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"Perfect" Klein bottle (now in full color too!) [message #91822] Thu, 12 June 2014 16:13 UTC Go to next message
avatar virtox  is currently offline virtox
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Registered: August 2008
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Hi all,

It's been a while since I posted here myself, but after five years in 3d printing it was high time I'd tackle the Klein bottle.
I been having a love/hate relation with this shape ever since I first saw it:
So elegant, yet.. something was wrong.

Well not any more!

Klein bottle - Voronoi weave:

index.php?t=getfile&id=61853&private=0

index.php?t=getfile&id=61854&private=0


The Klein bottle.

A mathematical classic, it was first described by the German mathematician Felix Klein in 1882 and is a great example of a non-orientable surface. It has no defined inside or outside, as the surface loops back on it self.

This is my take on one of the more popular exercises in 3d printing, hoping to complement the idea and perfection of the original surface and previous attempts before me.

Crossing borders

Because there is one thing with the physical versions I have seen so far. They lack the spirit and esthetics of the original concept and have an issue at the junction.
Whenever the bottle loops back in on itself, at the crossing, one usually sees a crude fuse/weld, or simply a blunt hole in the surface through which it passes itself.
Now for the transparent glass-blown versions that can actually function as a bottle, I think this is an acceptable compromise and I applaud the skills of the craftsmen.
But with 3d printing I felt we could do better.

Weave!
So to get around this issue, one can apply a pattern that allows for the surface to go through itself without touching or visually disturbing the flow of the surface itself.
I chose a cellular Voronoi pattern that is "self-aware":
It does not touch the passing surface, but weaves perfectly in between itself.

How was it made
This model was created using a custom build tool set which utilizes Voxels.
First, I ran a charged particle simulation, which distributes the particles evenly across the endless surface of the Klein bottle, while taking into account the different "planes" of existence. Then in a voxel-space the cellular pattern is created using those particles as voronoi cell centers, but again taking into account the different planes.
And finally the model was converted to polygon format for uploading and 3dprinting.

[Updated on: Fri, 10 October 2014 06:35 UTC]


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Re: "Perfect" Klein bottle [message #92065 is a reply to message #91822 ] Mon, 16 June 2014 21:08 UTC Go to previous messageGo to next message
avatar ttoinou  is currently offline ttoinou
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Awesome!
I didn't understand in your algorithm how did you manage to make voronoi cells not touching each others at the intersection ?
Re: "Perfect" Klein bottle [message #92067 is a reply to message #91822 ] Mon, 16 June 2014 21:53 UTC Go to previous messageGo to next message
avatar bulatov  is currently offline bulatov
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Congratulations Stijn!
You've made perfect virtual self intersection of that surface.

I guess we now need to add such cool cellular surface patterns to ShapeJS as well.


Vladimir Bulatov, 3D graphics researcher, Shapeways
Re: "Perfect" Klein bottle [message #92101 is a reply to message #92067 ] Tue, 17 June 2014 10:54 UTC Go to previous messageGo to next message
avatar Wahtah  is currently offline Wahtah
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two thumbs up!
Re: "Perfect" Klein bottle [message #92123 is a reply to message #91822 ] Tue, 17 June 2014 16:19 UTC Go to previous messageGo to next message
avatar EricHo  is currently offline EricHo
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I love this elegant design variation of the Klein Bottle Opener. Next step 3D print in metal?


Social Media Specialist | Shapeways
Re: "Perfect" Klein bottle [message #100954 is a reply to message #92123 ] Fri, 10 October 2014 06:28 UTC Go to previous messageGo to next message
avatar virtox  is currently offline virtox
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@all Thank you for the kind words! :-)
@ttoinou I hope to make a video showing how it's done.
@eric Metal is certainly an option, but not every Klein bottle is an opener, lol ;-)

Unfortunately the original in WSF and family is a bit overpriced with the new pricing.

But I figured I'd illustrate the shape even better with color anyway:

Klein Bottle - Voronoi Weave - Color:
index.php?t=getfile&id=73857&private=0
index.php?t=getfile&id=73858&private=0
Click here


[Updated on: Fri, 10 October 2014 06:35 UTC]


- Artist / Engineer / Designer / Shopowner / Volunteer / Moderator -
Re: "Perfect" Klein bottle [message #100969 is a reply to message #100954 ] Fri, 10 October 2014 12:41 UTC Go to previous messageGo to next message
avatar numarul7  is currently offline numarul7
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Registered: January 2013
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With color it is more visible the the surface forming in.

I`m not in to the "mathematical stuff" , but heh :)


numarul7 jewelry and design
Re: "Perfect" Klein bottle (now in full color too!) [message #101073 is a reply to message #91822 ] Sat, 11 October 2014 15:13 UTC Go to previous message
avatar RobTorres  is currently offline RobTorres
Messages: 68
Registered: August 2013
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Wonderful job at the intersection of the handle and the bottle!


https://www.shapeways.com/shops/robsmakershop

 
   
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