## Sunday, February 15, 2015

### A 3D Printable Model of Cloud Gate aka "The Bean"

There are few works of modern art as beloved as Chicago's Cloud Gate, aka "The Bean".  It is interactive without having any moving parts, and indeed without being mobile at all.  Nobody at any age can resist engaging with their reflection in its curiously curved surface.

I started playing with TinkerCad because I wanted to use the 3D printer at work, a Makerbot Replicator, to print custom enclosures for my other electronics projects.  I thought that printing a model of Cloud Gate would be an easy way to learn to use the system before building my enclosures.  It turns out that I had it completely backwards.  To print an enclosure out of basic shapes (cylinders and boxes) is many times easier than designing your own custom surface for printing, and it took me a very long time to finally get it right.

I learned a few things about Cloud Gate as I worked on this model:
• Cloud Gate as seen from above is not a perfect ellipse.
• Wikipedia and all other sources including Anish Kappor's own website as the dimensions of Cloud Gate wrong.  In particular, the height of the arch.  You only need to stand under the arch to see that there is no way that it is 12 feet high.  At most, it might be 10.
• It is not possible to continuously deform a sphere into Cloud Gate.  Its derivatives are discontinuous at certain points on the surface, so I had to resort to Bezier curves to model it.

 I am 6' 1" tall.  There is no way that the arch is 12 feet tall.  If I put my hand straight up, I can come within a foot of touching the arch.
Once I finally got the right form for the equations that generate the model, it was simply a matter of tuning the constants that generate the surface to match Cloud Gate as closely as possible.  I'm confident that my current version of the model is close enough that, while certainly not an exact copy, nobody would be able to tell the difference even if I scaled mine to the size of the real thing and put them side-by-side.

 The evolution of the model.  The earliest model was printed in 2 separate pieces connected with pegs before I realized that the model prints fine when it is printed upside-down with supports and a raft.
 The underside of the models.  I think that they look better printed at standard resolution because the natural color PVA comes out shinier.

 The model is well-balanced enough that it does not require a stand to sit normally.

 End-on, Cloud Gate has an egg-like shape.
 The underside of the model showing the omphalos, or navel.
I recommend printing the model upside-down using supports and rafts, 25% infill and standard quality.  The supports are straightforward to remove using a razor blade.  The higher infill is necessary because the flat surfaces have a tendency to sag a bit at lower infill, and the standard quality prints with a larger radius and gives a shinier result.

It's also pretty fun to take my shape generator on TinkerCad and play with your own variant of Cloud Gate by editing the parameters.  If I feel bold later, I may try having one 3D printed in steel then buffing it to a mirror finish for the ultimate desktop Cloud Gate.