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Sunday, May 1, 2011

Done


So here's the finished product. Neither as awesome, as legible, or as non-overlapping as I was hoping. Fun times though. I may have learned something interesting about topology.


Sisu Sphere

So I had the brilliant idea of making my Sisu ambigram (thats what it says, by the way) into a three dimensional object. My thought process was this: Its one continuous line, so it would be cool to describe it as a mathematical function. But it overlaps itself, meaning it can't be written as a single function. It could be written piecewise as maybe eight functions, but that's not what I was going for. Then I realized that if it were inscribed on the surface of a sphere rather than the two dimensional plane, it wouldn't have to overlap itself. And I think if it were done in polar coordinates it could be written as a single function. Then, if you projected light though it at the critical angle onto a flat surface, you'd get the original 2-dimensional image.



I went to bed dreaming about how to use Sketchup to do this, and figured I could use the reverse technique as well: project the two dimensional image into three dimensions and intersect it with a sphere (something both possible and easy in Sketchup!), then just cut away the surface of the sphere that aren't part of the letter-lines.

Here's the projection:

and intersected with the sphere:

After some cleanup, you get a sphere with the lines on it, which you can subtract the superflous parts from:


and lo, here's sortof what I was going for:



Only sort-of, though. It has the full ambigram as separate halves on the front and back, which is not what I wanted. Its neat, but its not a single piece, I'm trying to figure out if what I want to do is even possible now.

[update] IT WON'T WORK! YOU MANIACS! YOU BLEW IT UP! Or maybe that's just how I designed it. I think in order to do what I want I'm going to have to make some of the pieces cross through the center, which I'm having some trouble visualizing.