Comment by egypturnash | Hacker News Reader

Comment by egypturnash | Hacker News Reader

“ In particular, it can be tricky to maintain consistent curvature between adjoining segments of a path, which can lead to a ‘lumpy’ look; the following example is contrived, but in practice consistently getting smooth feeling curves with Béziers is challenging.”

It’s not that hard. I’m an artist who specializes in Illustrator, and I have some simple rules for its pen tool:

1. Drag curve handles out to 1/3 of the length of the curve segment they control.

2. Eschew s-curves between two control points.

3. Don’t turn more than about 90º between two control points.

There are people out there who have a similar set of rules but prefer to always put their control points at 12/3/6/9 o’clock; for more circular shapes this works, but it falls apart on anything interesting - try drawing an oval with its long axis at about 45° with my method and with this method, and observe how much more uneven the curve handles have to be for the 12/3/6/9 method.

These kinds of rules are common, but it also means you're only using a fraction of the expressive power of the Béziers. Why not draw actual S-curves? That way you're guaranteed an actual inflection point where curvature goes smoothly through zero, as opposed to two arcs joined. Why not explore control over tension by using curve handles greater than 1/3 (so curvature on endpoints is less) or less than 1/3, cranking up the tension in a way inspired by physical materials? Why not have the computer do the work of ensuring the joins are G2 continuous by construction, instead of having to eyeball it?

These rules create visually pleasing curves that are easy to manipulate. You can break these rules and get curves that have fewer points, but they will be very tough to tweak.

Break these rules and you will pay for it in more time spent when you need to change things.

You can make an analogy to programming rules that tell you to eschew excessive cleverness - sure, it may be more succinct, but are you gonna be able to edit it later? What about the person who comes in once you've left and has to deal with it?

(These are also guidelines, I do not obsessively follow these precisely; to be quite honest I mostly avoid using Illustrator's Pen tool for the organic shapes I mostly draw - but if I need to tweak a path, I'll use these rules and a couple other tools to quickly modify where the points are along a path, and do it easily.)

I think I miscommunicated a bit. I'm not suggesting you should be routinely breaking these rules with cubic Béziers. Rather, I'm saying that if you had a better underlying curve family, you wouldn't need these rules, as you'd get good results even with a freer approach to designing curves. That's basically the hypothesis we're testing.

These rules are interesting. How did you arrive at them?

I got 'em from a book I read standing around at the bookstore like twenty years ago. They were good rules. If I could go back in time and hand Broke 2000 Me twenty bucks to buy that book I would.

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