Hyperbolic Tiling Challenge
uberzev
 |
heh, that image wasn't made with FF. 
There's a simple windows program for making hyperbolic tiles I'm using that image as a template for now. If I can understand the pattern in which the arcs are placed and sized I can make an efficient FF version. What I've been doing is manually position everything. |
|||
| Posted: August 16, 2012 6:08 am | ||||
ThreeDee
 |
Unfortunately it is not a repeating pattern other than around the symmetry axes of the center polygon. You would have to calculate every arc size and location with a script in any case. It seems to me after some study of the math behind proper hyperbolic tiling that uniform tiling (equal corner angle hyperbolic polygons) would require a recursive calculation for each subsequent arc once you know the previous one. That is where I gave up on accuracy and settled for visual similarity. I have managed to get the input image to (sort of) tile in this nonuniform hyperbolic tiling now. It is anything but optimized or accurate, but probably as close as I will ever have the patience to get it.  |
|||
| Posted: August 16, 2012 1:50 pm | ||||
Morgantao
 |
WOW ThreeDee, how did you do that?
How did you write the visual guide in a language even I can understand?! |
|||
| Posted: August 16, 2012 3:18 pm | ||||
SpaceRay
 |
WOW!! This is really great and beautiful ThreeDee, very well done.
Thanks for the link is very interesting and useful |
|||
| Posted: August 17, 2012 12:14 am | ||||
|
SpaceRay
|
Sorry to ask this very basic question but, how do you convert the 2D line into a 2D circle?
Of course that I am very far away from all the knowledge about this that many of you have In all the filters available in FF to make this are for 3D Spheres and not for 2D ones, and they distort the images as they try to simulate the 3D effect on a ball instead of a plain 2D image  |
|||
| Posted: August 17, 2012 12:23 am | ||||
|
uberzev
|
Here SR...
http://www.filterforge.com/filters/1762.html You may need to flip your image vertical first. |
|||
| Posted: August 17, 2012 12:59 am | ||||
Skybase
 |
aka polar coordinates. Just another coordinate system AND the filter itself is also available in Photoshsop. Useful for wrapping 360 images. | |||
| Posted: August 17, 2012 5:59 am | ||||
|
SpaceRay
|
Thanks uberzev and Skybase, but I have tried all the unspherize and spherize filters available in FF and also the polar coordinates ones from FF and the one from Photoshop AND I am sorry to tell that I must be dumb because I have not been able to make the conversion from the straight line to the round lines.
I have made this right with a very basic color line to make a target like using any of this filters, BUT you convert the colors to real shapes they get very distorted and loose much the original shape and does not look at all as the very good examples shown. And I tried it with vertical rotation. 
Will have to search in Google how to convert 2D line to a circle in " Convert for dummies" |
|||
| Posted: August 17, 2012 8:34 am | ||||
|
ThreeDee
|
In FF3 it is like this: |
|||
| Posted: August 17, 2012 10:09 am | ||||
inujima
 |
ThreeDee,It is not a hyperbolic tiling.
A "Line" in Poincaré disk model must be a segment of a circle or a diameters of Poincaré disk. A curve made by above way is not a circle in x-y plane, so this curve is not a "line" in Poincare disk.  |
|||
| Posted: August 17, 2012 5:41 pm | ||||
|
inujima
|
I have some ideas to make a hyperbolic tiling in FF.
Although it needs a script component because using a loop processing, it is possible to make a hyperbolic tiling by FF.  |
|||
| Posted: August 18, 2012 2:39 am | ||||
|
ThreeDee
|
Hi Inujima,
Yes, I know, that described method gives you something resembling hyperbolic tiling that you have to distort by Curve and Lookup components (either before or after spherizing) to make them segments of a circle. You can output "proper" hyperbolic tiling with it if you do so. The limitation is that it is not regular tiling, meaning the tiles are not hyperbolic polygons with equal corner angles, just hyperbolic polygons. It definitely requires scripting to get the accurate position of the circles if you want to make regular tiling, for the reason you stated. |
|||
| Posted: August 18, 2012 3:04 am | ||||
|
ThreeDee
|
This is the tiling after distortion. It is pretty close to the real thing. (I just made the distortion curve by hand.) |
|||
| Posted: August 18, 2012 3:14 am | ||||
|
inujima
|
I say it is impossible to make circle segments from any half circles in polar coordinate by this way. If one half circle goes to a circle segment, then other half circle having different radius will not go to a circle segment. |
|||
| Posted: August 18, 2012 6:22 pm | ||||
|
inujima
|
I challenged scripting a hyperbolic tiling in Poincare disk model too.
It was faster than I had thought. This is the first step of hyperbolic tiling.   |
|||
| Posted: August 18, 2012 7:06 pm | ||||
|
uberzev
|
Scripting is cheating..
Nice job though. |
|||
| Posted: August 18, 2012 7:20 pm | ||||
|
SpaceRay
|
WOW! Inujima this look really good and very well !! Beautiful examples, specially this one
The tiling is very well done on all of them Congratulations!
Well I think is the best way to do it and if he can do it and said that was faster than he thought then I think is good to do it although perhaps you wanted to do it without scripting. |
|||
| Posted: August 18, 2012 9:04 pm | ||||
|
Skybase
|
2.0からいろいろと自分で試していたのですがやはりスクリプトにはかないませんね。犬島さん、すごいです！自分は使ったとしてもPythonかMelで単純作業用のスクリプトぐらいしか作れませんし、LUAなんて見てもなんかまだわからないことだらけで．．．． | |||
| Posted: August 18, 2012 11:13 pm | ||||
|
SpaceRay
|
Translation Google The script does not come true still I had to try a lot from yourself. Mr. Inujima is amazing! I can not make only about the script for simple tasks in Python or Mel even with myself, full of something that I do not know yet I can see LUA Translation Bing Was it yourself from 2.0 and is still the kanaimasen script. Mr. Inujima, awesome! Even myself using can't make only about working of simple scripts in Python or Mel, what LUA is something I don't know still fraught. I suppose that none of this both surely shows the real meaning of the text |
|||
| Posted: August 18, 2012 11:58 pm | ||||
|
Skybase
|
Now I feel like I spoke engrish. | |||
| Posted: August 19, 2012 12:03 am | ||||
|
SpaceRay
|
http://www.engrish.com/ there are 650 pages !!! of examples showing this "engrish" OH, yes this is very funny and do not know hown can they translate it in that bad and weird way |
|||
| Posted: August 19, 2012 12:17 am | ||||
|
Morgantao
|
Engrish? I thought it was Japlish! |
|||
| Posted: August 19, 2012 12:39 am | ||||
|
SpaceRay
|
I have just found that is also possible to make another kind of Hyperbolic tiling that is over a rectangular plane, I mean that is the same as the one above here BUT after reaching the end of the circle it continues beyond growing again outward.
This is from Vladimir Bulatov and have more in Deviant Art account that is here Also there are some other good examples 
and more in this google search |
|||
| Posted: August 19, 2012 1:49 am | ||||
|
ThreeDee
|
Excellent work, Inujima! | |||
| Posted: August 19, 2012 3:00 am | ||||
|
Skybase
|
Anything goes spaceray: http://skybase.wordpress.com/2012/01/26/what-i-saw/ | |||
| Posted: August 19, 2012 3:05 am | ||||
|
SpaceRay
|
Skybase I have already seen this beautiful and great creations you have with Artmatic and I like them much, BUT regretably Artmatic is ONLY for Mac |
|||
| Posted: August 19, 2012 5:23 am | ||||
|
inujima
|
このフィルターに関していうと、LUAのというよりは数学的な内容が大半を占めています。
実際にスクリプトの中を見てみると、多くは数学の数式で埋められているけどもスクリプトの構造自体は単純なものなのです。 My first step filter of hyperbolic tiling is here. For some time, I will make a filter putting on next target to Escher's Circle Limit III.
 Hyperbolic tiling v1.ffxml |
|||
| Posted: August 20, 2012 4:32 pm | ||||
|
SpaceRay
|
WOW!!! Inujima, I can´t believe the awesome and amazing filter you have done !!!!! I am breathless and speechless   
Love your filter and  love you for having made this in such a perfect and excellent way !!!!
When this thread started I never imagined at all that the result could such a beauty and real gem as the one you have done here Inujima. Thanks a million for making this fantastic filter!!!! AND furthermore is fast TOO !!!  |
|||
| Posted: August 20, 2012 5:22 pm | ||||
|
SpaceRay
|
here is bigger in more detail to see the beauty done by the filter |
|||
| Posted: August 20, 2012 5:28 pm | ||||
|
SpaceRay
|
and even more closer detail to see how really perfect and how beautifully is made the fractal tiling into far far away |
|||
| Posted: August 20, 2012 5:30 pm | ||||
|
SpaceRay
|
The above one has been done using the preset 1 included and this one is using preset 3 and making it more central, both is using the same source image |
|||
| Posted: August 20, 2012 5:35 pm | ||||
|
SpaceRay
|
and here in more detail, like much how the fractal tiling is done that looks so well even on the tiny parts |
|||
| Posted: August 20, 2012 5:47 pm | ||||
|
SpaceRay
|
and this is using a custom settings
Like much also that the tiling is made that you can rotate the tiling as it was a sphere so you move the textures like it was on sphere rotation.  |
|||
| Posted: August 20, 2012 5:51 pm | ||||
|
SpaceRay
|
This can have LOTS of possible and different combinations using just the same source and look different   |
|||
| Posted: August 20, 2012 5:57 pm | ||||
|
SpaceRay
|
By the way if you wonder how I have made the white lines , is very easy, this is JUST using a white frame in the border of the image as shown here
I will put more examples later  |
|||
| Posted: August 20, 2012 5:59 pm | ||||
|
uberzev
|
Amazing scripting. I don't understand any of it.
BTW this image can be reproduced with 3, 4, 1 in the settings.  |
|||
| Posted: August 20, 2012 6:56 pm | ||||
|
SpaceRay
|
I have seen furthermore that the SCALE setting brings hundreds more possible variations!!!
I am really amazed of what can be done with this filter. See how this filter have converted this shelf with clocks in such wonderfull way
If you that is one of the experts do not understand it, what I have to say? well yes I can say that this script looks to me like the japanese written above  |
|||
| Posted: August 21, 2012 2:09 am | ||||
|
SpaceRay
|
See the quality in more detail here |
|||
| Posted: August 21, 2012 2:17 am | ||||
|
SpaceRay
|
and another part showing better how the wood shelf is made in this beautiful way |
|||
| Posted: August 21, 2012 2:19 am | ||||
|
ThreeDee
|
I take it back. It is not just excellent, it is incredible!
I am feeling quite escheresque already.  |
|||
| Posted: August 21, 2012 2:23 am | ||||
|
SpaceRay
|
And also here to show all the tiling until the end
I still can´t believe that this can be done with this filter, and this has been a unexpected surprised as I imagined simple things could be done BUT never things like this one shown here  |
|||
| Posted: August 21, 2012 2:27 am | ||||
|
SpaceRay
|
I agree, Excellent is not enough, it is incredibly awesome and amazing AND IT ALSO WORKS PERFECTLY WITH NON SQUARE IMAGES !!! The clocks image here is really a rectangular photo BUT this filter does not care if it square or rectangular, it makes the tiling in the top part of the photo as it was square. SO, this also open a much wider possibilities as ANY image can be used and it does have to be square to work right in this filter. Here is the real result from the NON SQUARE image  |
|||
| Posted: August 21, 2012 2:34 am | ||||
|
SpaceRay
|
And how about a golden machinery with lots of mechanical gears? |
|||
| Posted: August 21, 2012 2:39 am | ||||
|
SpaceRay
|
and see more closer how excellent quality it brings on the tiling just adjusting a little the settings |
|||
| Posted: August 21, 2012 2:43 am | ||||
|
SpaceRay
|
I am still not really believing that this is possible !!!
Looking at this great beauty and I can´t help feeling really amazed when I see this jawdropping result The green arrows looks like it was perhaps the entrance for space ships into the tunnel of this giant steampunk alien ship.  |
|||
| Posted: August 21, 2012 2:54 am | ||||
Join Our Community!
Filter Forge has a thriving, vibrant, knowledgeable user community. Feel free to join us and have fun!
15,384 Registered Users
+9 new last day!
112,641 Posts
+20 new last day!
10,103 Topics
+15 new in 7 days!
Recent Forum Posts:
- Be able to replace and update obsolete components in some easy way by GMM
few minutes ago - Grouping and ungrouping sometimes does not work right by GMM
few minutes ago - Filter list preview much bigger? Filter library inside FF bigger too? by SpaceRay
10 minutes ago - Official discussion: upcoming Filter Manager by SpaceRay
40 minutes ago - Sketchy Painting by emme by SpaceRay
45 minutes ago - Beta Gallery by Ghislaine
50 minutes ago - Free Simplifier Plugin (Win only) by SpaceRay
1 hour ago - Photoshop CS6 - Interesting and useful information and free tutorials by SpaceRay
1 hour ago - Paint HDRtist by lipebianc by SpaceRay
1 hour ago - Flame Painter by SpaceRay
2 hours ago - Library Capability by SpaceRay
2 hours ago - Toonstone by jitspoe by Skybase
yesterday
Recent Wiki Edits:
- Indigo_
Ray by Indigo Ray
February 25, 2013 - Optimizing_
Filters_ by Crapadillafor_ Speed
February 22, 2013 - Feature_
Wishlist by Crapadilla
September 19, 2012 - Main_
Page by Crapadilla
September 19, 2012 - Filter_
Construction:_ by CrapadillaFundamental_ Techniques
September 19, 2012
