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

[Philipp Stephani]

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 (?).