The story of round rectangles

Bill Atkinson worked mostly at home, but whenever he made significant progress he rushed in to Apple to show it off to anyone who would appreciate it. This time, he visited the Macintosh offices at Texaco Towers to show off his brand new oval routines, which were implemented using a really clever algorithm. 

Bill had added new code to QuickDraw (which was still called LisaGraf at this point) to draw circles and ovals very quickly. That was a bit hard to do on the Macintosh, since the math for circles usually involved taking square roots, and the 68000 processor in the Lisa and Macintosh didn't support floating point operations. But Bill had come up with a clever way to do the circle calculation that only used addition and subtraction, not even multiplication or division, which the 68000 could do, but was kind of slow at.

Bill's technique used the fact the sum of a sequence of odd numbers is always the next perfect square (For example, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7 = 16, etc). So he could figure out when to bump the dependent coordinate value by iterating in a loop until a threshold was exceeded. This allowed QuickDraw to draw ovals very quickly.

Bill fired up his demo and it quickly filled the Lisa screen with randomly-sized ovals, faster than you thought was possible. But something was bothering Steve Jobs. "Well, circles and ovals are good, but how about drawing rectangles with rounded corners? Can we do that now, too?"

"No, there's no way to do that. In fact it would be really hard to do, and I don't think we really need it". I think Bill was a little miffed that Steve wasn't raving over the fast ovals and still wanted more. 

More @ http://folklore.org/StoryView.py?story=Round_Rects_Are_Everywhere.txt