[lltx] $n\choose k$-issue with OpenType math fonts

Philipp Stephani st_philipp at yahoo.de
Sat Mar 5 02:13:45 CET 2011

Am 05.03.2011 00:21, schrieb Khaled Hosny:
> On Fri, Mar 04, 2011 at 11:29:13PM +0100, Philipp Stephani wrote:
>> @Andreas: please use only the ZIP archive format since it's the only one
>> everybody can read.
>> Am 04.03.2011 22:50, schrieb Khaled Hosny:
>>> On Fri, Mar 04, 2011 at 09:53:10PM +0100, Andreas Harder wrote:
>>>> Hi all,
>>>> I was asked to post this also on the LuaLaTeX-list, so here it is.
>>>> I'm tying to draw some attention to the $n\choose k$-issue with OpenType math
>>>> fonts. 
>>>> I've made some test files:
>>>> http://dl.dropbox.com/u/151837/OpenType-Math.7z 
>>>> The best output is generated by LuaLaTeX (at least for Asana and Cambria). 
>>> So you are getting the best output which, IMHO, is a good thing, what is
>>> the problem then? :)
>> "Best" here unfortunately means "not very good, but not as bad as the
>> others."
>> For the following discussion, I use the notation LN, where X is the
>> letter A, C, or X, depending on the font, and N is a number representing
>> the N-th symbol from the left. I'm only looking at the document ending
>> in lualatex.pdf.
>> A1, A2, A3, A5, A6, A7, A8, A9, A11, C1, C2, C3, C5, C6, C7, C8, C9,
>> C10, C11, X5, X9, X10, X11 look good.
>> A4, C4, X4: upper and lower part are too far away from each other; as
>> there is no fraction bar, they should be closer to each other than the
>> numerator/denominator in ACX5.
>> A10: numerator and denominator are too far away from the fraction bar.
>> X1, X3, X6, X7, X8: lower part is too far to the bottom.
>> X2: parentheses are too high.
>> The issues that occur with Computer Modern are: 4, 10, i.e. those that
>> also appear with A and C; these are more-or-less design problems;
>> someone should check if they also occur in Word. X has more issues;
>> LuaLaTeX + A/C can be declared okay-ish, but not perfect IMO.
>> It would be interesting to know whether there are established
>> conventions regarding the vertical gaps in fractions vs. binomials.
>> Personally I'd prefer a smaller gap for the latter since the bar is absent.
> Thanks Philipp, that was very helpful.
> Comparing to CM I think Cambria's is OK, so 10 might be related to
> actual TeX math algorithms (someone have to check Appendix G rules
> regarding this).

Presumably something like "gap is three times the fraction bar width".
Not a real problem since very few people use different fraction bars in
one document ;-)
What is more annyoing in A and C is the inconsistency w.r.t. vertical
gaps in display vs. text style: CM uses binomial vgaps that are always
larger than the fraction vgap, but in A and C, the binomial vgaps are
smaller in text style, but larger in display style! I don't know whether
that is a design choice, but I find it a bit annoying.

> I'd be interested in knowing what MATH parameters are
> involved here to see what need to be fixed; the fonts or luaotfload.

Or maybe LuaTeX. Unfortunately I have absolutely no time to investigate
right now, only one observation: C has
FractionNumeratorDisplayStyleShiftUp = StackTopDisplayStyleShiftUp, but
the upper part of the binomial is positioned higher than the numerator
in display style. This may be because the StackDisplayStyleGapMin is too
large (?).

More information about the lualatex-dev mailing list