a short history of the lucida math fonts 2. -...

154 TUGboat, Volume 37 (2016), No. 2

A short history of the Lucida math fonts

Charles Bigelow

This talk is about the development of Lucida mathfonts from the beginnings of Lucida in the early 1980sto the most recent Lucida OpenType math fonts of2011 and later. The images included here, and more,are available online at http://tug.org/tug2016/

slides/bigelow-lucidamath.pdf.

1. The above shows a sampling of characters in Lu-cida Math fonts. There are letter-like symbols andalso different shapes and sizes of arrows, operators,relations, and delimiters.

Typography involves several kinds of harmonybetween graphical elements. Weight, height, width,stroke thickness, proportions, shapes, orientation,position, spacing, and stylistic features such as serifs,are the main relationships that may have to be har-monized. In the typography of mathematics, manysymbols are derived from letters but have becomeseparate semantic elements, not units necessarilycombined into words. Within the formal languageof mathematics, symbols become ideograms — repre-senting ideas — and logograms — spoken as a word orphrase. Naturally, the spoken version changes fromlanguage to language, while the meaning of the sym-bol is constant. Moreover, symbols for mathematicsmay need adjustment for optical scale because somemay be used large and small. And, of course theymust be legible.

2. What were the principles on which Lucida wasbased? Although we were designing a typeface fam-ily for emerging technologies — laser printing andscreen display — we tended to look backwards to thehistory of letter forms, in traditional handwriting orcalligraphy, which goes back more than two thou-sand years for Latin scripts and for more than fivehundred years before that for Greek.

3. We wanted the forms of the Lucida letters to berelated to traditional scribal handwriting, but notnecessarily “calligraphy” in its sense of “beautiful

Charles Bigelow

TUGboat, Volume 37 (2016), No. 2 155

writing”. Instead we aimed for simplicity becauseour goal was easy reading under difficult imagingconditions.

Our goal was to adapt traditional forms forsimpler rendering at a range of resolutions. We de-veloped the letters in outline formats, principallyusing Peter Karow’s Ikarus system, but the outlineswere then converted to bitmaps, either on-the-fly inprinters or pre-rasterized for screens, in the technol-ogy of the early 1980s. Laser printers of the late1970s and early 1980s had addressable resolutionsaround 240 to 300 dots per inch, and bitmap displayscreen resolutions were around 70 to 75 pixels perinch on screen.

We made many experiments constructing lettersfrom bitmaps, and then used a few digital systems ofthe early 1980s to study the different pixel patternswhen letters were rasterized at different resolutions.At high resolutions, the letters looked like analogtypefaces, but at low resolutions, the letters becameminimalist aggregations of dots, and many distin-guishing features that separated one type designfrom another were obscured by the rough, rasterizedstair-cased shapes and by data loss.

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz

1234567890


1234567890


12345678904. In 1984, Imagen Corporation released the firstLucida family of seriffed designs. They were simplein form and had several adaptations for lower res-olutions, such as short serifs and wide inter-letterspacing to prevent collisions of character elementsand clarity at small sizes and greater reading dis-tances from screens, for which loose spacing is oftenhelpful. We made the bold weight with twice thestroke weight of the normal weight, for unambiguousrecognition of weight changes at low resolutions. In-stead of a “just noticeable difference” we wanted a“dramatically noticeable difference”.

These designs constituted the first new familyof types for laser printing and screens. When wedeveloped Lucida, most typefaces being digitizedwere adaptations of existing metal or photo faces.

The adaptations were sometimes made ethically, butoften by plagiarism. We hoped that our develop-ment of new digital types would spur more originaland more ethical approaches to type, and the Imagenfirm, started by graduate students and AI researchersat Stanford, agreed. Another five years went by, how-ever, before major firms began to produce originaldesigns.

5. In 1985, also with Imagen, we brought out asans-serif companion to the original seriffed Lucidafamily. (The second stanza here shows the sans-serifvariants, compared to the seriffed originals in thefirst stanza.) Many of the sans-serif Lucida features,including slightly darkish weight, generous spacing,big x-height, simple forms, and a humanistic styledating back to legible letters of the Italian Renais-sance, made the family ideal for screen displays anduser interfaces. Lucida Sans Unicode and LucidaConsole have been bundled with Microsoft Windowssince the early 1990s, and a version of Lucida Sans,named Lucida Grande (because it had a much big-ger character set including Greek, Cyrillic, Hebrew,Arabic, Thai, and many signs and symbols) wereadopted as the user interface fonts for MacintoshOS X from the beta tests of 2000 until 2014, whenLucida Grande was replaced by a digitized versionof a more traditional “grotesque” sans-serif.

6. The individual letters of the first Lucida seriffedtype were crafted in some unusual ways. Serifs andtheir brackets and some other features were polygonal



rather than curved. At the time of its design, 1983–1984, some printing and imaging systems used polyg-onal outlines, whereas other systems used curvedcontours, including circular arcs or cubic curves inBezier or Hermite forms. We believed that it wouldbe better to design the polygonal serifs ourselvesrather than let some program automatically renderthem from curved forms. But, we kept curves for thelarger aspects of the letters, like arches and bowls.

klmno7. Here we see diagonal, straight, arched, and fullycurved letters in combination, with the characteristicopen spacing of the original Lucida.

klmno

klmno

klmno8. Comparison of the first Lucida (top) to TimesRoman (middle), which appeared under its own nameand in plagiarized forms under other names, to amodification of Lucida (bottom), fitted to the samewidths as Times Roman and with modified serifsbut keeping the x-height of Lucida (bottom). Itlooks condensed because the x-height is greater thanthat of Times Roman but the width is not. Welater released a free version of this design under thename “Luxi Serif”. It can still be found as a free fontfrom web font firms and others. They are gratis butnot open source, because we prohibited modificationwithout our permission. We felt that the artisticaspects of the designs should be ours to control.

9. Lucida Math Italic, in the same character setas Computer Modern Math Italic. We began thedesign of math symbols for Lucida in 1985, in partbecause of the influence of Donald Knuth, who hadinvited me to join the Stanford faculty and to workwith him. If there had been a guide to the variousharmonizations needed for math fonts, it would havesaved us a lot of effort and time, but there werenone, except for examples from which some principlescould be inferred. Also, we liked to figure out thingsby ourselves from first principles. We thought newtechnologies demanded new design ideas — a lessonwe learned by studying with Hermann Zapf — so evenhad there been guides for math characters, we mighthave ignored them, being young.

10. Lucida Math Symbol. We made the strokes ofthe math symbols fairly thick, in keeping with thegeneral Lucida parameters, and we made many of thesymbols fit in the standard figure widths, for easiercomposition of simple equations and usage in tabularcomposition, spreadsheets, etc. This tended to makethe operators smaller than the letter symbols usedfor variables. We did this because we thought thatthe majority of uses of the Lucida math fonts wouldnot be for traditional publishing of mathematics andscience, but for simpler uses on screens.

Charles Bigelow


11. We also produced a Lucida Math Extensionfont. In the first image, you can only see the topsof the characters, because to conform with DonaldKnuth’s approach with Computer Modern, manyof the big delimiters and extensions “hang” from acentral position in the character cell. The secondimage shows the full characters at a smaller size.

a = b c ≠ d

p ≥ q v ÷ w

a ⊗ b c ⊕ d

p ± q v ⊖ w

A ≤ B C ⊇ D

P ⊒ Q V ∪ W

12. Above is the original Lucida math operators ofvarious kinds with lower-case and capital letters. Theweights are harmonized and the symbols are clearand resist digital degradation. We developed thesemath fonts in 1985, but they were not released until1990 by Adobe. During that time, principally underthe influence of PostScript, laser printing became anenabling technology for digital prepress for print pub-lishing, and fonts intended only for lower-resolutionprinting were less favored. When the original Lucidaand Lucida Math fonts were used for more tradition-ally printed math publishing, they seemed too strongand dark, although they held up well on screens andlaser printers. As an editor at one academic press putit, “Lucida Math seemed too aggressively legible”.

13. For print publishing, and now for high resolutionscreen displays, we prefer legibility (at least whenit is more subliminal than aggressive). In 1987, forScientific American magazine), we made a modifi-cation of the original seriffed Lucida with increasedcontrast of thick to thin strokes, with more “modern”style serifs, and with tighter letterspacing. An editorat MacWorld magazine said it looked “brighter”, sowe named it Lucida Bright. It was used as the bodytext in Scientific American for nine years.

a = b c ≠ d

p ≥ q v ÷ w

a - b c + d

p ) q v , w

A 7 B C 6 D

P › Q V ~ W14. For Lucida Bright, we developed “brightened”math characters. These were released by Microsoftin 1992 in TrueType font format. This prompted re-quests for TEX-adapted versions in PostScript format.At this point, we came to realize that the productionof fully functional, TEX-compatible math fonts re-quired more knowledge of TEX and more effort thanwe two designers could accomplish on our own.



15. Over the next few years, we worked with Bertholdand Blenda Horn, of their firm Y&Y, at turning theLucida Bright Math fonts into fully functioning Post-Script TEX math fonts. It was a tremendous effortmade feasible only with the patient and extraordi-nary collaboration of the Horns.

16. During this development, we and Y&Y receivedrequests for more math characters, so we kept addingthem, and then came more requests for more char-acters. If we hadn’t declared a halt and frozen the

fonts for release, we would probably be adding morecharacters still. (In truth, we still are, but now tothe TUG releases, as we’ll see.) To distinguish theY&Y fonts from the previous Lucida Bright Math,which were in TrueType, not PostScript, and hadfewer characters and different encodings, we namedthe Y&Y releases “Lucida New Math”. I suppose wecould have called them Lucida Bright Math 2.0, butthat would have been confusing, too.

17. In the years since the Y&Y versions of the Lu-cida Bright New Math, the Unicode Consortiumadded math to the Unicode standard, with hundredsof characters beyond the standard TEX repertoire.Eventually, almost twenty years after the Y&Y Lu-cida versions, Karl Berry asked (following user re-quests) if we would like to work on OpenType ver-sions in collaboration with TUG, and we began towork on OpenType versions of Lucida Bright andLucida Math. The task turned out to be severaltimes greater than the original Y&Y development,and also much greater than we anticipated. Partlybecause we revised some of our design notions dur-ing the development process, and partly because weadded hundreds of characters.

a = b c ≠ d

a = b c ≠ d

a - b c + d

a ⊕ b c ⊗ d

A 7 B C 6 D

A ≤ B C ⊇ D

P › Q V ~ W

P ⊒ Q V ∪ W

Charles Bigelow


18. In developing the OpenType versions, we decidedto abandon our original notion that the math opera-tors should match the figure widths; a comparisonof the old and new operator sizes is shown above.Our experience over the years suggested that largeroperators were more readable by mathematicians.This is anecdotal evidence; we did not conduct con-trolled laboratory tests of mathematicians readingequations, which should be done. Nevertheless, wemade the math symbols bigger. (Interestingly, one ofthe most prolific legibility researchers of the 20th cen-tury, Miles Tinker, wrote his psychology Ph.D. thesisat Stanford in 1927 on “An Experimental study oflegibility, perception, and eye movement in the read-ing of formulae” . . . exactly a half-century beforeDonald Knuth began work on TEX at Stanford.)

a = b c+da = b c+da = b c+d

19. We also made a series of bold weight versions ofthe math symbols. Unlike the original bold weight ofLucida, which had stems twice as thick as the normalweight, the Lucida Bright bold is more accurately ademibold, with stems 1.5 times as thick as the normal.Still very noticeable but not as domineering in text.(The above shows Lucida Bright Math OT, LucidaBright Math Demi OT, and the original Lucida Bold.)

Not all these bold characters have well-definedsemantics in mathematics, but we became accus-tomed to requests for such things, so we believedthat if we designed the characters, mathematicianswould find uses for them.

20. In our experience, and evidently in that of othertype designers as well, the development of successful,original typefaces and fonts for mathematics requirestechnical collaboration. We wish to thank those whohelped with the technical aspects of Lucida Mathfont development. For the Adobe PostScript versionsof original Lucida Math: Daniel Mills. For the Y&Y

PostScript versions, Lucida New Math: BertholdHorn and Blenda Horn. For the TUG OpenType ver-sions, Lucida Math OT: Karl Berry, Khaled Hosny,and Michael Sharpe, plus a cast of testers, bug re-porters, commenters, and other advisers: BarbaraBeeton, Hans Hagen, Taco Hoekwater, Bogus lawJackowski, Mojca Miklavec, Norbert Preining, WillRobertson, Ulrik Vieth, Bruno Voisin.

ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ

21. Work on the Lucida math fonts sometimes re-sulted in new stand-alone designs, especially scripts.The first such spin-off was “Lucida Calligraphy”, a“brighter” version of the original calligraphic capitalsin Lucida Math. Above, the original capitals areshown first, with the bright Lucida capitals below.

22. Here is Lucida Calligraphy in the ASCII set.Originally distributed by Microsoft and now by othervendors, including Monotype. It is based on ItalianRenaissance chancery cursive, but, like the otherLucida designs, adapted to digital rendering at arange of resolutions and technologies. We see italmost every day somewhere, often used in somesurprising way.



23. We have since expanded Lucida Calligraphythrough a range of weights. Most of these are inASCII only for English-speaking users. We are nowdeveloping additional characters sets for Europeanlanguages and orthographies.

ABCDEFGHIJKLMNOPQRSTUVWXYZ

abcdefghijklmnopqrstuvwxyz1234567890

&@*?!


1234567890&@*?!

ABCDEFGHIJKLMNOPQRSTUVWXYZ

abcdefghijklmnopqrstuvwxyz1234567890

&@*?!


1234567890&@*?!

24. For the Lucida OpenType Math fonts, we haverecently developed an English Roundhand script.It is not a copy of a standard traditional round-hand, but a style with more “zip” (equivalent to“elan”) devised by Kris Holmes. This will soon bereleased in normal and bold weights, first throughTUG. (The name hasn’t yet been confirmed, butseveral dozen TUG members at the recent meetingin Toronto signed a petition requesting it be called“Typey McTypeface”.)

The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful;

the ideas, like the colours or the words, must fit together in a harmonious way.

G. H. Hardy

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25. Designing so many hundreds, eventually thou-sands, of characters for mathematics, starting fromscratch has been a thirty year adventure that is notover yet. The English mathematician G.H. Hardyonce wrote what could serve as a guide for type designas well as mathematics. “The Mathematician’s pat-terns, like the painter’s or the poet’s, must be beau-tiful; the ideas, like the colours or the words, mustfit together in a harmonious way.” (From A Mathe-matician’s Apology.)

26. Kris Holmes could not be at the conference,but she contributed most of what makes the Lucidadesigns exciting as well as legible, so I want to closewith a photo of her when she studied with HermannZapf many years ago, looking intently over Zapf’sshoulder as he demonstrates how to write with colors;and then again with Zapf, a quarter-century later,when Kris was one of the judges for a Linotype Arabictype design competition.

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Charles Bigelow

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