Monday, March 29, 2010

Mobius Stripping: Adventures in Infinity

I was at an art exhibit over the weekend and one of the artists was exploring the relationship between the finite and the infinite.

He postulated that the simplest finite expression we have is bianary language.  ON or OFF.  Yes or NO. 0 or 1.  And from those simple choices, stacked one on top of the next, we reach infinity.  Which got me thinking about computers and Revit.  I had never given much thought to the idea that everything we do on our computers boils down to a binary expression....and from those simple choices, stacked one on top of the next, we develop our work, our designs, our lives...out to infinity.  The concept stuck with me.

So in the spirit of the infinite, I wanted to look at how REVIT would deal with a MOBIUS STRIP....and thus far, I found that it deals with the form poorly.  But it did generate some of the wackiest errors I have seen so far while using the this one:

First I tried the easy way.  I swept a rectangle along a 180degree arc, rotated one end of the the form, and then made a mirror copy.

In essence it worked, but there were 2 problems. First, the ends of the form didn't blend very well, and Second, I was looking to make the impossible, a flat one sided object! I consider extruding a solid along a path, no matter how thin the solid, to be cheating.

My next attempt involved trying to stich some reference lines together.  I made a rig to 3d-Snap the curves to.  I was able to get 87.5% around the path like this:

But in the end, it didn't work either...I got a deformed clam shape that you'll see at the end of this movie:

My last attempt is as close as a i came to success.  First I made an arc surface family that i could also control the rotation angle of its ends.

Then i nested 8 of them together, worked out the connection angles and it worked pretty nicely.

The edges still don't blend perfectly but it got close enough to satisfy me...for now.

Hmmmm....Conquering the Infinite with Revit Architecture!!!!

Somebody call Carl, I smell a slogan for AU next year... 

3D Models to Share:

Mobius Strip Segmented.rfa
Mobius Strip from reference lines.rfa


  1. Very cool. Still trying to work out how you got the angle parameter???? Also, its just a shame we can't use an array parameter, to array the segments. :-)

  2. Hi Phil,

    Thanks for sharing.:-) Very cunning, I was racking my brain on how you resolved the rotation issue and failed to realise that you had nested a rotation family until I saw your file. :-)

  3. Thought I'd give this one a shot too. I went with v2011 and in a mass family.
    I used a variant of your first attempt, but added in more profiles to help smooth out the finished product. I think it looks pretty smooth. I also built in some parameters for the diameter, width and thickness.

    Family can be found here;

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