays a bit away from your purpose of rendering Jaap's spheres but do you plan on extended your code to accept planar-cuts in addition to conical cuts? I can't add support yet because I don't fully understand all of your code.

Thank you Brandon

I believe it was Carl's Code that first inspired me to try Pov-Ray.
It has delighted me that you have used the script from me. Your animated ETO is cool.
No it was as you suspected, fudge. I wanted to equalize the sizes of the different objects.
The upmost line of pixels on the rendered image was dark. The sky_sphere in the background seemed to be to small, and I didn't know how to resize it.
The direction-vector-sets I have all from Jaap's Sphere- sourcecode. Except the cube-wing-set with equal distances, which is the only set that uses dwing, but not phi. phi was to easyfy the construction of dodecahedron-faces/corners/edges.
dwing is to equalize the distances in the cube-wing-set. Here is the way it came from
c and d must be equal
d=c=sqrt(2)*t
so t=d/sqrt(2)
e=2*t + d
e=2*d/sqrt(2) + d
e=(1+2/sqrt(2))*d
d=e/(1+2/sqrt(2))
e was defined 4 by me
dwing had to be the half of d
the number is 0.828427. More precision is not needed.
Your "2 * (sqrt(2) - 1)" is correct (congratulation on finding it). It's used for constructing the shCW object, and for the cube-wing direction-vector-set, but this is not included in Jaap's Sphere. It was added by me for trying out the cube-wing set, as you know. And I don't know, wether it gives serious puzzles. Here is again the picture of it, that I posted in the gelatinbrain-thread.
Yes, maybe you can help me, the size relations have to be defined. If you have an idea, maybe we can do a 'joint-venture'

Thanks Brandon

Here are dodecahedra from gelatinbrain, I could sketch.

Could you please tell how they all turn Stefan Schwalbe? The reason why I ask is that I don't go on there at all like I use to and that was after my best friend help me put a program on my computer so I could and play with the puzzles. I'm sorry I accidentally deleted it. So if anyone wants to help me with this please send me a PM through twisty puzzles and I'll give you the info. Did I mention I love that website?

The direction-vector-sets I have all from Jaap's Sphere- sourcecode. Except the cube-wing-set with equal distances, which is the only set that uses dwing, but not phi. phi was to easyfy the construction of dodecahedron-faces/corners/edges.
dwing is to equalize the distances in the cube-wing-set. Here is the way it came from
c and d must be equal
d=c=sqrt(2)*t
so t=d/sqrt(2)
e=2*t + d
e=2*d/sqrt(2) + d
e=(1+2/sqrt(2))*d
d=e/(1+2/sqrt(2))
e was defined 4 by me
dwing had to be the half of d
the number is 0.828427. More precision is not needed.
Your "2 * (sqrt(2) - 1)" is correct (congratulation on finding it). It's used for constructing the shCW object, and for the cube-wing direction-vector-set, but this is not included in Jaap's Sphere. It was added by me for trying out the cube-wing set, as you know. And I don't know, wether it gives serious puzzles. Here is again the picture of it, that I posted in the gelatinbrain-thread.
Yes, maybe you can help me, the size relations have to be defined. If you have an idea, maybe we can do a 'joint-venture'

Thanks Brandon[/quote]

Great...and WOW, it happens!



Don't mean anything but you are great to add this equalized distance feature into the program. It will actually bring a series of jumbling puzzles.

Thank you Stefan Schwalbe for sharing.

Hi Leslie, I think you should add one level of unbandaging to that.

See: viewtopic.php?p=285908#p285908

WOW again. I think I missed a lot here.

Unbandaging is OK however just the plain cuts are already quite challenging. I agree that there can be many variations when unbandaged and difficulty is unpredictable(like Bermuda series).

All platonic solids are applicable with this idea but manufacturing will be challenging with many axis basis. In my head, I call this procedure 'axis splitting'.

Hi Darren Grewe

the 1.1.* puzzles are face-turning dodecahedra
the 1.2.* puzzles are vertex-turning dodecahedra
the 1.4.* puzzles are edge turn
the 1.3.* are mixed face turn and vertex turn
the 1.5.* are mixed face turn and edge turn
the 1.6.1 is mixed vertex and edge turn
the 1.7.1 is mixed face turn, vertex turn and edge turn

installing gelatinbrain: Executable Jar Installer
If you still need help running gelatinbrain on your computer please pm me. I will try to help.

Thank you, Stefan.
You must have spent enormous amount of time and labor for this.

Thank you for the replies, guys!

I was specially pleased about your reply, Leslie Le

@Leslie Le I'm very interested in your project. Can you pm me your progress



I would like to see, how it scrambles, someone has to make a proof. I will try it myself asap


@gelatinbrain
configuring for a puzzle cost about 1 minute. All together it took about 3 hours
Thanks to you again, your Virtual Magic Polyhedra are great.

Here are icosahedra from gelatinbrain, all that I could visualize with the Pov-Ray script.
The 2.1.n puzzles are faceturning icosahedra
The 2.2.n puzzles are vertexturning icosahedra
The 2.3.n puzzles are edgeturning icosahedra
The 2.4.1 puzzle is a mixed faceturning and vertexturning icosahedron

I changed the script another time. Now planar and conical cuts can be mixed, and conical cuts can be defined more general, in freely moving the cone apex on the axle:There are 5 cases for the cone apex:
1. under the origin (negative)
2. on the origin (0)
3. between the origin and the divider (between 0 and 1)
4. on the divider (1), planar cut
5. above the divider (higher than 1)

I have attached the new script at the place where I attached the first script (in the first post of this thread).
Stefan

Hey Stefan, very elegant way to handle planar cuts as cones. I love how the curvature can now be varied by changing the cone's vertex.

I'm having a good time playing with the code:

I couldn't figure out how to make the Dreidel Skewb (my avatar) though. I thought the cone vertex would have to be > 1 but that doesn't seem to create the backwards curvature I'm looking for.