Unraveling Geometry

A game development Odyssey

This is the story of the making of Hypotenuse, a game that explores the harmony between Geometry, Color, Sound, and Mind. It is a tale of adventure, mathematics, and programming.

It has been said one can go mad playing around with magic that one does not understand, and perhaps the same is true of mathematics. One must truly already be mad to attempt to harness the language of the universe and the music of the spheres in a few thousand lines of code. Fortunately, I am rather qualified in that department; my math, on the other hand, is mostly hitchhiker math that I’ve picked up along the programming road. But hitchhikers know the best songs, so it all balances out.

I believe the dream of this game began back some time ago on the Upper West Side of Manhattan. I had been working at an advertising agency among some tremendously damn smart programmers (see niltoid, onedayitwillmake, dhaakon, midnightsnacks, mstudio, jlaquinte, hikirsch to name a few). We would encourage each other to read books like Daniel Shiffman’s The Nature of Code and learn as much as possible about animation, ML algorithms, Arduino, everything. They were a tough bunch of dudes to keep up with especially with the Margaritas!

I had just finished building a JS/CSS3 3D flip book for British Airways and was still recovering from having taken the red pill and woken up in the Matrix of linear algebra and CSS transforms. But with the taste of this Math blood in my mouth, I was excited to help out on the Fractalizer project for IBM ( celebrating the anniversary of Mandelbrot’s Fractal ) with my bud onedayitwillmake, who did most of the fractal code, but, as usual, showed me all his cool tricks. While doing research on L-systems, I came across a pdf called The Algorithmic Beauty of Plants. It just so happened that that summer, I had been taking a weekend Botany class at the New York Botanical Gardens, being a nature-starved New Yorker at the time, and I had gotten rather deep into Earth’s Friendly Genius, Buckminster Fuller, while fantasizing about roof top greenhouse gardens. I had built a few model Geodesic Domes, made a Bean-segrity project and was curious enough about this thing called geometry to even tackle a bit of Euclid.

So I would ride my beautiful old dark blue Raleigh single speed up the epic Hudson, up under the George Washington Bridge, and across the potholed Bronx to go and look at some plants on the weekends. Occasionally, I would stop at the Cloister’s on the way back and admire the beautiful medieval herb garden, look at the old herbals in their book shop, and, of course, check out all the dead knights and things. I sensed that there was something I was missing among the uprooted gothic columns, arches, and stained glass windows, some idea, like some fairy darting in the sparkling leaves of the sun drenched trees that you can only see out of the corner of your eye, some Chalice of Perceval’s or some lost recipe for some alchemical potion of Paracelsus.

But then I found Michael S. Schneider’s thrilling book A Beginner’s Guide to Constructing the Universe, the keystone of this great arch. This book indeed was so intriguing and magical and I just wanted to, not only draw all of the polygons and stars that the book details and illumines, but to figure out how one would go about programming all of them. And so, that’s how I found myself on this Spira mirabilis.

It has been quite an amazing adventure so far and, hopefully, it is only just the beginning. And though the game is nearing completion ( well, the MVP anyway ), I did pull a Penelope a month or so ago ( i.e. I had to stay up all night and unravel the whole damn thing ) and it occurred to me that I should start documenting some of the programming and math tricks I’ve learned along the way. So stay tuned.