![]() OK, so now you know how a computer renders a bézier curve: If we track it’s path while traveling, voilá, we have our quadratic curve rasterized: Now, let’s add a new point, one that travels between the two orange points, taking the same time to travel from one point to another (shown below in light gray). And for the sake of this exercise, we’ll also add a straight line that connect the two traveling points (shown in orange, below): Now, we’ll add two points: one that travels from A1 to C and another that travels from C to A2, and they’ll take exactly the same time to make their trip. Let’s connect A1 to C and C to A2 with straight lines, as shown below: ![]() Let’s say that the anchors are called A1 and A2, and that the control point is called C. ![]() So, we have our 3 points: 2 anchor (in and out) and 1 control point. So how are Bézier curves calculated? Let’s start with quadratic curves. If this is so, it seems that cubic curves win over quadratic ones so why aren’t quadratic curves obsolete? 3. Quadratic curves force the user to add more anchor nodes (since the addition of every angle per curve can’t be bigger than 180º), adding difficulty to the process of drawing a clean curve. Two control points per node allows more freedom while drawing, since it gives more control on the curve itself.The most obvious one is about file size: less points, less point coordinates, which means a smaller file size.Cubic: 4 anchor points + 8 control points = 12 points.Ĭounting points might seem unpractical and silly, but it can tell you a couple of things right away:.Quadratic: 8 anchor points + 8 control points = 16 points.Let’s count the number of points needed for each circle: So, if we were to draw a circle in both curve equations, they would be drawn the following way: A cubic Bézier curve (read PostScript) has four: insertion, end and two handles.Īnd for the visual type of guy, here’s an image:.A quadratic Bézier curve (read TrueType) has 3 points: an insertion one, a control one and a end one.Usually, all of this revolves around how PostScript and TrueType deal with outlines: TrueType uses quadratic Bézier curves, and PostScript uses cubic Bézier curves. So even if you are doing something in Illustrator to use in 3DS Max, for example, read on, it might save you some trouble. Some programs, like 3D applications, simply break the curve into several facets. If fonts are not embedded, the same happens. It does so, based on the size of your vector artwork, in order to keep the smallest file possible. More so, each one of them is going to convert the curves through their unique algorithm, sometimes unleashing hell.įlash IDE, for example, is notorious for wrecking curves. Problemsįirst of all, we should understand that each desktop publishing software is going to compile the font files in it’s own way. So, in order to save some people from this hassle, in advance, read along. When I am asked to calibrate a typeface or logo, or when someone asks me for help with their typefaces, one of the most common problems I find is bad Bézier curve design.Īnd every single time this happens, it’s not people’s fault: they just don’t know better.Īnd there’s that heart-stabbing situation when someone pings and says “Hey, I just finished this font, can you have a look and see if something’s missing?” and I feel obliged to say, with grief, “You have to redesign it all over: it’s poorly designed, bézier-wise”.
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