# No Subject

• To: math-font-discuss@cogs.susx.ac.uk
• From: H Sami Sozuer <sozueh@rpi.edu>
• Date: Thu, 5 Aug 1993 00:53:42 -0400

Concerning the new decisions on the encoding scheme to be used in
LaTeX, I will  make the following points:

1 - It is my understanding that new encoding schemes are being
planned to accomodate the usage of calligraphic, fraktur and
blackboard letters in math formulas, and that these will
have to be assigned to distinct families (6 in all). I believe
this is a serious mistake. Many PostScript fonts are available
for calligraphic, script and fraktur typefaces and these can
one does not have to waste many fonts even if they may never
used in a particular document.

2 - I believe that NFSS is a major improvement over the
default scheme used in LaTeX 2.09. However, it leaves a lot
to be desired for. Namely:

NFSS assigns *all* the math fonts at each *size* command.
This means that even if one never typesets a single formula
in, say, \Huge (which is used to typeset the Chapter headings),
NFSS still assigns all the three appropriate sizes of each
and every math font currently used. So, for example, if one were
to "fill" all the families in a given math style, then
typesetting a chapter heading requires the assignment of
3 * 16 =48 fonts!!!
Similar "waste" of the fonts from the 255 font limit also
applies for \section, \subsection and \footnote
commands---or any command that executes a size command.
If, furthermore, one were to issue a size changing command
while in \boldmath (or in any other math style) *all* the
fonts currently loaded to that math style, in all the 3 sizes
of course, are assigned again.

The solution to these problems is to load math fonts *truely* on
demand, that is *within* each math formula. Also, only fonts that
are used within a given math formula need to be assigned
families, and only  *temporarily* for that particular formula,
but they should not be permanently added to the mathstyle for the
*whole* document. This means that one could use an *arbitrary*
number of fonts ( <255 of course) in any math style, provided
one does not exceed the 16 family limit within *each* formula.
This approach of course would be most efficient, if a minimal
number of families were forcibly assigned, and the rest
assigned only on demand, and only for that particular
formula, *not* permanently for the whole document.
TeX requires that families 2 & 3 be assigned or else it will
simply refuse to typeset the formula. Therefore, ideally,
only families 2 & 3 should be assigned to please TeX, but no more.
This requires that \mathchardef command (and a few similar commands)
be replaced by new commands such that, for example, \Gamma
could be defined as \MathCharDef\Gamma7\rm00 .
This means that the \rm command would load the default
font for \Gamma and then typeset the 0'th character in the font.
To get a \sf \Gamma, you would say \sf\Gamma of course.

One could also modify \MathCharDef so that these symbols can be used
both in math and in text modes freely. The obvious advantage
of this is to avoid having to load all three sizes if
you just need a \Gamma or a \bullet, say, at the current size,
which is very often the case.

2 - The upper and lower case greek letters are treated
unsymmetrically in TeX/LaTeX. This means that although one
can get even a "dunhill" \Gamma, one cannot even get
a \rm or a \sf \gamma. I believe that all greek characters
should be available in all text fonts. This can be done
very easily by simply adding a line to roman.mf that
generates the lc greeks at appropriate locations. I have
tried this and although the lc greek characters generated
using the current cm parameters look somewhat less than
ideal, it's a start! The lc greeks can be put
at positions oct"337" to oct"377" such that the characters
produced by afm2tfm (StandardEncoding of Adobe)
are not overwritten. The Cork encoding
unfortunately does not allow this because it is already
full. By the way, adopting the Cork encoding would also mean
that a lot of characters that only Europeans use would take
up large amounts of disk space on the computers of people
who only rarely use accented characters. This problem
could best be solved by adopting a separate European
style that one could choose, instead of building the
standard permanently right into LaTeX.

3 - I have often found myself wondering whether the
"design size"  approach has lived out its usefulness.
This subject is unfortunately somewhat of a taboo and
I wish people were more forthright about whether
or not it's meaningful to allocate vast amounts of
disk space in order to be "faithful" to typesetting
traditions. It's quite clear to me that, with low
resolution devices, using a font with the appropriate design size
(rather than a merely scaled font) improves readability of smaller
sizes because the interletter spacing is larger so letters don't
"fuse", the letters are wider and drawn with thicker strokes.
However, as high resolution devices become more and more
affordable, and as PostScript fonts gradually replace many of the
cm fonts, I think it may just be the right time to adopt a single
design size, 10pt, for all fonts.

4 - TeX's current magnification system based on the
number 1.2 could also use some revision. One could see this
simply by looking at printer ads in a recent magazine. More
often than not, the printer resolutions come in sizes which
differ by factors of 2. 300, 600, 1200 and 2400 dpi for example.
It seems to me that a scaling system based on the factor of 2
would be most efficient. Hence replacing 1.2 in the current system
by 2^{1/4}=1.189207 would mean that many of the fonts that are
used with 300dpi printers can still be used with
600dpi or even 1200dpi printers. With the current system,
however, reproducing the same set of fonts for a 600 dpi printer
would take roughly twice the disk space occupied by the 300dpi
fonts. If one were to maintain fonts for both printers,
the disk storage requirements could become prohibitive.

I have been working on developing such a system of
font usage and I now have a fully functioning LaTeX style
that assigns all math fonts within each formula, and
>from a font utilization point of view, it is very very efficient.
I would be glad to send anyone a copy along with a few new fonts
that it uses. Compared to NFSS, it takes about twice
as long to process a document, but this also depends on
how often one enters the math mode and which implementation
of TeX one uses. emTeX is very efficient in this regard.

I hope this rather long piece of "complaints" will be viewed
as a constructive, albeit possibly naive, attempt to stimulate
discussion.

Cheers,
Sami Sozuer