Preprint of my TUG paper on math fonts

[Ulrik Vieth]

Hi all,

I have provided a preprint of my paper for the TUG 2008 Conference at
Cork:
http://unimath.googlegroups.com/web/tug2008.pdf

Besides recounting the history of work on font encodings since Cork
1990, this paper reviews recent developments of math fonts and
discusses a number of topics such as Unicode, STIX, OpenType MATH,
Microsoft, XeTeX, LuaTeX, Latin Modern and TeX Gyre.

If possible, I would like the relevant people involved these projects
for feedback and/or suggestions. In particular, I would like to ask
you to verify the accuracy of my statements or predictions about your
projects, so that I won't misrepresent you in front of a bigger
audience.

Regards,
Ulrik Vieth

[Ross Moore]

Hi Ulrik,

On 09/07/2008, at 9:56 AM, Ulrik Vieth wrote:
>
> Hi all,
>
> I have provided a preprint of my paper for the TUG 2008 Conference at
> Cork:
> http://unimath.googlegroups.com/web/tug2008.pdf

I'd love to read this, as some of it surely will
be closely related to my work.

However, this link doesn't seem to work for me.

>
> Besides recounting the history of work on font encodings since Cork
> 1990, this paper reviews recent developments of math fonts and
> discusses a number of topics such as Unicode, STIX, OpenType MATH,
> Microsoft, XeTeX, LuaTeX, Latin Modern and TeX Gyre.
>
> If possible, I would like the relevant people involved these projects
> for feedback and/or suggestions. In particular, I would like to ask
> you to verify the accuracy of my statements or predictions about your
> projects, so that I won't misrepresent you in front of a bigger
> audience.
>
> Regards,
> Ulrik Vieth

Cheers,

Ross

------------------------------------------------------------------------
Ross Moore ro...@maths.mq.edu.au
Mathematics Department office: E7A-419
Macquarie University tel: +61 (0)2 9850 8955
Sydney, Australia 2109 fax: +61 (0)2 9850 8114
------------------------------------------------------------------------

[Will Robertson]

On 09/07/2008, at 11:05 AM, Ross Moore wrote:

> I'd love to read this, as some of it surely will
> be closely related to my work.
>
> However, this link doesn't seem to work for me.

I had the same problem; you can grab it here:
<http://groups.google.com/group/unimath/files>

W

[Will Robertson]

On 09/07/2008, at 9:26 AM, Ulrik Vieth wrote:

> I have provided a preprint of my paper for the TUG 2008 Conference at
> Cork:
> http://unimath.googlegroups.com/web/tug2008.pdf

Hi Ulrik,

Great to hear from you on this topic.
I've found your article very informative!

Very few suggestions for the text itself:

"such as task" -> "such a task"

"assigned to slots at U+1D400"
-> "assigned to slots starting at U+1D400"

"math alphabets at U+1D400"
-> "math alphabets starting at U+1D400" or
-> "math alphabets from U+1D400"

***

From the point of view of XeTeX, it doesn't really matter if the
optical sizes are contained within the font or not, because a single
"font" has a fixed set of features. I.e.,
\font\1="Cambria Math:+ssty" at 7pt
could just as well be
\font\1="Cambria Math Scriptsize" at 7pt
But I do prefer the idea of bundling it all together.

***

> In the XETEX implementation the parameters of
> the OpenType MATH table are mapped internally to
> TEX’s \fontdimen parameters. In most cases this
> mapping is quite obvious and straight-forward, but
> unfortunately there are also a few exceptions where
> some parameters in TEX do not have a direct cor-
> respondence in OpenType. It is not clear, however,
> whether these omissions are just an oversight or a
> deliberate design decision in case a parameter was
> deemed irrelevant or unnecessary.

I didn't realise this! Can you give an example?

> At the time of writing, the extra parameters
> introduced by OpenType generalizing the concepts
> of TEX have been silently ignored. It is conceivable,
> however, that future extensions of new TEX engines
> might eventually start to use these parameters in
> the math typesetting algorithms as well.

Some of the math parameters come in handy even before we start talking
about extending XeTeX or LuaTeX themselves.

A good example is n-root superscript positioning. LaTeX's \sqrt macros
internally use hard-coded values to get the height and offset correct,
whereas unicode-math will (when I get around to it...) extract these
parameters from the font itself (the parameters for CM don't work very
well with Cambria Math).

In cases like preceding sub-/superscripts, it's unclear whether
there's an advantage to add a primitive to the engine; maybe it's just
better to use macros in these cases and insert the kerning "manually"
in the macro definitions.

***

I wish I could make it to Cork this year :)

Cheers,
Will

[Ross Moore]

On 09/07/2008, at 11:37 AM, Will Robertson wrote:
>>
>> However, this link doesn't seem to work for me.
>
> I had the same problem; you can grab it here:
> <http://groups.google.com/group/unimath/files>

Thanks Will. Got it.

>
> W

[Taco Hoekwater]

Your statements about the current state of Unicode math in luatex
are correct: it is essentially absent, except for a few small frontend
things like being able to assign \mathcodes to unicode code points
and that is is possible to use BMP-only fonts.

Work on an overhaul of the math engine in luatex is planned for the
coming autumn, and then the internals will be extended to make use
of (hopefully) all the 'new' features in OpenType MATH.

So I am perfectly happy with the text you have now.

Best wishes,
Taco

[Jonathan Kew]

Hi Ulrik,

Thanks for posting this. Looks good to me; no worries about
misrepresentation! :)

See you in Cork,

Jonathan

[Ulrik Vieth]

On Jul 9, 3:59 am, Will Robertson <wsp...@gmail.com> wrote:
>
> From the point of view of XeTeX, it doesn't really matter if the
> optical sizes are contained within the font or not, because a single
> "font" has a fixed set of features. I.e.,
> \font\1="Cambria Math:+ssty" at 7pt
> could just as well be
> \font\1="Cambria Math Scriptsize" at 7pt
> But I do prefer the idea of bundling it all together.

I suppose you would probably need something like this to set up the
math families:

\textfont<n>="Cambria Math" at 10pt
\scriptfont<n>="Cambria Math:+ssty0" at 7.3pt
\scriptscriptfont<n>="Cambria Math:+ssty1" at 6.0pt

Ideally the sizes should be taken from the parameters specified in the
font as "(Script)ScriptPecentScaleDown" in the MATH table, rather than
specifying them at the macro level.

> > In the XETEX implementation the parameters of
> > the OpenType MATH table are mapped internally to
> > TEX’s \fontdimen parameters. In most cases this
> > mapping is quite obvious and straight-forward, but
> > unfortunately there are also a few exceptions where
> > some parameters in TEX do not have a direct cor-
> > respondence in OpenType. It is not clear, however,
> > whether these omissions are just an oversight or a
> > deliberate design decision in case a parameter was
> > deemed irrelevant or unnecessary.
>
> I didn't realise this! Can you give an example?

There is one very obvious example: In TeX there are 5 parameters for
big operators, but in OpenType there are only 4 parameters.

It is not clear what happened to the 5th parameter affecting the
outside clearance on both sides. Maybe someone reasoned that this
parameter was unnecessary and decided that it could be thrown out.

In XeTeX another parameter such as StackGap is used as a workaround,
but this dilutes the intended meaning of StackGap and relies on the
typical values being of similar magnitude (e.g. 3 rule thickness).

Another less obvious example are the parameters sigma_20 and 21: It is
a bit difficult to explain what these parameters mean and why there is
a different logic at all for the size of delimiters
in cases of \atopwithdelims and such compared to the usual case.

> > At the time of writing, the extra parameters
> > introduced by OpenType generalizing the concepts
> > of TEX have been silently ignored. It is conceivable,
> > however, that future extensions of new TEX engines
> > might eventually start to use these parameters in
> > the math typesetting algorithms as well.
>
> Some of the math parameters come in handy even before we start talking
> about extending XeTeX or LuaTeX themselves.
>
> A good example is n-root superscript positioning. LaTeX's \sqrt macros
> internally use hard-coded values to get the height and offset correct,
> whereas unicode-math will (when I get around to it...) extract these
> parameters from the font itself (the parameters for CM don't work very
> well with Cambria Math).

Yes, there are indeed some improvements related to the radical signs,
which I forgot to mention specifically. Since OT math provides extra
parameters such as RadicalRuleThickness, there is no longer a need to
have radical signs hanging below the baseline (finally after 30
years).

> I wish I could make it to Cork this year :)

Hope to meet you at some other occasion.

Cheers, Ulrik.

[Will Robertson]

On 10/07/2008, at 8:19 AM, Ulrik Vieth wrote:

> I suppose you would probably need something like this to set up the
> math families:
>
> \textfont<n>="Cambria Math" at 10pt
> \scriptfont<n>="Cambria Math:+ssty0" at 7.3pt
> \scriptscriptfont<n>="Cambria Math:+ssty1" at 6.0pt

Yep, exactly.

> Ideally the sizes should be taken from the parameters specified in the
> font as "(Script)ScriptPecentScaleDown" in the MATH table, rather than
> specifying them at the macro level.

That's on my todo list for unicode-math :)

Thanks for the extra info, very interesting.
All the best,
Will

[Chris Rowley]

My understanding is that the 'OT math tables' can be extended to
contain more parameters.

What we have at present is only what the Microsoft designers decided
they needed to produce the 'not at all bad' stuff from just one font:
Cambria Math in Office2007.

Likewise Don set up only the parameters he (and maybe Richard
Southall) decided was needed for CM.

Richard Southall certainly believes that different math fonts need
different sets of parameters (not just different values) although I
would have thought that a reasonably sized superset might cover all
the needs of math fonts that will ever be used with L-R alphabetic
languages. But I doubt if anyone can be bothered to investigate this
superset.


chris