Unsuspectingly I learned what a Bezier curve truly is by attending a talk on four dimensional math. Though the Bezier, which you might know better as the “curve tool” or as the “pen tool” or as its proper pronunciation the “beh-zee-aye” is a heck of a lot simpler than you ever would have guessed.

One bezier curve is nothing more than a quarter circle inside of a trapezoid where the handles are 5/9ths (or 55%) out.
bezier2
Really you can sort of imagine that curves follow a “half” rule if you imagine a box that envelopes each quarter circle, but it’s useful to know that you need to push those handles just a little further to get the full effect.
bezier1
It might seem terribly nerdy at this point, but the next time you start drawing with curves, this information really comes in handy. The model is only an artistic tool however. Bezier curves are actually much uglier in their mechanics, and give me a flashback to 3rd grade graph paper exercises.

Personally, I prefer the quarter-circle model. Though the above diagram is mathematically correct, it’s a lot harder to come to terms with a curve that seems so hard to imagine as circular. The circle, after all, is a powerful design element that we all push towards and like to think about.

bezier 3

With any luck, the newer and easier Spiro Curve will soon be overtaking the place of the bezier, but that’s another blog post.

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