brainwagon

I’ve mentioned it before: when you are interested in as many strange things as I am, web surfing can be dangerous to your time. Lately I’ve been going through my blogroll with two purposes in mind:

• Delete the stuff that I don’t read anymore, or consider boring.
• Tag the remaining links with slightly more meaningful tags in Google Reader.
• Lastly, find more cool stuff by mining the links of blogs I already have.

Courtesy of one of the mathematics blogs (I can’t remember which one), I located The Fitful Flog, a fascinating blog which had many interesting bits of paperfolding. Not the traditional crane stuff mind you, but interesting stuff that used a combination of straight and curved folds to make things that I have known as “developable surfaces”. Don’t know what that means? It means that is has zero Gaussian curvature. That didn’t help? It means that you can flatten them onto a plain without distortion (stretching, compressing, tearing). In other words, it is the class of surfaces that you can get by folding paper.

The thing that piqued my interest was this Champagne Flute, which I folded up…

It’s a very simple pattern, using a series of straight and curved folds. Very neat.

I meantioned this to Tom, who reminded me that the person that probably brought the term “developable surface” into my vocabulary, Paul Haeberli (one of the many notable computer graphics people with the initials PH) had some interest in the topic, and, in fact, had recently received a patent on the topic as well as apparently developing some commercial software for the design of developable surfaces. Very cool. It reminded me of this cool paper from SIGGRAPH 2004, as well as perhaps this successor. It’s all very cool.

Isn’t it amazing where the stream of the web can carry you on a Friday?

[tags]Origami, Mathematics, Developable Surface[/tags]

Addendum: Here are some more papers that could be relevent.

Addendum²: I was pondering this paper pattern, and realized I knew how it was created. To prove it to myself, I wrote a little C program that spit the model out in the form that my homebrew raytracing program could render. Voila.