kerning principal: The Law of Optical Volumes. Huh? Monospacing?

MarvinMe's picture

The Law of Optical Volumes:

here’s a definition: The Law of Optical Volumes states that the area between any two letters in a word must be of equal measure throughout the word, and remain consistent throughout the body of text.

Wouldn't this yield a monospaced font if you applied this law to a font or logotype?

John Hudson's picture

No, because the 'law' refers to the optical space between letters, not the space within letters. In a monospaced fonts, all the glyphs are on the same width, therefore a monospaced font is much less likely than a proportionally spaced font to conform to Dadich's dictum, because normally narrow and wide letters are procrusteanly fitted to a common width.

MarvinMe's picture

Hi John,

Thank you for the reply. I see what you meant that the letters themselves are of different sizes (generally differing in horizontal widths), but the entire optical space between the letters still remains proportionally equal, is that correct?

MarvinMe's picture

Lastly, as shown in the enclosed image, how does one apply the 'law' to the optical space between the letters once step#3 is achieved? That is, now I have a bunch of proportionally squal pillars (for lack of a better word) so how do I apply them between letters? Do I allocate the spacing between the farthest inside edge of each letter?

William Berkson's picture

Rob, to get equal *areas* between two 0's and two n's, the sidebearings between the two o's have to be tighter than two n's because at the top and bottom of the oo space there is a lot more area than at the top and bottom of the nn space—near the baseline and x-height. See: oo nn?

MarvinMe's picture

Hi William,

Thanks for the reply. Maybe I'm not able to see the forest for the trees here. I get that the sidebearings need to be tighter on the o's versus the n's. Let's say you have an outlined font in Illustrator, a single word: volume (see previous post image). Now I've captured the proportional area between the letters and I want to apply the "pillars". What is the procedure? Take for example the V and the O in VOLUME. Where do you draw the lines for allocating the pillar space?

Perhaps it is the serifs that are throwing me off...

Bert Vanderveen's picture

You can not use straight lines for the top and bottom of these interglyph spaces. They behave more like a viscous fluid, where the mass ‘pulls in’ when the distances lengthen.
If I had the time I could make an illustration, but maybe this helps: in a container oil will be higher nearest to the walls and deeper in the middle. Start from there… : )

William Berkson's picture

1. Have a look at Briem on spacing, which follows Tracy's Letters of Credit.

2. If you want to do a font, you need font production software, which enables you to set sidebearings and generate a font.

3. What you are going for is *visually* equal, which means that it is not a precise geometry. Also you can't achieve it strictly, as in the case of the vo, or for example LA. In a font, as opposed to a drawing, sidebearings and kerning have a different definition. Sidebearings apply always, kerning are special exceptions like VA, or your vo.

4. How you design the glyphs will make them easier or harder to space...

MarvinMe's picture

Such is the beauty of type design...

My interest is predominantly based in logotype design. I like to customize outlined font glyph's in Illustrator and I always run into a wall with sidebearings and proper spacing. I've read up on all the books and scoured the internet for answers, but all I seem to come up with is the need to "train your eye". I also tried turning fonts upside down and several other suggestions to no real avail. Sure, I get a result, but it is so subjective.

The Law of Optical Spacing seemed really promising because my interpretation was that there was a mathematical way to approach the issue.

Bert, your explanation makes perfect sense.

William, thanks again for your insights. I wish there was a more precise geometric method for achieving the desired result.

It seems somewhat archaic to subjectively decide on what is visually equal. Glyphs have a certain ascender height, descender height, x-height, etc. Typically, these values are interlocked or repeated through a logotype or font depending on the letters. The one element of type design that seems the most "artsy" is the spacing and kerning, but perhaps that is what makes it human. It is still such a mystery...

William Berkson's picture

A lot of people have also felt that there *must* be a formula, but nobody has found it. Even ikern, which is the most automated thing I've heard of, has variables for the designer to set.

But when you think about it, you're designing the spaces as well as the interior of the glyphs and the curves and strokes. So it's not totally surprising that there's no formula. And if you think about a character like a c or v, the question of how much of the 'open' part to count in the between-letter space, and how much to count as part of the letter isn't clear, and may vary with the neighbor...

That being said, if you kern a whole font you will get very quick and sure at it by the time you finish!

charles ellertson's picture

A lot of people have also felt that there *must* be a formula, but nobody has found it

Getting even spacing is much easier with Chinese. The formula would just involve changing the Latin alphabet...

brianskywalker's picture

If we design our letters on a strict, and small grid (such as perhaps an 8x8 or 10x10), with no curves, we will be able to use a very simple mathematical formula.

hrant's picture

Well then, I can think of an even simpler approach: don't make type. ;-)

BTW, nobody has mentioned Kindersley yet. There.


MarvinMe's picture


All good stuff. I don't give up easily and this unresolved issue still perplexes me.

With regard to Kindersley:

"Kindersley's "optical kerning": for the purposes of kerning, each character is replaced by a circle placed at the center of gravity of that character; the radius of the circle is determined by the fourth moment of the character (that is, the fourth root of the sum over all black pixels of the fourth power of their distance from the centre)

Now if that isn't complicated...

hrant's picture

The important element of Kindersley's approach is that the more outlying bits have more weight, which makes total sense. So it's not just about surface area, but how "well-behaved" the profile is.


MarvinMe's picture

William shared this little nugget in 2006 and this sounds like the right path to me as well:

"Right now my working hypothesis is that the optical center is one factor in good spacing, and there are others such as roughly equal area between letters. What I think may be worth pursuing here is the idea of 'designing around the optical center'"

MarvinMe's picture

Perhaps there is an answer waiting to be unlocked between a combination of finding 'optical center' and the Law of Optical Volumes. Hmm...

William Berkson's picture

Rob (Marvin), I don't know if I mentioned in that thread on typophile, but while I was trying to understand Kindersley's ideas, I did have an e-mail exchange with the computer guy who helped develop a kerning program based on Kindersley's ideas.

The problem is that it never worked automatically. In particular I remember that a problem they never cracked was applying a single formula to both round and straight letters, and getting results that met the demands of Kindersley's eye. So that decision had to be imposed by human intervention. And it is a key one, and as came up in a recent thread, also varies by optical size of the letters (the visual angles spanned by a letter).

I still think the idea of 'optical centre' is a useful concept, but setting the overall advance width his theory never cracked successfully.

His effort is one of the more interesting ones, but ultimately like all the others not fully successful.

charles ellertson's picture

To quote myself (at least) "remember, what we read are clumps of words, not pairs of letters." In fact, depending on whatever other letters lie next to a pair, the optimum value with that pair will change, when considered in context. If you do not have contextual kerning, you should probably limit your kerning to the worst situation -- the "first, do no harm" aspect of design & composition.

In my view, proper letterfit & kerning is what helps us take in word boundaries without paying attention to them. The more distinct these are, the tighter the word spacing can be, if one so chooses. Letterfit is one key factor in effective word spacing.

And by the way, the better the word boundaries, that is, ones that don't call attention to themselves by being too close or too loose, the more leading choices that will work.

Try setting some type. For text, try esp. (approximately) a 10/13 and a 10/15 setting for a full page. If you can get both to look good, you're onto something.

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