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Klein Bottle


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yeah, I tried to post just as the forum went down. Here it is.

 

This is something I've been wanting to try for a long time. It's a Klein Bottle, a 4D shape with zero volume. This is its 3D immersion- it usually hums along in 4D, without intersecting itself. Find out more at Acme Klein Bottle. Anyway, some weird things happened when I finished this model. First, all the normals ended up pointing the right way. I thought I might have a place where two adjacent patches would have opposite normals, but it all worked out (aside: why isn't there a feature where you select a patch, and all the surrounding surfaces mimic the normal of that patch?). Also, if I select a point on the "outside" and press "/" the entire model is selected. Weeeeird. Anyway, here it is. A short animation is on the way. Catch you on the flip side... oh, wait....

-Zev

bottle.jpg

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An odd thing happened during rendering. This is something that I've noticed during a lot of long renders, but I remembered to document it this time. I'm running 10.5 on OS X. I'm waiting to upgrade until I absolutely need a new feature- haven't yet for the occasional school project, etc. Anyway, notice the abnormally large numbers. This happens at a certain point in all my long renders. This was rendered with the following settings: 320x240x24 targa, final, multipass 16x, shadows, reflections with 2 bounces, 20% motion blur, although I think it happens with all settings. Has anyone else had this happen? Is it fixed in the new versions?

-Zev

Picture_1.jpg

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Think two Möbius strips stuck together. Sorta. But not. Same principal: it's nonorientable– that is, you could stick a label on it, then slide it around so it was on the back of the same face, reading in mirror. It's all detailed on the ACME kline bottle website as linked earlier. There is also a fascinating page about it on Wolfram's website.

-Zev

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My first question would be...

 

How would you flatten that model so you can texture it?

 

-----------------------------------

 

Klein bottles freak me out... so do Möbius strips...

 

Neither of which is in my spell checker... I wonder if there is a connection?

 

If you cut a Möbius strip in half... lengthwise, you end up with 2 separate connected loops... what happens if you cut a Klein bottle in half?

 

I get so freaked out looking at that thing....

 

p.s. I have problems with infinity. As a child I was horribly frightened when I realized the never ending repeating reflection when you pointed a mirror at another mirror, would never ever stop...

 

Vernon "!" Zehr

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Not sure if this is what you had in mind, but http://www.kleinbottle.com/sliced_klein_bottles.htm has some sliced bottles. And regarding the mirror thing, you could set that up in A:M and view it from an angle that a human never could because our heads are in the way. I'll set it up if I get a chance... You'd just have to set the bounces reeeally high... I know that a thing called radiosity exists, but I haven't the foggiest idea how it works or how to set it up. Would this image benefit from it? How would I go about creating it? Yeah, infinity freaks me out too. I'd suggest reading the book "Zero: the Biography of a Dangerous Idea."

-Zev

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dang it Zev... now I want to know how it is rendered in the 4th dimension... And, I spose I'll never get to see that...

 

I don't understand this thing... this klein bottle.. Isn't the 4th Dimension time? What has time got to do with the bottle?

 

If you fill the bottle, from the "bottom" does it not fill? I understand how the Klein mugs work... standard cheapo magic trick... but I don't "Get" this bottle.

 

Your render seems accurate though... and I look forward to the mirror render too!

 

Charlie

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  • 4 months later...

Wow, this is an old topic... Did anyone happen to download the model and keep it? I lost this model and a few others I did in a weird backup thingy, and This one in particular I'd like back. Anyone? Thanks.

-Zev

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