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**To**:*math-font-discuss@cogs.susx.ac.uk***Subject**:**Bert Horn on New Math****From**:*lcs@suntopo.matups.fr (Laurent Siebenmann)***Date**: Mon, 11 Oct 93 01:04:02 +0100

********** Bert Horn on New Math ********** Dear Math Font enthousiasts, Berthold Horn has kindly answered some technical and aesthetic questions I have posed concerning the new TeX mathematics systems that have recently become available: MathTimes and the Lucida New Math. Since I am sure most of you are as interested as I in these important developments, I am posting a fairly complete compte rendu below. Basically I have just suppressed ripples of confusion caused by one ambiguous sentence in Berthold's first reply. Laurent Siebenmann *** math in Lucida bright *** Dear Berthold, Quick question: Do you recommend Lucida bright for heavy mathematics. I am interested but fear the math sys has never been debugged. Cheers, Laurent Siebenmann <lcs@matups.matups.fr> >From CompuServe.COM!71172.524 Fri Sep 24 17:08:43 1993 Date: 24 Sep 93 17:04:34 EDT From: Louis Vosloo <71172.524@CompuServe.COM> To: Laurent Siebenmann <laurent@math.toronto.edu> Subject: LB + LNM Dear Laurent: Nice hearing from you again! > Quick question: Do you recommend Lucida Bright for heavy mathematics. Yes, I can recommend Lucida Bright + Lucida New Math for heavy math. The fonts and the TeX macro files have been thoroughly tested. There are several text books that have been done using LB + LNM, mostly with a lot of math. > I am interested but fear the math sys has never been debugged. Oh, no, an enormous amount of work went into making sure it works correctly. And as a straight replacement for CM math it is easy to see that it should work, since the 0 - 127 range in LBMS is the same as in CMSY*, the 0 - 127 range in LBMO is the same as in CMMI*, and the 0 - 127 range in LBME is the same as in CMEX*. [Berthold means to say that the glyphs are similarly named and similarly encoded although quite *different* in details of design.] (Its harder to convince oneself everything is OK with MathTime, since in that font set there is *not* a complete match with CM, which in fact does lead to some minor problems --- not insurmountable, just distracting). The upper ranges of the LBM fonts have additional glyphs, which cover the LaTeX symbol font, the AMS math symbol fonts and more. TeX macro files `lcdplain.tex' and `lcdlatex.tex' are included for switching easily from CM to LB + LNM in both plain TeX and LaTeX. And the file `amssymlb.tex' defines most of the AMS math symbols (without need for loading AMS TeX). There *are* things in the 75 CM fonts and 89 AMS fonts that are missing in the 25 LB + LNM fonts, most notably bold math, and a script font (but there is a calligraphic font and a fraktur font). So its mostly a matter of taste. LucidaBright text fonts have a larger x-height than CM, and less delicate tendrils and swirls. Lucida New Math fonts have math relations and operators that are relatively small compared to the variables, at least in comparison to CM, which has relations and operators that are relatively large when compared to the variables. Cheers, Berthold Horn ** NEW MATH *** Dear Berthold, I am pleased to hear that Lucida New Math has been well tuned. The divergence from CM is interesting. I am all for the x-height increase and operator size changes. Math Time seems *not* to have style variations according to point size --- which seems natural because Times itself does not. However the great use of math at small size (5 and 7 and 10 points versus 9 and 10 points for prose) makes me wonder about the wisedom of this decision. Where does Lucida stand on this matter? And you? How many Lucida New Math fonts in all --- not counting Lucida Bright. I do use bold math for bold titles. What do you suggest with Lucida? A very high percentage of Adobe distributed roman fonts cannot be directly used in math as math-roman parallel to math-italic. I know this from bitter experience because the French classically favor math-roman caps for math symbols over math-italic caps --- an interesting stylistic tradition. In contrast, Knuth tailored cmr to be acceptable as math-roman, ie fam0 --- accepting some constraints on cmr. Thus he does not have a cmmr, although conceptually I feel it is there but coincident with cmr. I wonder whether Biggelow & Holmes did the same for Lucida Bright roman?? Or does Lucida New Math provide a special math-roman (.tfm? shapes?) ... Larry S PS. With your permission I will post this exchange of views on the math font list of Alan Jeffries. *** NEW MATH again *** Berthold! More quieries. How does Lucida New Math x-height compare with that of BlueSky's CM/PS? You are probably aware that BlueSky increased the "true"="measured-on-output" x-height without changing the metrics of CM. And what do you think of using the symbol font LBMS of Lucida New Math to replace that of CM/PS? Reciprocally, what about using the bold math of CM/PS as an additive to Lucida New Math? Does the B in the names LBMS, LBME, LBMS say Bright? A bit of history. Lucida as text cum TeX math were "air-ware" in 1985-6. What has in the interim? Both I and the math font list members know your standard blurb on Lucida and I guess it will appear as an advert in the Aston proceedings. Here I want more technical information. Larry PS. I hope the AmS math symbols are improved. Msam and msbm seemed a bit tentative to me. ... >From CompuServe.COM!71172.524 Mon Sep 27 12:02:55 1993 Date: 27 Sep 93 11:45:51 EDT From: Louis Vosloo <71172.524@CompuServe.COM> To: Laurent Siebenmann <laurent@math.toronto.edu> Subject: reply again Dear Laurent: 1993/Sep/27 > How does Lucida New Math x-height compare with that of BlueSky's CM/PS? The XHeight is substantially larger. Note that this is *independent* of any particular implementation or rasterization. The CapHeight and Ascender are also larger (which is why we recommend using 9.5pt for LBR text where one might use 10pt for CMR), but not as much. Here is CMR10: CapHeight 683.333 XHeight 430.556 Ascender 694.444 Descender -194.444 Here is LBR: CapHeight 723 XHeight 530 Ascender 771 Descender -193 > You are probably aware that BlueSky increased the > "true"="measured-on-output" x-height without changing the metrics of CM. The BSR CM outlines are *perfectly* accurate --- they correspond *exactly* to the METAFONT code (we did the hinting work and conversion to Type 1 format). What you are referring to is a difference in rasterization between METAFONT and Adobe Type 1 at 300 dpi. The grid-fitting in the two rasterizers work *very* differently. And at that *particular* resolution, it happens that the XHeight ends up locked in one pixel higher in ATM than it does in METAFONT output. ... > Does the B in the names LBMS, LBME, LBMS say Bright? Yes, when we started, we used these short files names (for TFM files e.g.). Then another vendor used LBM for an inferior, buggy, incomplete, non-TeX compatible set of math fonts in TT format. So we had to change the PS FontNames, but it was too hard to change the short font file names at that point (since these are what TeX uses). > A bit of history. Lucida as text cum TeX math were "air-ware" in > 1985-6. What has happened in the interim? Not sure what that means? The old Lucida (1987) and the old LucidaMath (1990) from Adobe were rarely used because (i) the bold fonts were generally considered too heavy (ii) they were expensive (iii) TeX support was lacking (iv) there were no previewers and printer drivers at that time that could properly exploit them. LucidaBright + LucidaNewMath benefitted from that experience. ... > I hope the AmS math symbols are improved. > Msam and msbm seemed a bit tentative to me. I think the corresponding symbols in Lucida New Math look better, but thats a matter of personal taste. There has been a lot of noise about in particular the AMS version of black board bold (old and new). Some in fact prefer the Adobe MathPi interpretation of open-face (a.k.a. black-board bold). Regards, Berthold. *** NEW MATHs again *** Dear Berthold, I have partially checked your assertion that the superiority of the Blue Sky CM/PS font series on 300dpi PostScript printers is a rasterisation phenomenon and not at all a matter of deformed outlines. Indeed at very high resolutions the measured x-height : capital height converges to the same value for Blue Sky CM/PS and for metafont versions. I recall however that the superiority of BlueSky's CM/PS to BlueSky's or OzTeX's bitmapped CM is noticeable on many fonts at moderate resolutions. This suggests that PostScript Type1 hinting will usually produce better quality at 300dpi than Metafont, even with the various grid-fitting parameters that Knuth provides. For the record, I note the x-height / capital height ratios for cmr10, Times, Lucida Bright Roman are in sharply increasing arithmetic progression: cmr .63 Times .68 Lucida Bright Roman .73 In CM, in spite of the marked shape changes with *point size*, this ratio is one thing that does not change to my knowledge with *point size*. (However it changes with style eg. for cmcsc). A high value of this ratio (ie near 1) is helpful in math fonts, because in $X^n$, $x^n$, it is distracting if the top of n falls below the top of X or if the base of n falls above the top of x. ------------- LS> Math Time seems *not* to have style variations according to point LS> size --- which seems natural because Times itself does not. LS> However the great use of math at small size (5 and 7 and 10 LS> points versus 9 and 10 points for prose) makes me wonder about LS> the wisedom of this decision. LS> Where does LucidaBright / LucidaNewMath stand on this matter? And you? BH> There is only one design size of each font. It would, BH> of course, be possible to make other sizes (as in the CM BH> fonts in Type 1 format), but its hard to justify the BH> enormous amount of work for the small improvement possible. BH> Keep in mind that the market for these fonts is under BH> 1/1000-th (!) of the market for the MicroSoft TrueType BH> font pack for Windows, and that just the *hinting* for a BH> commercial grade font may take from a few man days to a few BH> man weeks depending on tools available, complexity of the BH> font and how good a job one wants to do. Eventually tools BH> for Making Multiple Masters may improve, but one still has BH> to design the `master fonts' at the corners of the BH> parameter hyper-cube. BH> BH> Despite this, math looks good. One thing one should *not* BH> do, however, is use the CM scheme of 10pt for text size, BH> 7pt for subscripts, 5pt for subsubscript. That set of BH> sizes works *only* if the smaller sizes are extended, i.e. BH> proportionatly much wider than the larger sizes (when BH> scaled to the same x-height). Instead use something like BH> 9.5pt, 6.9pt and 5.2pt for LucidaNewMath (For MathTime use BH> 10pt, 7.6pt and 6.0pt). I have recently run tests with MathTime on an algebraic topology monograph containing many sub- and super-scripts of both first and second order. (Third order scripts are forbidden and relatively easy to eliminate in practice.) The 10pt, 7pt, and 5pt script sizing that has been preprogammed by M. Spivak produced disastrous results with 10-point type. Although I have not verified, I feel the results would also be disastrous at resolutions higher than 300dpi, and even at infinite resolution for people with not-quite-perfect vision. The 10pt, 7.6pt and 6.0pt was I my opinion much better, approaching the readability of the CM scheme of Knuth using 10pt, 7pt, and 5pt. Incidentally, I feel that the distribution of Spivak's macros using 10,7,5 will cause a a lot of damage to readability of math in the near future unless warning is sounded and the distributions are soon revised. To get a scheme in which I was happy about the readability of the second order subscripts, I had to make them about 6.5pt!! Then there was then a problem that in $x_N$, the N is about as big as the x. This problem is admittedly less severe for Lucida Bright because of the proportionally greater x-height. In conclusion, in spite of the difficulties involved, I conclude that shape variation for script and scriptscript is a goal that should be kept prominently in view for math font systems. I suspect the CM system will not be distinctly surpassed without it. ----------- BH> Maybe wait for an `expert font pack' ? Interesting; do explain! ----------- BH> In fact, CMR does *not* work well as a math roman font, BH> since it has to work as a text font. A math font has to do BH> weird and wonderful things. For example, in a math fonts, BH> character widths are *not* character widths, but where to BH> put the subscript, italic corrections are *not* italic BH> corrections, but where to put the superscript, kern pairs BH> are *not* kern pairs, but where to put the accent, etc. BH> So, for a start with cmr as a math roman font, subscripts BH> and superscript of necessity have to be directly above one BH> another, which for some letters means there is too much BH> space between sub/superscripts and the letter. At the BH> minimum, one has to create a new font with altered BH> character widths and side-bearings, and added bogus kern BH> pairs for accent positioning. Basically I agree. Nevertheless I still conjecture that Don Knuth constrained cmr to be a reasonable good Math Roman. No one did this for Times Roman. With Adobe fonts there is a tendancy, very evident with Baskerville, to anticipate kerns. For example the T does not have its full width but rather anticipates a kern with a following lowercase. Conflict with the superscript in $\fam0 T^n$ results. The same problems seem present with Times although I have not observed outright collisions; just very uneven and incoherent spacing. Thus as matters stand the MathTime fonts cannot be used for classical French math typography. And in the Anglo-German tradition one has to treat what rare Math Roman there is with extreme care, say by forming operator symbols with special spacing. Perhaps the mere use of an altered .tfm could sort things out pretty well in the case of Times!? LS> I wonder whether Bigelow & Holmes did the same LS> [as Knuth did for cmr] for Lucida LS> Bright roman?? Or does Lucida New Math provide a special LS> math-roman (.tfm? shapes?) BH> Maybe wait for LNM-Roman ? Sounds like a fine idea! Best wishes. Laurent Siebenmann <lcs@matups.matups.fr>

**Follow-Ups**:**Re: Bert Horn on New Math***From:*jeremy@cs.aukuni.ac.nz

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