>Why don't you make them _S_ shaped?
To some degree, this problem was eventually solved, c.f., the five volume set _Computers and Typesetting_:
https://www-cs-faculty.stanford.edu/~knuth/abcde.html
but then one had the effort to create a new typeface set for math equations by the AMS, eventually named Euler as written up in "AMS Euler — a new typeface for mathematics". _Scholarly Publishing_ and so forth, but arguably, things went awry in that rather than capture the ductus of Prof. Zapf's pen, and model based on that stroke and a pen shape, the expedient approach of simply modeling the outline was arrived at and implemented due to the difficulty and lengthy time required for the idealized approach.
Another consideration may have been that there doesn't seem to be an available algorithm which is robust and accurate and automatic for determining the curves which describe the union of arbitrary Bézier curves (some projects get around this by making high resolution pixel images and tracing them).
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1. Funnily enough this is the second time in two days that I’ve shared this article, albeit in different contexts.
2. As far as I know, although I could be wrong.
Fig 9 stood out to me as obviously wrong. The two glyphs on the left are pixel by pixel identical, as are the three middle ones, and the two on the right. Quite mysterious though considering this PDF appears to be a scan.
https://www.dkriesel.com/en/blog/2013/0802_xerox-workcentres...
See the definitions of "O" and related glyphs for a good example[2].
[1] https://github.com/be5invis/PatEL
[2] https://github.com/be5invis/Iosevka/blob/main/packages/font-...
Thanks for giving us beautiful layout and better-looking fonts. Every time I write a new paper when I press "compile" in Overleaf I'm greatful that he made our work more beautiful, and it motivates me to make the content matter, too.
Having models attempt an SVG letter S remains one of my personal/informal LLM benchmarks. They are still pretty bad at it.
This results in a more complex and less obvious mathematical definition.
Also, a naively symmetrical "S" tends not to look good, probably because of these same issues, so needs further adjustment to match our visual expectations. This complicates the definition further.
This is all fine. What fascinates me with Knuth's work is how he applies mathematical rigour to concepts like these which are generally considered "artistic" and subjective. It underlines how mathematical ideas of symmetry etc. play a role in making the world we live in beautiful.
