Scroll down for commentary/discussion.

I couldn't find a quick easy demo on the Net, so I made one.
All my knowledge of the Affine Transform comes from:
     This demo, which I made, to learn about the Affine Transform, so...
     The Paper.js site, which for some unfathomably reason has Matrix as the 5th item on their reference Page
         (I like Paper.js. I just think this should be somewhere near the bottom of the reference stack, rather than the top.)         
But, hey. What do I know? I still think getting a computer to make circles is pretty nifty.
     Don Fussell's CS384G PowerPoint slides for his 2010 course (as found on the web as a pdf)
So, I'm not saying I understand this or even that this program works right. (How would I know?)
But from what I gather:

Affine Transform Demo
Copyright © 2013 Brett Paufler