## absolute values

For feedback and discussion for testers of the MathTime Professional II fonts.

Moderators: PTIForAdmin, WaS, Michael Spivak

stubner
Posts: 7
Joined: Tue Mar 14, 2006 12:55 pm

### absolute values

Hi everybody,

it seems I ahven't used much absolute values lately since only yesterday I found that things like $|x|$ or $|o|$ look offbalance to me. The space to the right of the latter looks larger than the space to the left of the letter.

In order to test this systematically, I have taken some code from testfont.tex (without fully understanding it ;-):

\documentclass{article}
\renewcommand{\rmdefault}{ptm}
\usepackage[slantedGreek]{mtpro2}

\def\math{\def\ii{i} \def\jj{j}
\def\\##1{|##1|+}\mathtrial
\def\\##1{##1_2+}\mathtrial
\def\\##1{##1^2+}\mathtrial
\def\\##1{##1/2+}\mathtrial
\def\\##1{2/##1+}\mathtrial
\def\\##1{##1,{}+}\mathtrial
\def\\##1{d##1+}\mathtrial
\let\ii=\imath \let\jj=\jmath \def\\##1{\hat##1+}\mathtrial}
\newcount\skewtrial \skewtrial='177
\def\mathtrial{$\\A \\B \\C \\D \\E \\F \\G \\H \\I \\J \\K \\L \\M \\N \\O \\P \\Q \\R \\S \\T \\U \\V \\W \\X \\Y \\Z \\a \\b \\c \\d \\e \\f \\g \\h \\\ii \\\jj \\k \\l \\m \\n \\o \\p \\q \\r \\s \\t \\u \\v \\w \\x \\y \\z \\\alpha \\\beta \\\gamma \\\delta \\\epsilon \\\zeta \\\eta \\\theta \\\iota \\\kappa \\\lambda \\\mu \\\nu \\\xi \\\pi \\\rho \\\sigma \\\tau \\\upsilon \\\phi \\\chi \\\psi \\\omega \\\vartheta \\\varpi \\\varphi \\\Gamma \\\Delta \\\Theta \\\Lambda \\\Xi \\\Pi \\\Sigma \\\Upsilon \\\Phi \\\Psi \\\Omega \\\partial \\\ell \\\wp$\par}
\def\mathsy{\begingroup\skewtrial='060 % for math symbol font tests
\def\mathtrial{$\\A \\B \\C \\D \\E \\F \\G \\H \\I \\J \\K \\L \\M \\N \\O \\P \\Q \\R \\S \\T \\U \\V \\W \\X \\Y \\Z$\par}
\math\endgroup}

\begin{document}
\math
\end{document}

IMO most lower case letters look off-center to me with to much space to the tight of the letter (f,v,w,e are exceptions). The greeks are fine, while the uppercase letters are mixed (R has to much space to the left, U and M on the right). The other tests (besides absolute values) look fine.

Other opinions?

cheerio
ralf
jautschbach
Posts: 11
Joined: Fri Mar 17, 2006 11:21 am

### Re: absolute values

stubner wrote:Hi everybody,

it seems I ahven't used much absolute values lately since only yesterday I found that things like $|x|$ or $|o|$ look offbalance to me. The space to the right of the latter looks larger than the space to the left of the letter.

ralf
|i| and |\pi|, for example, seem to have too much space on the right. |\eta| looks like there is not enough space on the right.

Jochen
Michael Spivak
Posts: 52
Joined: Mon Oct 10, 2005 2:10 pm
Basically, I want to reiterate the remark I made in the last post to the "firstimpressions" posting by stubner. If you start looking carefully
at any mathematical typesetting (as opposed to just reading it) you will find thousands of non-optimal things. Some of these are actually due
to the design of TeX (see some remarks of mine in the "spacing" posting by zeller), and some to the varying circumstances of individual characters.
All sorts of things that one would never even notice while reading a mathematics paper can stand out when one looks at things a character at a time, and sometimes one becomes overly concerned.
(The link

http://support.pctex.com/files/JWPXMWRZTYLV/abs.pdf

shows Computer Modern and MTPro2 characters inside absolute values
and parentheses, and I think that you will find cases where CM is spaced better than MTPro2, but also cases where the opposite is true.)

For example, although I agree that |M| and |U| have too much space to the right of the letters, I wouldn't agree that |R| has too much space to the left of the R, or at most just a tiny extra bit of space. By contrast, in Computer Modern, the |R| definitely has this problem to a much greater degree.

Notice, moreover, that in MTPro2, (M) and (U) and (R) look nicely balanced. Of course, that's partly because of the character of the right parenthesis---it has a top piece that extends backwards, unlike almost
all characters! In Computer Modern this doesn't pose as great a problem
mainly because the ) is much thinner and unshaped.

The case of |i|, where there is certainly more space on the right, is also instructive. Notice that the dot on the Times-Italic i is very close to being the rightmost part of the character, while in CM it is nowhere near the right, because of the curlicue at the bottom. For this reason, I had to make the italic correction of the i rather big; otherwise, superscripts would
be very close to the dot, making reading very unpleasant. Since the italic correction is always added to the i, this gives the extra space before the |
or the ). Naturally, I had to compensate for this by adding more negative
kerning between the i and all other characters, but you can't kern with the ), as I've mentioned before, in one of the two postings I mentioned.

Similarly, if you compare x^i in CM and MTPro2, you'll see that the superscript i in CM has a curlicue to the left, which keeps it separated from the x, while in MTPro2, I needed to make a greater italic correction to the x in order to get superscripts adequately far away.

TeX has \scriptspace to determine extra space after a subscript or superscript; alas, that it does not also have a \prescriptspace, to determine some extra space _before_ superscripts! (And similarly, see
one of the previously mentioned postings, the spacing in scriptstyle and scriptscriptstyle should be more flexible.)

At any rate, for now, I'll leave things as they are. Possibly in a future release I'll try to address some of these questions, though it simply isn't possible to optimize all spacing.