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Erik van der Poel wrote on 1999-11-29 21:38 UTC:

*> I don't really know exactly what the STIX project intends to come up
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*> with, but if other math fonts (e.g. Mathematica's) are any indication,
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*> then they will presumably include whole glyphs at different sizes within
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*> a single font (e.g. the square root thingie at various sizes) as well as
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*> partial glyphs that are supposed to be glued together (e.g. top part,
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*> straight part, middle part and bottom part of curly braces '{' and '}').
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I hope not!

I strongly advise against doing portable mathematical typesetting this

way! Placing square roots of different sizes and bracket fragments that

are to be glued together into a font will create a very tight semanical

bond between the font and the application. This is guaranteed to become

a major obstacle for the free exchangeability of fonts and applications

and only works in practice if you get the application and the fonts from

the one and same developer (as you do with TeX and Mathematica). TeX

(which is de-facto almost exclusively used with only the Computer Modern

fonts!) has set a very bad precedent here, which we should see as an

opportunity to learn from, how to do it better, and not to copy it

blindly.

There is a conceptually much neater and cleaner solution:

If you want your typesetting system to be strong enough to support the

mathematical notation, then include in the style-sheet language (CSS,

DSSSL, XSL, whatever) a small and simple functional programming language

and graphical primitives, such that style-sheet designers can write

algorithms for plotting beautiful variable-size brackets and

square-roots and do not have to depend on the fragments they find in the

fonts.

Stop seeing variable-size annotations of mathematical formulae as

characters, but start treating them as what they really are: graphical

ornaments composed of graphical primitives (line strokes, polygons,

arcs, splines, etc.), just like the rules in a table or other page

layout features.

Adding small graphics algorithms for plotting calculated objects to a

style-sheet language has many advantages:

- The existing Unicode 3.0 repertoire will be sufficient for most

mathematical publishing needs.

- Arbitrary existing fonts can be used to do mathematical typesetting,

you do not have to know any more, what the designer was planning

exactly for the bracket fragments and their detailed alignment

properties.

- Algorithmically calculated square roots will lead to more satisfactory

results than those plugged together from a small number of

ready-made components.

- The trickier aspects of mathematical typesetting become handled

by a powerful universal mechanism in the style sheet language

that has no intrinsic dependencies on the current fashions of

19th and 20th century mathematics. It will be able grow with the

field and will also cover other scientific graphical notations

(chemistry, may be even music). All that has to be changed are the

application-dependent style sheets, not the base standards.

One of the big practical problems with TeX was always, that TeX only

works well with fonts that were specifically designed for it, because

(especially for the math symbol fragments), TeX makes a lot of detail

assumptions about the precise shapes of the glyphs. TeX's major flaw is

the lack of any more powerful graphical primitives than horizontal and

vertical rules that could be used in its macro language. TeX users have

to struggle with hacks such as special-purpose fonts and embedded

Postscript files every day to work around the limitations that were

probably only motivated the limitations of Knuth's original 1970s

phototypesetter.

You break a neat modularization boundary in a typesetting system, if you

move graphical style elements into the glyph repertoire of the font.

I hate to see the same mistakes made by TeX being repeated in MathML

implementations and other more modern mathematical typesetting systems.

Markus

-- Markus G. Kuhn, Computer Laboratory, University of Cambridge, UK Email: mkuhn at acm.org, WWW: <http://www.cl.cam.ac.uk/~mgk25/>

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