From the course: Adobe Pen Tool: Mastery

Bézier curve fundamentals

From the course: Adobe Pen Tool: Mastery

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Bézier curve fundamentals

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- [Instructor] In this movie, we'll take a look at the fundamentals of Bezier curves, starting with the anatomy of a path, and we're going to do so on a molecular level, that is to say, we're going to take a look at a single segment right here. And so the segment, as you may recall, is the portion of the path outline that falls between two anchor points. So a segment always begins at one anchor point and ends at another. In the case of a curving segment, we also have a couple of control handles as we're seeing here, and these handles are connected to the anchor points by levers. Now the reason I've made the word lever blue is because you can't manipulate it directly inside the Adobe programs. And to see what I mean, I'll go ahead and press the A key to switch to the white arrow, AKA the direct selection tool. And then I'll just go ahead and click on this segment right there, and you can now see these green anchor points, and these round control handles. And notice I can drag that control handle if I want to, I can drag the anchor point as well, but I cannot drag the lever. If I try to do so, then I'll just end up deselecting the path. Alright, now Adobe and I don't always get along where this terminology is concerned. In their documentation, they call control handles direction points, and they call levers direction lines. But this terminology varies inside Illustrator, inside the application itself. In the Preferences dialog, they're referred to handles, under the Select -> Object submenu, they're called direction handles, and inside the Tweak dialog box, they're called control points. And so as you can see there, we're starting to agree with each other at this point because I'm calling these things control handles. But it's important to note that these are the industry standard terms. They've been out there ever since Illustrator first hit the market, followed by Aldus Freehand, and so forth. And another great thing about calling these guys anchor points and control handles is that if you're feeling casual, you can shorten things to just points and handles, and everybody will know what you're talking about. Alright, so let's consider a straight segment, which begins and ends at anchor points. So all you need is two anchor points for a straight segment. Whereas with Bezier curves, specifically cubic Bezier curves, which, you know, the kind found inside Illustrator, InDesign, Photoshop and many many other applications. And I should note, by the way, cubic Bezier curves were first implemented back in 1984 when Adobe's John Warnock and Chuck Geschke integrated cubic Bezier curves into PostScript, which was a precursor to PDF and the Pen tool. And in fact, I wouldn't be the first person to suggest that in the context of freeform, expressive graphic design this variety be termed Warnock-Geschke curves. But in any event, they are actually called cubic Bezier curves, and they require four points per segment, which I've gone ahead and numbered here, but in truth, they're numbered this way: that is to say, we start with zero and end in three. So points zero and three are the two anchor points, as you can see right here, and they pin down the locations at which a segment begins and ends. So it's important to know that anchor points force segments to move between them. They are quite literally anchors. Whereas points one and two right here are the control handles, and they pull on the segment like magnets if you will, forcing it to bend. And so in this case, the handles attract, but don't actually touch the segment. And so whether you prefer to think of these things in terms of anchors and levers, or pins and magnets, those are the fundamentals of cubic Bezier curves.

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