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bézier

After roughly ten years working as a graphic designer, Bézier curves still elude me. I normally just place control points as I go and then retouch the less natural looking curves, which works well enough but produces a lot of points, i.e., hard-to-maintain vector work. I want to perfect my technique.

There are several very interesting articles regarding Bézier curves applied to type design like this, which revolve around using as few points as needed, and limiting handle angles to 0°, 45° or 90º with a non-variable width.

So I tried applying that technique to the tracing you can see above.

You can see many curves still look bad. Plus it seems way harder to do it this way and infinitely more time-consuming than the quick and dirty solution (five minutes vs. an hour).

Am I doing something wrong? Maybe it’s not a good idea to apply a type-related technique to a general drawing? Maybe I just need to readapt to this way of working? Is it this hard for everyone else to get Bézier curves right? How should I approach this?

  • Your over ephasizing 0 degree tangents, from the looks of it you would probably prefer b-splines. – joojaa Jan 7 '16 at 13:09
  • yeah, in this particular case b-splines might work better, but only if working on a 3D grapics package. I'm actually asking about a 2D workflow, as in Adobe Illustrator and others. – MrMerrick Jan 7 '16 at 15:54
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There are several very interesting articles regarding Bézier curves applied to type design like this which revolve around using as few points as needed, and limiting handle angles to 0°, 45° or 90º with a non-variable width.

This advice is indeed specific to type design, where the extreme points of curves (which would be at 0° or 90° angle) are of particular importance for rendering and making the type look harmonic. I would not even recommend this for every kind of type design. For example when designing capital letters for a blackletter font, I did not adhere to this (coincidentally, I am using exactly this as an example below).

When using Bézier curves for other purposes, the essence of my personal technique and what I would recommend is this:

Place control points on inflection points of the curve.

If the mathematics is not your thing, just imagine that you are steering a car along the curve. Whenever you switch between turning right and turning left, you are at an inflection point.

In most cases, these are all the control points you need. The main exception is when you have a curve that makes a turn of more than 180°, which for example happens in simple circles or spirals. If you need to use additional control points, place them where the curvature is strongest, i.e., where you need to steer most.

For example, here is a quick attempt to trace your bottom example, which took me five minutes. With one exception (in the bottom left), all control points are on inflection points.

enter image description here

Here is another stylised example using only quadratic Bézier curves, which I happen to have at hand. The control points are where a black line intersects with the border of the red Bézier polygon. The handles are on the intersections of black lines. (This only holds within a calligraphic stroke.)

enter image description here

While you best see whether this works for you by trying it out, here are some reasons why this works well in my opinion:

  • While cubic Bézier curves can contain inflection points between control points, they are difficult to handle.

  • With quadratic Bézier curves, every inflection point has to be a control point anyway.

  • When tracing, the direction of the original curve at a turning point can be particularly easily identified and translated to your new curve.

  • As the curvature of a curve is lowest at turning points, inaccuracies in the direction of the curve and placing of the control point have comparably little impact.

  • Thorough and on point, this was exactly what I was looking for. Thank you very much. I must note however that somehow, your tracing is still a bit far from what I expected in terms of faithfulness to the original and smoothness. It's an absolute improvement over my attempt, but I found that my "quick and dirty" technique yields, to my eye, better results in this particular case. HOWEVER, I guess it's just because you don't know what I was aiming for and you didn't take the time to tweak it as needed. I'll rework my tracing with your "only inflection points" technique. Again, many thanks! – MrMerrick Jan 7 '16 at 21:14
  • By the way, nice quadratic Bézier curves example. If only Illustrator let you choose which one to use! Oh and finally, thanks for editing my sloppy question. English is not my first language, so hard trying to explain myself... – MrMerrick Jan 7 '16 at 21:16
  • I must note however that somehow, your tracing is still a bit far from what I expected in terms of faithfulness to the original and smoothness. – Well it was a quick example and I couldn’t trace from the original. And as you already noted, I do not know which compromise between faithfulness, smoothness and simplicity you were aiming at. You can always add control points where the curvature is highest, if you feel you need it. – Wrzlprmft Jan 7 '16 at 21:47
  • Absolutely! By that I just meant that I'll have to check if a proper technique like this will save me time and the curves will come out better/smoother, see if I can get "fluent" on it. I think it will. As I said on the original post, Bézier curves have always eluded me. I can use them, my vector work looks good most of the time, but then you see the points and... ugh! Thanks again. By the way, that Unifraktur is coming along nicely, keep it up! – MrMerrick Jan 7 '16 at 23:15
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If you have Illustrator CC you can try drawing the shape with straight lines with the pen tool, with the lines over the side edges and the point beyond the edge of the curve. The use the direct selection tool (A) and select the point. You will see a little "target" appear. Put your curser on it and move it in or out to change the radius of the curve. It takes some practice, but it creates even handles and fewer anchor points. In CC you can also use your pen tool on a path with the opt/alt key to reshape paths without manually adding anchor points.

I also use Vector Scribe by Astute Graphics in Illustrator. There are some tools that you can use with CS that create smoother curves. I am a big fan of scripts for Illustrator. If you find you are taking more time to edit curves, maybe the limitations are in the way you have your Illustrator set up rather than your tracing skills.

  • Thanks for your answer. Yes, I'm aware of the radius onscreen tool and use it sometimes in corners. In this particular case though, you wouldn't be able to model the whole thing with it. So I was asking about the "hardcore", so to speak, way of doing it. With the basic tool, and advanced techniques. Also aware of tools like Vector Scribe but again, would like to know how other pros do it and hone a basic technique without depending on 3rd party tools. – MrMerrick Jan 7 '16 at 15:57

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