What should go into \textfont1?

[Jan Michael Rynning <jmr@nada.kth.se>]

(I apologize for sending this to both lists.  I'm not on dcfonts-l
myself.  Maybe I should be.)

At the European TeX Meeting in Paris last year Mike Spivak said that
it's important to put Latin and Greek math italic letters and certain
symbols into the same font, so we can kern them.  The experiments I
have done recently confirm that this is indeed very important.

I have typeset a number of test pages using Linotype Times fonts with
Latin and Greek letters.  The typesetting TeX normally does with CM
fonts is ``sparse''---there's whitespace between most of the glyphs.
The typesetting I'm trying to imitate with Times fonts is ``dense''---
the letters are close together and there's little or no whitespace
around the operators (in text mode there's no whitespace around the
operators; in display mode there's 3mu on each side of the relational
operators).  Dense math typesetting makes greater demands on spacing
than does sparse math typesetting.

I shall give two examples of problems I have run into, explain how I
solved them (if you have a better solution, please let me know) and
what conclusions we may draw from that.

Problem 1:
  There are six letters in the Times fonts which extend so far to the
  left that they run into the left parenthesis: $(f)$, $(j)$, $(p)$,
  $(y)$, $(\beta)$, and $(\mu)$.
Solution:
  Increase the left sidebearing of those letters.
Side-effect:
  Pairs of letters like $d\beta$ become separated by whitespace.  That
  really looks bad.
Solution:
  Kern all letters to those six to compensate for the increased side-
  bearing.
Conclusion:
  Latin and Greek math italic letters should be in the same font, so
  that we can kern them.

Problem 2:
  About half of the letters require an italic correction, to stop them
  from running into the superscripts in expressions like $f^0$.  I have
  seen no such problem with the subscripts.
Solution:
  Add enough italic correction to those letters.
Side-effect:
  Expressions like $f(x)$ look strange, because the italic correction
  generates whitespace between the $f$ and the left parenthesis.
Solution:
  Add a left parenthesis to the font.  Add kerning between the letters
  which require it and the left parenthesis.  Make TeX use this left
  parenthesis rather than the one from \textfont0: \mathcode`\(="41xx.
Conclusion:
  There is more than letters which needs to be in the font, so that we
  can kern it.

Jan Michael Rynning			
Department of Numerical Analysis	Internet: jmr@nada.kth.se
  and Computing Science			UUCP: {uunet,...}!nada.kth.se!jmr
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