[lucida] Large braces, question and/or feature request

[Bruno Voisin]

Le 4 avr. 2013 à 14:46, Tobias Columbus <tobias.columbus at gmail.com> a écrit :

> That sounds very promising! Thanks a lot! I had a look at an unimath-symbols.pdf from 2011, where Cambria Math has curly braces at least at a slightly larger size than Lucida Math. Said document can be found here: http://meeting.contextgarden.net/2011/talks/day3_05_ulrik_opentype/Samples/unimath-symbols.pdf
> I do not own Cambria Math or MathTimesPro, so that I cannot check up to which size they support curly braces.

Cambria Math has seven sizes of big curly braces, appearing as braceleft.vsize1 to braceleft.vsize7 and braceright.vsize1 to braceright.vsize7 in FontForge.

However, not all of them are necessarily used and there are still threshold effects (such that two different specified sizes lead to TeX picking up delimiters of the same size, either both curly, both straight or one curly and the other straight).

Attached are test with braces of size increasing, as in plain TeX and LaTeX, by 6pt increments (3pt above the math axis and 3pt below), from 17pt to 107pt. Tested fonts are Lucida T1, Lucida OT, Cambria Math and MathTime Pro 2.

Using the standard TeX sizes for delimiters, there are no threshold effects for Lucida, contrary to my tests of yesterday (which used a scaled font size or scaled delimiter sizes taken from lcdplain.tex). One more curly brace size is used for Lucida OT as for Lucida T1.

For Cambria, only 6 curly brace sizes are used, not 7. There are threshold effects.

Curly brace support in MathTime Pro 2 is really a hack and cannot be generalized. There are 3 types of braces:

- Curly: this is the default, braces are curly in their first 4 default sizes then straight.

- Straight: straight braces at all sizes.

- Morphed: shape morphing continuously from curly to straight as the size increases.

These are either selected at any point within the document with \curlybraces, \straightbraces and \morphedbraces, or as a package option modifying the default.

As seen in the test file, in curly mode the first 4 standard sizes are curly, and the following sizes straight. No threshold effect. Morphed mode is simply not working.

There is a separate command \LEFTRIGHT\{\}{<formula>} replacing the standard \left\{<formula>}\right\}, and selecting curly braces at all sizes below 4 inches. It's really a hack: three additional math extension fonts mt2exe, mt2exf and mt2exg are provided in addition to the standard extension font mt2exa, and they contain predesigned curly braces of various sizes. \LEFTRIGHT tests for the vertical size of its argument, and picks up the curly braces from the appropriate font for this size.

In the test file you can see the effect is not that good: a number of threshold artifacts, compared with the continuous evolution in size in standard mode.

So it seems that what you've seen is not a defect in the OpenType font. It's rather an apparently unavoidable threshold effect in TeX's algorithms. With the standard TeX sizes for delimiters (17pt, 23pt, 29pt, 35pt, 41pt, etc.), the effect seems to be hidden. But in your case, with sizes 36 pt and 37 pt, it seems you have just hit sizes at which the effect shows up.

Bruno Voisin

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