Glyph design: the trick to drawing the letter s

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The letter ‘s’ is considered one of the hardest letters in the alphabet to design. It is utterly unrelated to any other letter we have designed so far. Most people can’t handwrite this letter and produce a passable print rendition.

If you are learning the latin script and are struggling with handwriting this letter, do not despair—most of us don’t have a firm grasp on its construction either. Most neat writers (mostly teenage girls) handprint the letter something like a number ‘2’ reflected vertically and rounded slightly. Some people overexaggerate the hooks of the ‘s’ to the point where it approaches a figure ‘8’, others render the letter like a mirrored ‘z’.

Some common handwritten forms of the letter ‘s’.

 Even worse is when people try and make bubble letter ‘s’s. Except by experienced bubble letterers, one of two results is almost invariably produced.

I won’t dwell on better techniques for bubbling the letter ‘s’. My point is, that most people utterly fail in drawing this letter because they try to freehand it. You can’t blame them—the ‘s’ contains no straight lines and it has no visible geometric basis. But we type designers must be better than that. Here, I’ll show you an easy, relatively painless method for drawing this letter that relies on its hidden geometric structure.

How to deal with font extremas

I don’t know about you, but this is definitely my least favorite font error. If your glyph outlines aren’t constructed in just the right way, fontforge will complain about missing “extremas”. But what are extremas anyway?

An extrema is a special kind of point that helps define the edges of a glyph. The word is Latin—technically a single extrema is called an extremum, with extrema being the plural. But the term has become so common among type designers, that extrema and extremas have become the terms used to describe these points in a glyph outline.

An extrema is just a curve’s minimum or maximum in the xy coordinate plane. This is just like finding the maximum of a parabola or some other curve, except applied to bézier curves.

Each bézier segment of a glyph’s outline (read: each segment between two points, not the entire glyph outline) must be a one-to-one function*—i.e. it has to pass both the horizontal and vertical line tests. A bézier segment in a font shouldn’t change direction in either the x or the y direction—otherwise it should be split into two one-to-one segments. A handy (but not foolproof) way of checking this is looking to see if the curve fits into the rectangle determined by its endpoints (though an ‘s’ shaped curve can pass this test and still not be one-to-one).

The curve on the left is acceptable—it doesn’t change direction in the x or y axis. The curve in the middle folds back on itself, so it needs to be split in two (right).

Why is this a thing? Well apparently it helps with hinting, by letting the renderer know the bounding boxes of the glyph outline. It also makes it easier to measure stems and set sidebearings, since you can measure distances between points instead of vague spots along a curve. But the truth is, most renderers get along fine without any extremas. No vector illustration program requires extremas on its paths. Extremas are just extra points on the ends that help protect glyph outlines, since fonts undergo much more heavy-duty scaling and rasterizing than most other forms of vector art. Think of them as protective bumpers on your letters that keep your font from getting distorted by dumb renderers.

Glyph design: how to draw the looptail g

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The lowercase looptail ‘g’ is perhaps the most poorly understood letter of the alphabet. Its serif form has an extremely intricate architecture that virtually nobody knows how to write these days.

Just like with the ‘a’, there are two accepted ways to write the letter ‘g’. On the left below is the “proper” form, called the looptail or double story ‘g’. The script form (right) is much less common, and is generally only found in sans serif and decorative typefaces (and even then only occasionally). But since it is much easier to draw than the looptail ‘g’, most people handwrite the script ‘ɡ’. In proper serif type, this ‘ɡ’ is exceedingly rare. In fact, the only place this construction is found is as a phonetic glyph, and very few fonts include IPA support.

Linux Libertine is one of the few fonts (commercial or free) that contain the phonetic ‘ɡ’ along with the alphabetic ‘g’

The calligraphic roots of serif type

If you’re new to serif type design, you might be wondering what’s going on with all that thick–thin stroke stuff. For example, why are the sides of an ‘o’ thicker than the top and bottom? The reason serif type has all that stroke contrast is because serif type evolved from broad-nibbed calligraphy, which produces such contrasting lines.

A long time ago, before ballpoint pens, people wrote with what were essentially sticks dipped in ink. But these writing instruments couldn’t be too pointy—or else they would break. So the nibs (writing points) were made wider to give them more strength. This became what is now known as the broad-nibbed calligraphy pen. Though they’ve since been eclipsed by the ballpoint pen, they are still somewhat common and there are many places you can buy them.

Glyph design: the lowercase k

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The letter ‘k’ is made up of a single ascending stem, and a diagonal arm and leg protruding to the right.

Components of a lowercase letter ‘k’

The left side of this letter is essentially identical to the lowercase ‘l’. Considerable variation exists in the right half of the letter, especially where the arm and leg meet, called the join of the letter. Sometimes, particularly in older style typefaces, the join is an extension of the arm and the leg offshoots from it, other times, the arm and leg are disconnected from the stem and the two parts meet at an invisible point.

Glyph design: the lowercase x

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The lowercase ‘x’ is one of those letters that isn’t hard to make, just tedious. The ‘x’, while seemingly simple, requires numerous (but well documented) optical corrections. You also have to consider the negative space in the letter, something you usually only have to think about with round letters like ‘p’ or ‘e’.

The superficial structure of the letter isn’t complicated. It has a single thick diagonal, crossed optically by two arms, collectively called the letter’s hairline, since it is supposed to represent the hairline thickness of the font.

The ‘x’ isn’t a very common letter. The most abundant English letter, ‘e’, is eighty-five times as common. In a typical page of English text, ‘x’ only occurs once every seven hundred letters, on average. Only ‘q’ and ‘z’ are rarer. But the letter is of great interest to typographers, since it stores a a lot of a typeface’s measurements. The height of the letter determines the optical size of the lowercase letters and sets the mean line of the typeface. This is why font size is sometimes expressed in terms of “x-height”, especially when point size is unreliable. The letter’s four corners (including serifs) roughly form a square in a normal style typeface—if it’s wider than it is tall, the font is extended, if it’s significantly narrower, the font is considered condensed. The width of its arms sets a typeface’s hairline thickness, and its hairline compared to the thickness of its diagonal can be used to measure the stroke contrast.

Components of a lowercase ‘x’

The diagonal of the letter can be made from the diagonals of two ‘v’s. It is important that the serifs of the ‘v’s align exactly to the baseline and the meanline of typeface, or else you will create an ‘x’ that is too tall or too short, which will be very hard to correct later on. The diagonal should be sheared over so that it spans slightly less than the width of the ‘v’.

Glyph design: the lowercase j

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The letter ‘j’ can be built straight from the ‘i’—in fact, long ago the two letters were one. The only difference is that the ‘j’ has a slightly curved tail descending below the baseline.

Components of a lowercase ‘j’

The top half of the letter is exactly identical to the ‘i’. The bottom half can be made from the hook of an ‘f’, though in most serif type, the two arcs of stem appear very different (in sans serif type, it is common for the ‘j’ to simply be a rotated ‘f’ with a tittle and no crossbar).