What constitutes a "bad curve"?

russellm's picture

Per Goran Soderstrom's comment about nodes in the Traffic System Typeface thread about the quality of curves in a "terribly badly digitized" font, what constitutes a "bad curve"? Eg, if I'm comparing a professionally designed typeface to one by an amateur, what would tell you who did which font?

Tim Ahrens's picture

I am convinced one major possible flaw, probably the only one, is discontinuous curvature, like in this example:
 


 
See how little the shape needs to be changed to make it look harmonious:
 

 
The good thing is that fixing this is an objective task and can even be automated.

blank's picture

A bad curve has bumps that stick out in like tumors in places they shouldn’t, usually because someone is using too many BCPs. Curves that do no smoothly transition to straight lines when they should can also be considered bad. This sort of stuff is often unnoticeable at text sizes, but in signage it can be pretty gross.

The easiest way to understand this is to open a font by Christian Schwarz or Hoefler & Frere-Jones and compare them with some of the crappier free fonts out there.

Alessandro Segalini's picture

J.P. De Gregorio has a good article, scroll down.

Goran Soderstrom's picture

Top: Bad Curve

Below: Good Curve


(Just to be a little more drastic than Tim Ahrens rather advanced description of a bad curve)
;-)

Alessandro Segalini's picture

I'm missing the photographer here, but that's a good curve,

jupiterboy's picture

less than good (although appropriate for the baked goods)

russellm's picture

Thanks everyone.

Alessandro / Jupiterboy,
":¬)

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dux's picture

just an observation, but it's interesting to read the opinion that pure curves are necessarily good. I feel that creating smooth curves in this way leaves me wandering what I am giving away, what I am letting myself being deceived into accepting as 'true', precisely because they are clean. There's a funny blandness to smooth bezier curves that inhibits drawing I feel. It takes a while to become confident enough to intentionally throw bumps into the mix. Or maybe that's simply a case of understanding lettershapes better. I don't think so. I spent several months painting letters with gouache, and when first drawing by computer, the technology naturally at first inhibited. In fact it did for a long time.

Don McCahill's picture

Blandness is a good thing with fonts. Normally fonts are a container of information, not a piece of art of themselves (I know this will be disputed by some). To condust their primary goal, of smoothly conveying information, they should not draw attention to themselves. (At least to the normal reader. A typographer will look at type in an altogether different way.)

Mark Simonson's picture

A smooth curve is the most efficient curve. It's harder to do, but looks more effortless.

William Berkson's picture

I think this is more complicated than Tim indicates.

Getting smooth curves with the pathway and weight you want is indeed a key challenge in drawing with bezier curves. But less smooth curves, and even discontinuity are not necessarily design flaws. In the case of the Tim's S it is, because the design calls for a smooth curve. But other designs call for less smooth curves. Sometimes these are clear corners, but other times they are more complex shapes. If you look at some old style ampersands you will see clear examples. Also Dwiggens introduced discontinuities where they weren't traditionally. And you can see also these in Kent Lew's beautiful Whitman, influenced by Dwiggens.

It is less clear, but more accurate to say that you shouldn't have discontinuity except where it serves a design purpose. And then it can be very good, if the design is good.

James Arboghast's picture

I think this is more complicated than Tim indicates.

Ah, yep. Complicated and "complex" too. Like life itself, truly interesting type outlines are often not simple or smooth, and contain interesting anomalies, bumps, quirks, discontinuities, as part of their design.

Things can quickly become boring when technology makes it easy to put life in the new economy can. It's not much fun, but it's efficient.

j a m e s

Tim Ahrens's picture

Dux, William, good points. My proposal only covers one specific aspect, and that is not even obligatory. It may be possible to describe a harmonious curve mathematically but it gets more difficult when you try to describe beauty (in fact, imperfect faces are perceived as more beautiful). And even then, beauty is not the same as good design.

William, the discontinuities in Dwiggins' types you mention are discontinuities in direction. I was talking about discontinuity of curvature.

My tool is just that - a tool, not a design machine. Just like with other tools, it takes a designer to use it and to decide when it makes sense.

Note that it was a direct reply to the initial question, and as such I believe it makes sense. Don't put it like I advocate perfect curves. The initial question was not about "truly interesting type outlines" but about “terribly badly digitized” curves.

dux's picture

Blandness is a good thing with (some) fonts.

a presidential campaign logo, could smoothly present both the name of the candidate, AND the feeling of trust, power etc. nearly-illegible, grungy types can enforce the message. Conveying a message 'smoothly' is not an indication of lettershape. sharp types change visual shape at small sizes.

A letter itself is a container of information and has I suppose, a meaning seperate from visual interpretation. Visually representing a concept, like it or not adds another layer of meaning however large or small.

I don't think we look at type in *much* more of a different way to the uninitiated. The difference being we can more easily articulate ourselves. That is to say analyse and describe the psychological effect, as well as the effects of functionality.

dux's picture

of course blandness itself has a meaning even if it's deliberately evasive

James Arboghast's picture

Note that it was a direct reply to the initial question, and as such I believe it makes sense. Don’t put it like I advocate perfect curves.

Sorry Tim, but your initial post made it  l o o k  that way, and I was responding to that rather than the initial question.

To condust their primary goal, of smoothly conveying information, they should not draw attention to themselves.

For some kinds of text or content, yes, transparency is key, but it isn't always desirable. Some kinds of content benefit from conveying information in less than transparent fashion.

I don’t think we look at type in *much* more of a different way to the uninitiated.

I think the difference in the way typographers, type designers and type experts look at type compared to the uninitiated is colossal.

j a m e s

William Berkson's picture

Tim, is it possible to describe the continuity of curvature in a simple geometric way--such as the relationship between the handles on two sides of a smooth point? The handles between two points on segment?

Mark Simonson's picture

I think of it like driving a car. You want to ease in and out of curves, slowing down and speeding up as needed, so as to make good time while not spilling the bags of groceries. "Bad" curves are like an inattentive driver, constantly going off course and trying to make corrections.

russellm's picture

Thanks again.

I'm sort of not interested in what the curve looks like, strictly speaking - if that makes any sense in the context of my question. How it is constructed matters to me. If there are kinks and quirks in a curve, do they work aesthetically, or are they the result of inattention to detail? Could you demonstrate that a typeface was well or poorly drawn by "reverse engineering" it. I know, ultimately what matters is how it reproduces in a given medium, what it looks like and how it "reads". My medium is mostly cut vinyl.

If a typeface were specified for a company that is then going to make thousands signs using it, then the quality of the vectors it's made up of may make a significant difference to down loading, plotting and weeding time on the one hand and on the other perhaps you can just say "this is good (or bad), and here's why."

From the standpoint of designing type myself, (which I really have not done much of at all and don't claim anything other than green-horn status) I find the templates I make to construct characters can get very complex, as I want to make sure everything that needs to stay consistent does and sufficient variety and character is allowed and that shapes are constructed in the most elegant and precise manner possible. (...for me.)

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mr's picture

Tim, may I ask how you calculated those curvature plots? Do you have a tool that does it? I once tried to do something similar, but my understanding is that to calculate curvature you need the curve to be parameterised by its length, and I bit of work with the Wolfram Integrator showed that this was impossible (I needed to evaluate a *four*page* formula at every point).

Tim Ahrens's picture

William,

Tim, is it possible to describe the continuity of curvature in a simple geometric way

Unfortunately, not. Of course, curvature is defined mathematically and can be calculated relatively easily for any point on the outline but you cannot formulate a necessary or sufficient condition in terms of handle lengths.

The handles between two points on segment?

In many cases, in a range between elliptic and slightly hyperelliptic, you can make one handle shorter and the other one longer and you will hardly see any change in the shape of the curve. I have not made any calculations yet as to where this range is and what degree of change in handle ratio is possible within a threshold.

You can easily test that in FontLab: just draw a slightly hyperelliptic curve element and play with the handle lengths, keeping the curve as close as possible to the original shape. You will notice there is quite a bit of leeway, there is one redundant degree of freedom if you want.

as the relationship between the handles on two sides of a smooth point?

The above partly answers this question: No, the handle ratio on one node is totally irrelevant. It is a common misconception that the handle lengths play a great role.

If your curve looks un-smooth with bumps or dents and you want to fix that you need shift the nodes. Finding the right position for the extremes is crucial, the relative handle lengths are not so important. Note that in my above example, only the nodes were shifted in order to establish continuous curvature. The handles were merely adjusted to compensate for this so the curves do not get pushed out or in.

If I have some time I might put my Brighton presentation on Bézier curves on-line with some comments on. That is more detailed and graphic than what I just described.

William Berkson's picture

Tim, that's interesting about the node position being critical. That explains why I have found that often the easiest way to smooth out bumps is to slide the node while keeping the handles fixed. (Shift key in FontLab.) Then if need be I play with the handles, and as a last resort start moving the node at right angles to the line. --All the while keeping the original in the mask layer. The Brighton presentation sounds interesting.

The relative handle length often only makes a very subtle difference, but it is sometimes a difference between what really looks polished and only OK. The recommendation to equalize handles between nodes, which I have read, I find does seem help if an imaginary straight line connecting the nodes in question is around 45 degrees, but if closer to horizontal or vertical, the curve usually looks better with unequal handles...

dux's picture

That explains why I have found that often the easiest way to smooth out bumps is to slide the node while keeping the handles fixed.

Ditto.

dezcom's picture

"In many cases, in a range between elliptic and slightly hyperelliptic, you can make one handle shorter and the other one longer and you will hardly see any change in the shape of the curve."

I have found this seemingly subtle difference to be quite critical. For me, if the elongation of one handle is too great compared to the other side, the curve becomes dysfunctional. It makes a speed change that is too abrupt. It is like driving a car through curves--you can drive hard and slam on the breaks before accelerating or you can drive more smoothly. You end up with a more frantic line in the 1st case. That is not to say this is wrong, it just has a different character.

ChrisL

russellm's picture

This has been instructive.

Good curve:

and..

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William Berkson's picture

>For me, if the elongation of one handle is too great compared to the other side, the curve becomes dysfunctional.

Chris, have you found, as I mention in my last post, that whether equal handles for nodes at extrema is good depends on the relative position of the nodes?

--For example, with a circle you'd want equal handles, and for a narrow ellipse you'd want unequal handles.

dezcom's picture

I have trouble with the term "good" since the change of speed may be desirable in some cases. I think of it like pronunciation in different languages. A 'good' vowel sound in French will differ from a good one in Italian or German. Context is the decision maker for me.

ChrisL

jupiterboy's picture

Right. Good is a bad generalization. The racing line is a good analogy though. Whatever the desired effect, it can be created with an ultimate economy—in number of points and in extension of handles.

fonthausen's picture

A curve is to me like the mimic/behaviour of an actor in a play. It adds something to the role, or it can be disrupting, smooth or ...
In a play, actors interact, like characters do.

To put it short, the micro level (character/mood) within a typeface is interacting with the macro level (character/mood), creating a story, that is your typeface.

This can even mean, that both levels can even differ very much in their story(telling), but end up in a perfect/interesting play.

Were you put your extremepoints is crucial. A curve is not an outline between two points. It has a start and an end.

– Jacques

ebensorkin's picture

I think that there are such things as best practices - but also that there are going to be isolated times and places where you need to break with those rules. It's always going to be your own eye that should guide you here. Not a a rulebook.

Tim Ahrens's picture

It’s always going to be your own eye that should guide you here. Not a a rulebook.

But what if you find out that your eye follows certain rules?

crossgrove's picture

Russell,

I don't know if the latest plotters still have this limitation, but years ago there needed to be some attention to the location of the outlines' start points, because the plotter started cutting (or drawing) the letter from that point, and finished there as well. Origin placement has different meanings when it comes to other kinds of digital imaging, but for plotters, there can be a significant time waste if start points are not in ideal locations.

This is an element of outline quality if you use a plotter, but may not have been on anyone's radar for years; I think origin point location is essential for TrueType hinting, but not for the same reason.

Efficiency is probably something else that would improve plotting times; fewer points, smoother outlines. But that doesn't mean the appearance of the letters or art is "smooth" or slick or bland; even rustic or "antiqued" letters can be digitized efficiently. I think there was a typeface by Spiekermann that had rounded corners for the speed benefit in plotting; more continuous curves might give a speed advantage, but you can watch your plotter to see if sharp corners really slow things down. If they do, you can surmise that sans faces are quicker to plot; serifs add a lot of extra direction changes.

Re: visual smoothness and endpoints vs. handles; both can have a visible effect on the "rightness" of your curve; I think it's a mistake to say that either endpoint location OR handle length is more important to getting a good curve. Plenty of times I slide both handles and the endpoint back and forth to get the curve right. See Mundo Italics for lots of this.

Tim, this kind of fiddling is the exact thing you talked about in Brighton; I have spent so much time messing with these shapes precisely because the beziers aren't behaving well and they need firm control to get them to do what you want. They can easily influence your results.

William Berkson's picture

>what if you find out that your eye follows certain rules?

I think everyone in this thread agrees that what is a "good" curve depends on context. But in context there are, as Tim says such things as bad curves, and his "before" S shows them. There is a certain kind of lumpiness that arises from clumsy Bezier curves, a kind of badness which would not arise with handwritten or draw letters. And in a letter with these lumpy Bezier curves side by side with an improved version almost everyone would say the improved version looks better. So yes, there is such a thing as good curves.

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