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Re: math fonts

Johannes Kuester wrote:

> Some comments on MC: the ordering of the Greek glyphs seems to be somewhat
> arbitrary, they should either be ordered in the order of the Greek
> alphabet or according to the input conventions of e.g. Haralambous's
> Greek fonts (I think the first is preferable, but the current alpha,beta,
> delta,... gives a new ordering never to be seen so far). I also think that
> upright and slanted/italic glyphs should reside at a multiple-of-8 distance
> in the font; e.g. upright Alpha at "81, slanted Alpha at "B9, to make
> then more easily findable and comparable.

I'd agree with that, and if possible I'd even argue for a multiple-of-32
distance in the font, e.g. upright Alpha at "81, upright alpha at "A1,
italics Alpha at "C1, italics alpha at "E1.  This would obvioulsly make
it necessary to rearrange some of the extra characters and perhaps even
restricting the number of variants.

> There are some glyphs for
> which I don't see any reason for being in the core, namely "5F, "61,
> "F8 and "F9 (barred V, upright and slanted, thorn (variant) and Thorn),
> as they are very rarely used in mathematics (if at all?). Justin didn't
> give any example of their usage.

I don't know where the barred V is used, but there might be a valid
reason in some field.  However, I severely doubt the necessity of
having \eth and \thorn in a math font.  AFAIK, these are icelandic
text characters left over from the AMS symbol fonts, which simply
weren't available otherwise.  Anyone from the AMS knows better?

> Also, to include the upright "d" seems
> arbitrary, as other upright glyphs aren't taken into account.

NO!!!  The upright "d" and upright \partial are despartely needed for
differentials, at least according to typesetting rules applicable in
physics.  The reason to have them in the MC font is kerning: If you
run the math test of the MFbook testfont.tex program, you'll find that
there are numerous kern pairs between italics "d" and other italics or
greek letters.  Kerning between upright "d" and other letters may not
be as critical as for the italics "d", but one shouldn't rule out this
possibility by banning the upright "d" from the MC font prematurely.

BTW, from the point of view of physics requirements, I'd also like to
have an upright "i" (and perhaps also "j") in the MC font for kerning
reasons.  I'm afraid that this suggestion somehow never made it into
Justin's report.  Just look closely at

  \mathrm{i}k,  \quad \mathrm{i}\omega, \quad
  2u + 2\mathrm{i}v, \quad  \mathrm{e}^{\mathrm{i}(kx - \omega t)}


> I have metafonted a few glyphs which I could contribute
> (in rather poor METAFONT, as these were among my first glyphs,
> but I think they look the right way, even when their programs need
> to be polished). Namely:

> a special symbol for the Laplace operator and a matching Nabla
>     (looking like a \bigtriangle, a bit larger and bolder though;
>      may be useful as I think \Delta (the upright one for Laplace) is
>      overused and ambiguous)

Very good idea!  Reserving a slot for \Laplacian would allow the font
designer to choose between different styles for \Laplacian and \nabla,
either in ``Greek'' style (upright and inverted \Delta) or geometric
(upright and inverted triangle of uniform line thickness).  Another
symbol in this grooup would be the d'Alembert operator (a.k.a. quabla),
usually just a geometric square, but it should match the size of
the Laplacian.

  \quabla = \Delta - \partial_t^2 = \nabla^2 - \partial_t^2

BTW, here's my metafonted suggestion for \quabla:

% A square matching the size (height) of \triangle from mathsy.mf
cmchar "Quabla operator";
  adjust_fit(0,0); pickup rule.nib;
  bot y1=0; y1=y2; top y3=h; y3=y4;
  x1=x4=good.x (w/2-h/2); x2=x3=x1+h;
  draw z1--z2--z3--z4--cycle;

> upright lowercase Greek glyphs
>     (these are merely a matter of taste, I made them by "unslanting"
>      the usual ones and changing the code when it seemed appropriate
>      to get a goodlooking glyph. May be Greek has to be redesigned
>      completely anyway, as I don't see a reason for having uppercase
>      Greek letters which are undistinguishable for their Latin counterparts)

I also experimented with making a cmmr10 font by unslanting cmmi10
quite a long time ago.  It was very obvious that the design of many
lowercase greek required ajustments to prevent them from looking like
slightly backslanted.  In addition the kerning tables needs to be
redone completely.

>     Here again, Justin's proposal seems to be too restricted: There
>     are at least two variant glyhs for each of Qoppa, qoppa, Sanpi and sanpi,
>     and there is "stigma" (merely a sigma-tau ligature, to be found in
>     Unicode), which hasn't been considered yet.

Question: Are these really math characters, or just greek text characters?
Remember, we want to do a math font not a greek text font, so if they are
never ever used in math, I'd suggest to get rid of them.

> And as for font naming conventions: please do use preliminary names
> for the fonts (how about "d" instead of "e" as a starting letter?).
> I don't see a good reason for the naming "emsp", I think this should
> just be the first math symbol font, named "emsa" ("dmsa" for now?),
> the other names shifted accordingly, thus it will be privileged enough.

I don't think it is a good idea to discuss font naming at this stage.
However, if we're already talking about it: What about font names
starting with "x" for experimental and including the initials of the

x mc  NN 10
x msp MC
x msa JK
x msb UV
x mxa NN
x mxb NN

So much for my random comments.
Cheers, Ulrik.