Don't know if this will help, but here's how some sans fonts construct their u's.

Some of these have extra points between the extremas - I don't think this was usually a conscious design decision. Probably those points were added in conversion.

Looking at your example and these - the leftmost set of points might want to be slanted too.

Thanks for responding Brian. Studying various grotesque alphabets confirms the conventions but doesn't give much away about how the contours are formed - I suspect that in all of your examples they are determined by eye and iteration.

A broad nib pen moving along a central path informs the contours of calligraphic lettering. A traditional grotesque font is an abstract interpretation of this image - these fonts were conceived as outlines from the outset. However, the computer allows us to, where appropriate, reinstate a direct relationship between contours that is longed for when working with outlines only - the crudest expression of this is an /o/ constructed with two parallel paths but naturally this particular function can't cope with more complicated situations.

Don't get me wrong, I am not searching for a holy grail solution to stroke fonts, just different functions to aid consistency between various components. I hope that somebody can point me in the right direction.

I didn't want to focus too much on the /u/ as this kind of joint is common to the /n/m/r/b/d/p/q/g/a/. It is because of this recurrence that I am keen to find functions capable of generating contours from a central or single path in each incidence.

"…but doesn't give much away about how the contours are formed"

What makes you assume they are / should be formed by extrapolating from an inner single line?

"the computer allows us to, where appropriate, reinstate a direct relationship between contours that is longed for when working with outlines only"

I would debate that such a «direct relationship» between the contours is necessarily «appropriate», or desired, or even «longed for», in a sans. (If you make an extremely pen-informed font that may be different.)
I would rather see the necessary optical corrections, like the thinning you show, as reasons to deviate from any sort of «monoline» ideal. For one thing, if this is the way you'd like to construct a font, how do you intend to account for the necessary different thicknesses of vertical and horizontal strokes?
It seems to me like you're clinging to a logical model that you don't need to need.

>I suspect that in all of your examples they are determined by eye and iteration.

I think that's probably the case in all the best typefaces. You can certainly expand paths using a non-uniform brush (Illustrator I believe has quite powerful functions to this effect) but you'd have to tell it which paths to expand and contract in the 'right' places and at what rate (for example the SE curve of u needs to thin much more than the SE corner of an o, and different again for a d)...so you'd end up iterating anyway.

NIna thanks for your response though I think there is some confusion that I best correct. I was worried I'd be mistaken.

Of course I want to produce an optically adjusted font. It is precisely because I don't want to produce a monoline font that I started this thread. I thought I'd managed to make that clear initially! Please assume that I have a reasonable grasp of the necessary optical adjustments and I am making inquiries into something beyond this, about how to manage these adjustments.

How do you intend to account for the necessary different thicknesses of vertical and horizontal strokes?

Even the basic expand/parallel paths function can accommodate this adjustment as there are input values for height and width!

Back to my original questions:
What informs the position of the sheared BCPs on the tapered strokes?
How can I translate this sentiment using functions applied to a path?

I hope I've managed to clarify my questions. It's much harder to make myself clear in a forum than if I were sat opposite you with a pen and paper sketching out my concerns!

I would debate that such a «direct relationship» between the contours is necessarily «appropriate», or desired, or even «longed for», in a sans.

If possible I'd like to avoid debating here, we can start another thread for that! Right now I'm asking for technical advice, and I don't want debate to obscure that. Please trust that I already have some sensibilities!

:-)

You can certainly expand paths using a non-uniform brush (Illustrator I believe has quite powerful functions to this effect) but you'd have to tell it which paths to expand and contract in the 'right' places and at what rate (for example the SE curve of u needs to thin much more than the SE corner of an o, and different again for a d)...so you'd end up iterating anyway.

This is the kind of intelligent function I'm getting at, thanks Ben. I know I will be tidying up in the end, that's not a problem. I know that I can't apply one function to all parts of a central skeleton path but I could certainly apply different functions to separate sections of this path and join them myself. Powerful functions are what I am interested in, even if it is necessary to apply them to very specific areas individually. Maybe working on this level is akin to drawing in speed, but for me the advantage is that I'd only have to edit the central path directly and keep varying the function until it felt right, this suits my way of working!

Are there similar but more powerful functions than expand/parallel paths in FontLab buried in the macros somewhere? I'll have a look at Illustrator in the meantime.

Something on similar lines to this: Replica from Lineto.

It doesn't have thinned joins in the same way, but is is constructed. Optical compensation with thinner horizontals is made by using and oval that is squished.

Andrew, thanks for starting this discussion! I am also very interested in these issues.

On a related note, I think the joining of the straight part of the u to the curve is also a tricky thing. As shown in the images posted by brianskywalker, sometimes the points are horizontally aligned, sometimes the inside is higher, sometimes the outside is higher. I think the appropriate choice is highly dependent on the "shear" of the bottom that you mentioned.

A short discussion of these issues appears in a thread I started a while ago: Aligning points on outline of straight to curved stroke.

Brian, I'm really glad that you uploaded that image of Replica as that is exactly what got me thinking about a hypothetical variable gauge ball. The Replica ball accounts for adjusted stroke width and height as it travels from vertical to horizontal. I then tried to imagine what kind of movement and transformation the ball would have to make to negotiate the tapered joint of a lowercase letter, in the case of my example a /u/, and I concluded it would have to shear to achieve this. Also I imagined that the ball would get slightly wider to produce optically adjusted width in the curved stem of a character such as /R/. Looking at the above image I think NORM chose to standardize this but there is no reason not to add more 'standards' to achieve a more adjusted font. For example, maybe for a /B/ the ball gets a fraction wider again for the lower right hand extrema.

So I'm talking about a hypothetical, flexible gauge. Maybe I have to tell it how to respond to different scenarios, for different components of letters, based on our well established optical adjustments, but it will nevertheless inform the inside and outside contours by following one path and producing contours either side based on parameters. If this hypothetical 'clever gauge' was a function in software, which function is it?

Hi Stephen, glad you found this interesting, I just linked this thread to yours. Hopefully we can evolve some solutions.

I also dared to mention a pen - this seems to induce some skepticism from Nina in both threads ;-)

The reason I mentioned a pen was because I enjoy the fact that the inside and outside contours are related. I want to achieve a more complicated relationship between these contours than produced by a fixed width traveling at a fixed angle.

That is not to say that I want to make a calligraphic font. I want to make a sans serif font on a computer - that is why in my mind's eye I replace the pen with this ball. This imagined 'ball' is more flexible than the pen in the hand, it does not need to be kept at the same angle like a pen does and it can change in width much more than a nib splayed by pressure - on a computer it is not bound by physicality! Again, I don't want to get into the philosophical rights and wrongs of this - there are plenty of fonts on either side of that debate - I'm looking to make something that reconciles the two, a midpoint - and I need to find the tools to do it. Often on Typophile the 'why' stands before the 'how' but I'd like to reverse that order here. It's often easier to ask why than to explain how!

I think I need to add some more illustrations.

First:

One central path - three different areas might that might require different parameters - as Ben says earlier tell it which paths to expand and contract in the 'right' places and at what rate. This illustration establishes that I want to make several optical adjustments, but I want to control them from a midpoint. This could be three separate functions that produce segments that I have to connect manually - I'd be happy with a fairly spartan method of application.

Second:

The basic function of a gauge dealing with adjusted height and width as in the Replica illustration above.

Third:

And /o/ showing a two different balls to the second image (the size of these balls could always be determined by eye - it's optical - left and right widths are slightly wider than stem width in image two - the conventional adjustment). Obviously this one can be constructed without gauges by making parallel paths.

Fourth:

The point at which it becomes more confusing, applying these ideas to the structure /u/ from the first image. Imagine the yellow ellipse moving along the red path to become the green ellipse, creating the green contours as it moves. The angle of the shear is something I have decided without any method, this is the first issue I'd like to address.

Appendix to fourth:

Trying to establish the value of the horizontal curve thickness and the subsequent shear from a pen like brush. The relationship between the contours is too direct for a grotesque font - the capability of the brush is not complex enough. This is where the pen allusion ceases to be relevant and some kind of variable gauge more appropriate.

You should sign up for a type design course. This stuff gets covered in the first class.

You may be working with digital tools, but you still have to draw.

James I'd relish the opportunity to undertake such a class. Honestly, I'm currently tied down by lymphoma (ENTER VIOLINS*), so Typophile is one of my few links to education of any sorts, or even the outside world! I'm really conscious that there is a wealth of information out there that would allow me to progress - Typophile don't disappoint me in my hour of need. I have the time, point me in the right direction.

You may be working with digital tools, but you still have to draw.

Don't worry, I hear you! I still think there is something of value in what I am trying to achieve, at least to my practice anyway. As I mentioned at the start of the thread, I have been drawing for a little while (don't look for evidence of that in these rushed illustrations) but I still have a curiosity about more powerful functions to help me along the way.

*Black humor, I remain in good spirits.

As for other attempts to educate myself I am reading Typeface as Program by ECAL and The Stroke.

Gerrit Noordzij on Vimeo

Watching this video forced me to reconsider how I had been drawing - that I want something to inform the outlines, even in a sans. I'm not promoting this philosophy, it's just where I find myself at present.

I think this is possible in Illustrator, I don't know about doing it in an font tools. I don't think this will work in Fontforge, to make paths like that, although I think you could do a basic stroked path with oval settings like in the Replica example.

You can also easily recreate something like the Replica example, in Illustrator, with a "scatter brush":

I have an older copy of Illustrator (CS2), but I think I can make a thinned stroke like in your example with art brushes (like others have stated). Of course you'll have to use separate paths.

Here, this is my test with an artbrush:

It works, though I'm not sure how you'd do a sheared join of two paths like this.

Also, this is a bit off topic but:

> Black humor

What's that?

Thanks Brian. I'm not trying to reproduce the artwork for Replica. That image is important to this thread because it reveals parallel paths - the circles are just illustrative. The circles allow us to see what is going on between the contours. They illustrate, rather than plot the contours. I want to plot the contours. The moving ellipse is just a way of us humans engaging with two abstract lines by aiding our imagination in how they might relate.

A hypothetical ellipse that transforms smoothly along a single path would always plot smooth and corresponding contours from its extrema. Maybe this is not the optical ideal, but it's what I am endeavoring to produce nonetheless!

But this is working backwards. I am not trying to invent a function based on the a moving ellipse - I imagine a function capable of tackling my problem already exists - a function where more parameters than height and width can be stipulated when expanding paths. The function does not have to be intelligent enough to know which set of parameters to apply to different parts of the curve, I can expand them separately and specify the parameters such that the ends of each segment correspond.

I fear I am struggling to convey my ideas.

That artbrush is quite interesting, thanks Brian. For the moment let's not get hung up on beauty. Now I wonder what would be possible with more powerful functions!

(The off topic bit - Black humor - read that same post (26.Oct.2010 5.16am) again and all will be revealed.)

I wish you well.

In your exploration of what purely digital tools can do, I suggest you either, review the work of, or contact, two people who I think are the ultimate masters of Adobe Illustrator as it relates to drawing letterforms.

Gerard Huerta

Daniel Pelavin

Thanks, I get what you mean.

On that note though, those gauges were only ever meant for just that - gauges. Knowing how to do them in Illustrator means you can use them as intended.

I think with art brushes you could easily replicate your examples, and then reuse those art brushes on other glyphs. I'd like to show you how, but I don't have time. You might be able to figure it out yourself, perhaps? If you need explaing of the custom brush tools, just look up tutorials and they should explain.

Also just remembered that there is a plugin for illustrator that does thinning and expanding of strokes - without converting them to outlines. Can't remember what it's called though. Using art brushes would still do the job, though, but that plugin might better work for what you want.

James

I wish you well.

Many thanks, I'll be enrolling in some classes as soon as I can. In the mean time I'll be sure to check out your links.

Brian, thanks for the time you have invested in this thread. I'm going to spend some time looking at all the possibilities of brushes and plugins in illustrator, which without your recommendation I might have discounted too easily. If you remember the name of that particular plugin add it to the thread in the future.

Thanks to all who have replied thus far.

Variable stroke width is a new feature in Illustrator CS5, along with the ability to save and reuse "width profiles." It's comparable to using art brushes, but more versatile.

http://tv.adobe.com/watch/learn-illustrator-cs5/using-variablewidth-prof...

Oh man, I've only got CS2...

Please keep us posted on your progress with this!

CS5 Huh, I too only have CS2.

I'll keep you posted, though it may be some time before I make any progress.

I recently did some experiments with the variable stroke feature. And I think it is more or less useless because you can not really define mono-thick lines which come after a line that gained weight. Plus you have to edit more points to get the same result as you would have to with the outline approach in fontlab.
And if you finally have an Illustrator result that you like and want to make it bolder it will just give you bad results.

@1985:
Maybe you should also have a look into kalliculator from Frederik Berlaen. Especially his researchpaper. But even though it is computed correct it does not mean it looks correct.

Thanks Christoph, I sent you a message via your blog!

Enough with the deluded expanded-skeleton business, people.

hhp

As Hrant says, Noordzij's model of the stroke only takes you so far. It seems to me that while Romain du Roi, Metafont or expansion/translation/rotation models do produce sort-of usable results, true Design comes in when you move away from these limiting geometric, modular or algorithmic approaches, and start to draw things optically, with new ideas, critically. I think type design is way too interdependent and complex to reduce that way: the human eyes have to be the final arbiter in all decisions, no?

Hail brother.

hhp