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Bert Horn on New Math seq

 **** Bert Horn on New Math continued ****

 Date: 10 Oct 93 11:07:46-0400
 From: Berthold Horn <71172.524@CompuServe.COM>
 To: Laurent Siebenmann <laurent@math.toronto.edu>
 cc: Laurent Siebenmann <lcs@matups.matups.fr>
 Subject: reply to reply
 Message-ID: <931010150346 71172.524 DHQ63-1@CompuServe.COM>
 Status: R


Thanks for your comments.

>       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(!?)

One has to be careful to avoid being accused of blasphemy, but
generally speaking METAFONTs mechanisms for grid-fitting are not as
good as those in Type 1 fonts, particularly at very low resolutions,
such as on screen (around 72 dpi).  Also, METAFONT's grid-fitting
has not changed over the years, while Type 1's declarative hinting
style allows improvements in rasterizers to lead to improved
rendering, *without* any changes in the font (a big advantage over
TrueType, by the way, which uses imperative hinting). Adobe Type
Manager (ATM) has distinctly better rasterization than older PS
printer rasterization. Fortunately the ATM rasterizer has now been
ported to PS printers as well (and unfortunately some PS `clones'
have distinctly inferior rasterizers).

However, a lot depends on how much work goes into hinting.  An
`auto-hinted' font made by Fontographer say, can be noticable
inferior to a really well made METAFONT with careful attention paid
to grid-fitting issues.  The BSR CM fonts were hinted by Y&Y and
have full hand hinting, including hint replacement.  The work was
done several years ago when tools for doing this were not as easy to
use as they are today, and it was a truly huge job, with almost
9,600 glyphs to work on.  So one might expect that some small
improvements could be made today if someone wanted to really invest
a *great* deal of time.  But on the whole the hinting in these fonts
is very good, certainly way beyond todays `auto hinting'.

> in practice.)  The 10pt, 7pt, and 5pt script sizing that has been
> preprogammed by M. Spivak produced disastrous results with 10-point type.

> The 10pt, 7.6pt and 6.0pt was in 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.

I agree completely.  He does warn about this near the end of his
manual. But most users will just us `mtmacs.tex' as it comes out of
the box. Which is why, when you get the MathTime version 1.1 font
set from Y&Y, the macros are instead set up for the default of 10,
7.6 and 6pt. Which I think will prevent the generation of a lot of
hard to read material.

>    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.

Well, its just a matter of demand and allocation of resources.  The
demand for TeX fonts (that one pays for) is very limited.  And there
is a need for several other things that require a lot of work also,
such as bold Greek, a real small caps font, a Script font.  In the
case of MathTime there is also need for open-face, black-letter and
other stuff.  So designing other sizes of the main fonts may have to
be a job that stays on the back burner until either demand picks up
or the other needs are all met.

It's also quite clear that the `right' way to do this is with
Multiple Masters.  For one thing, instead of designing a subscript
size *and* a subsubscript size, one can then get away with just
making *one* new font. MM works fine on the Mac and has been there
for a while, but has only just been released for PC/Windows and of
course Unix (except NeXT) is still light years behind in use of
scalable outline fonts (although Display PostScript for X Windows is
almost a reality).  Also, since *real* font work means proprietary
tools, there is going to be some time while proper tools for MM are
developed at various small foundries.

> > Maybe wait for an `expert font pack' ?

> Interesting; do explain!

No comment at this time.

> Basically I agree.  Nevertheless I still conjecture that Don Knuth
> constrained cmr to be a reasonably 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.

Any text font has to have its side-bearings and advance width
adjusted to work properly  in math.  This is absolutely critical for
an italic font (regular or bold), but is also important for upright
(regular or bold). CMR10 and CMBX10 are set up for text.  To be used
in math, there should really be versions of these fonts that have
been tuned for math.  For a start, if the text fonts are used, then
subscripts and superscripts appear directly above one another,
independent of the shape of the letter.  This is particularly
irritating for the upright Greek upper case letters, which are drawn
from CMR10.  For Gamma, Upsilon, and Psi, at least, the subscript
should be much closer to the letter than the superscript (this is
not a problem in LucidaNewMath, since there the upper case upright
Greek letters are drawn from a math font, where subscripts can be
placed independently of where superscripts appear).

> 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!?

A TFM file *must* agree with the actual font.  The advance width
recorded in the TFM file *must* be equal to the actual advance width
in the font. Otherwise all sorts of hell can break loose.  The right
way to solve this problem is to adjust the font.  For a Type 1 font
one can use a utility called SIDEBEAR, rather than starting over
from scratch.  It's very easy. The hard work is the individual
tuning of the left and right sidebearings. One must look at lots and
lots of possible combinations to get it perfect. Or, if proper tools
are missing, one can resort to virtual fonts, although then what is
produced cannot be used with anything but TeX...

Regards, Berthold.