Yesterday was our final meeting of the Bay Area Mathematical Artists for the academic year 2017–2018. We were back at Santa Clara University to visit their virtual reality lab, the Imaginarium! It was an amazing visit, coordinated by Frank Farris, Tom Banchoff (who is visiting Santa Clara University this semester), and Imaginarium director Max Sims.
While we were waiting for everyone to arrive, Tom generously provided donuts for us to snack on. But not until we were given a short presentation on a very special property of donuts — the “two-piece” property, which Tom discussed in his doctoral thesis.
A perfectly smooth donut — this is important, since bumps or ridges are problematic — has the property that if you take a knife and make a planar cut, you always get exactly two pieces.
Of course any convex shape automatically has this property. Donuts, however, are not convex, so they are special in this regard. Tom remarked that discussing this makes good breakfast conversation, since smooth bagels also have the two-piece property. But a sufficiently curved banana does not (think of the letter U and make a horizontal cut to get three pieces).
Once everyone arrived, Tom began with a presentation of his forays into computer graphics and animations. The first video he showed was made in 1968 with computer scientist Charles Strauss, also at Brown, which showed a torus turning inside out.
What was fascinating was how the video was made. Keep in mind this was long before platforms like Processing were available…. Even though each frame was black-and-white and consisted of line drawings of a torus in various different configurations, it still took about a minute to create each frame.
Then, each frame had to be photographed — using film, if you remember what that is. Then another minute, another photograph. Next, the film was sent on to Boston, where it was processed into a movie. The movie was sent back — and hopefully, it was just what you wanted….
Fast-forward to 1978, where the subject of the video was rotating cubes and hypercubes. I won’t try to describe it in words, but you can actually see the video online here.
It looks like the graphics in this movie were color graphics! But no, that wasn’t available yet. You see color because each frame used four photographs — each taken with a different filter on. These were overlaid to create a color graphic. Very creative, and again, certainly much more work than it would take today. Keep in mind that 1978 was forty years ago….
There were still three movies to go! Next, Tom showed us his 1985 movie about the hypersphere. We then got to see Tom’s animation of donut slicing, which was the virtual version of our initial demonstration. Finally, the last video was from 1999, which was a rotation of the flat torus.
The movies and talk took us halfway through the afternoon. Now it was time to try on the headsets and have our very own virtual reality experience!
We learned from Max Sims a little about the technical challenges of creating a good VR experience. First, 90 frames per second is ideal — contrast that with 30 frames per second when creating movies with a platform like Processing. And second, the response time of the headsets needs to be no longer than 11 milliseconds — that is, when you turn your head to look at something, the image has to change that fast — or else you’ll get motion sickness.
The way the lab was set up, everyone got their own computer (although it took me three tries to find one which had everything working properly). You can see people with headsets on and controls in their hands.
It is very hard to describe what it feels like with the headset on without experiencing it for yourself. But when you put on the goggles, you’re in a 360-degree visual environment. That is, when you turn your head to the right, you are seeing what’s to the right of your visual range in the VR simulation. You can even look down and see what’s underneath you! It was a little dizzying to look down and see a stream running underneath you, since that meant you were suspended in midair….
The hand controls were different for every experience. Some allowed you to move things, or select different types of building blocks to make 3D images, or select a different simulation. It took a bit of getting used to, and I didn’t fully get the hang of it in the hour we had to play around. But Max said we were welcome back to try out the lab again, and I do intend to take him up on his offer.
After our incredible experience, we went out for Thai — sixteen of us, this time! We spent over two hours at dinner, which is typical. These gatherings bring together a diverse group of people interested in all aspects of mathematics and art, and it seems we never run out of things to talk about.
Then the drive home. I was driving Nick, and we were amazed by the cloud formations we saw all along the way. Despite my rather dirty windshield, Nick snapped this gorgeous pic.
The clouds were like this for most of the drive home, and were a very fitting end to our last gathering of the semester.
Plans are underway to continue meeting throughout the summer, so stay tuned!
Creativity in Mathematics 