Gigagiggles Public Service Announcement #1
April 18, 2005

A friend of mine has a son in elementary school. He'd been assigned the following math problem: What's the sum of the internal angles of a 22-sided polygon?

I knew there was a formula for this but darned if I could remember (it's been WAY too long). So I grabbed a post-it note and scribbled some polygons...

3 sides = 180 degrees (that one I remembered)
4 sides = 360 degrees (pretty easy to figure out)
5 sides...
Well, I can make a pentagon out of a square and a triangle, so it must be 180 + 360 = 540.

Aha! I'm adding 180 degrees every time I add a side starting at 3 sides. If we call the numer of sides "n," the formula is (n-2)*180, and the 22-sided polygon has 3600 degrees among its internal angles. I proudly handed over my mess of a post-it note and finished my beer.

But I couldn't stop thinking about it. Why was I adding 180 degrees every time I added a side?

Later that night it suddenly struck me that geometry had something to do with my life (Yes, Mr. Cole, you were right. Sheesh). I make video games. Everything that you see in a modern, 3D game is constructed of polygons. Triangles more specifically. If you wanted to make a crate, you'd make a 6-sided cube with each face built of 2 triangles. The whole crate would cost you 12 polygons. Note the word "cost." The fewer polygons an object has, the faster your PC or Xbox or PS2 or whatever can draw it. Fewer polygons is faster. Faster is good. And now we know the formula for the minumum triangles you need to make an object...it's the "n-2" part of the equation above.

3 sides costs 1 polygon
4 sides costs 2 polygons
5 sides costs 3 polygons and so on.

Now look at this:



The figure on the left is the result of making a stop sign the fastest, easiest, most common way I know how in a program called 3D Studio Max (the program we use to do all of our 3D modeling for Uru and Myst 5: End of Ages). Look at how many sides it has and how many polygons it uses. There are two triangles too many! Every elementary school kid knows that you don't need 8 triangles to build an 8-sided polygon right? The figure on the right is my new stop sign that I built by hand. That's much better. There are 25% fewer triangles in that stop sign. OK, so 8 triangles vs. 6 triangles isn't going to be a noticable difference at all on your Xbox. But these things add up. Quickly. Reducing an entire scene that's drawing several hundred thousand triangles by 25% would be a huge savings.

If your production director (that's me) came to you and said "Hey you! I need 400 stop signs, and your budget is 2000 polygons," could you do it? No! You'd need at least 400*6 = 2400 polygons. So you hit him with your big geometry hammer and take his job and his parking space. Life is good.

In conclusion, whether you want to be an artist or a programmer, pay attention in school. If you do, someday you can make stuff like this (from Myst 5):



or this (also from Myst 5):



Support geometry! Buy Myst 5: End of Ages this Fall. Thanks.

We now return you to your regularly scheduled non-sequitar.