# What methods exist for determining if a font is similar or derivative work?

I've always assumed that the vector outlines contained in a font file are essentially mathematical formulas describing each of those shapes; and that no matter how similar two fonts might appear, the combination of characteristics (proportions, contours, angles, spacing, etc) results in a vector equation revealing more differences than the eye might be able to decipher. I don't know how accurate this is, but as I am familiar with the concept of vectors in algebra, it seems that it should at least be possible to tell if a given font was produced by altering the outlines of a paid font whose EULA forbade such alterations.

Now that live typographic interpolation and parametric fonts are being used in web browsers, and foundries are able to create enormous font families extrapolated from as little as one master, I wonder how difficult it will become to tell original work from derivative work. By derivative I mean originating from the same digital source.

My becoming a typographer was born of a need for a typeface for projects when nothing in existence seemed to fit. So I am asking as an artist, out of curiosity ... not as a crybaby complaining that someone stole my shapes, er, intellectual property. Plagiarism offends me more than capitalism or piracy combined, because of the sheer lack of imagination.

So my question has two parts:

1. What methods exist for determining the similarity or difference of fonts?

2. How do they function? Specifically, can they measure both qualitative and quantitative changes to the original's outlines? Some seem to assume that making a font slightly heavier means the outlines are unique, but as math based shapes, I would expect that the bulk of the equation is proportionally identical, even if the glyphs have grown along one axis.

• Interesting question, I don't think its been done but if you could find (for example) 20% of coordinates across the set match (+- a bit) another font then you'd have grounds to suspect it's an rip-off – Digital Lightcraft Aug 3 '17 at 7:35
• Font outlines themselves dont fall under copyright in several jusridictions, so your EULA may be null and void for the outlines. Only the whole font program does, if even that, so its the kerning and other tables that really make the font copyrightable. Also the name can be protected. So what you can do depends on your locale. – joojaa Aug 11 '17 at 10:17
• We need some context here. Are you asking in the eyes of the law (whereas computer code can be copyrighted)? Or just in general from an ethical designer standpoint? – DA01 Aug 11 '17 at 19:38
• @joojaa it's sort of a loophole, but computer code can be copyrighted--even though the shape of a letter can not. – DA01 Aug 11 '17 at 19:39
• @DA01 yes but that means if i, or better yet somebody else extract the path and from that make a font then i havent broken copyright. Likewise if i redraw paths . – joojaa Aug 12 '17 at 7:37

I can't say for sure what methods are used by the large font outlets to combat derivative work, though I imagine it begins with manual scrutiny. But even the most sophisticated methods could never be foolproof.

Essentially, because it is legally permissible in the USA to trace another person's font by hand and digitize that tracing (but please check the legality yourself, with a lawyer), an unscrupulous person could create an automated tool to simulate that process, complete with minor distortions of contour and substantially different control points, slightly different spacing, different metrics, differently-ordered tables, etc.

Even with all these differences, and depending on the tracing algorithm, it's conceivable that statistical methods could be used to determine if the differences resulted from artificially generated noise or from a manual tracing process; but this would be mathematically difficult to achieve and relatively easy to defeat.

Creating automated derivatives is illegal in the US, but proving that the new font was an automated ripoff would be impossible, if the person was thorough in covering their tracks.

Creating such a tool seems like an awful lot of work that could instead be spent on creating original designs. And it's a dangerous gambit. Any accidental traces left from the original could prove the person's guilt. If they were churning out a lot of fonts, a court might simply conclude that creating them all by hand was clearly impossible, and they must therefore be ripoffs. And an aggrieved company could ruin the person through drawn-out litigation, even if their case was ultimately unprovable.

Basically, it's better for everyone when people play nice.

• I wholeheartedly agree with all of what you said. I think readers are assuming my question was a precursor to either a pro-piracy project or a way to police new fonts. Both the language of EULAs as well as my mathematical fascination with vectors just had me curious! – Moscarda Aug 18 '17 at 15:29

Simply put technically your question is hard to answer. There is no surefire way of doing this. Offsetting a font may change the number and location of points and the points can be re-parametrized. Different tools may choose to do this differently.

Image 1: Offsetting (here non-uniformly done). Does not preserve the number of points.

This feature makes it hard to match the fonts. While adding points in each glyph can be somehow handled its really hard. If you really need to be forensically accurate you can draw the actual tangent of the curvature (the curvature stays much more similar but thisis not equal to the tangent points position) and compare those endpoints. But if the person fixed things after offset then you don't have much to go on on the outline data.

Personally I would for legal and amount of work reasons check to see the kerning table. Or possibly any of the other features not in the outline and see how similar that is. Because that is easy (also check for uniform offsets), and fast to do. Hiding and redoing the kerning table is hideously hard and slow to do anew. If they have in fact done that your on thin ice anyway. Also you could encode your font is a peculiar order, if they have the same order they are quite easily caught.

Legaly, you may or may not have a case. See some jurisdictions do not give copyright to the font outlines per see*, while others give them really good protection. Yes, copyright is totally wacky, some things can not be copyrighted, although the font program has copyright. For example if I make a technical drawing of a chair I don't get a IP on it, though I can in some cases submit for patent protection. Even though So there might not be any IP to defend.

So you need to talk with a lawyer, since you are not saying your locale.

* Like United States of America

• Again, I'm not asking for legal advice. Just what is in use or possible. – Moscarda Aug 18 '17 at 15:30
• @Moscarda given how few people get caught i would say that this kild fo crawling is not done. They just check if it is their font or not. Determining what to over a derivate sork is too hard. – joojaa Aug 18 '17 at 16:10

Copyright is a gray area in general in that what is or is not an infringement is usually decided on a case-by-case basis. So there's always some level of subjectivity to it.

With typefaces, it gets even weirder--especially in the US--where letterforms, themselves, can not be copyrighted.

And then there's the very muddy areas of 'homages' and 'inspired by' releases. A lot of typefaces released are based on historical typefaces--or even more contemporary faces--and is part of the selling/marketing of said typeface.

That said, compute code can be copyrighted. So, to answer your question from a technical standpoint, some judge would have to compare two sets of code and decide if there is enough similarities to consider it derivative.

As with most issues of copyright, the 'method' used to determine whether something is derivative or not is 'going to court'.

• Yes i am aware of the legal standing, and i'm not asking from a legal/moral standpoint. My views aren't relevant to the question of are there tools in use to detect if a font shares enough mathematical similarity to determine a common source. – Moscarda Aug 18 '17 at 15:23
• @moscarda typically you'd just open the fonts up on font editing software and look at the nodes. Pretty easy to eyeball it and tell if one font was just a manipulation of the other. – DA01 Aug 18 '17 at 18:46
• Regarding computer code. Wouldn't the font just be data, not code? The code resides in the application interpreting the font data. – rebusB Sep 29 '17 at 16:56
• @rebusB well, data can also be copyrighted. But in terms of fonts, I believe it's been traditionally seen as 'software' and, as such 'code' that can be protected. However, the cases of that are few and far between from what I understand. – DA01 Sep 29 '17 at 16:58