% language=us runpath=texruns:manuals/math

\environment math-layout
\environment math-fonts-helpers

% todo: use "keep-latin-modern-math.otf" and "keep-texgyre-pagella-math.otf"

\startcomponent math-fonts

\startchapter[title=Fonts]

\startsection[title=Introduction]

In this document we will discuss how we deal with \OPENTYPE\ math fonts. There is
a set of samples that are used for testing. One problem is that these fonts
evolve so what we discuss and fix today might not be applicable tomorrow in which
case this document can also be seen from a historic perspective. We will mostly
use \CONTEXT\ speak.

The examples that we show use test files and normally they should render okay. If
not, we need to fix something. They are part of a set of test files by Mikael
Sundqvist and Hans Hagen made in the perspective of defining proper goodie files
and this chapter summarizes our journey.

{\em This chapter is uncorrected work in progress.}

\stopsection

\startsection[title=Italics]

First of all we need to mention some fundamental differences between a
traditional setup and one for \OPENTYPE\ \UNICODE\ fonts. When \TEX\ showed up,
fonts had at most 256 characters. Sets of characters are organized in so called
families of which there are 16: family zero is the one used for what is called
roman (upright), family one for so called math italic characters, family two for
all kind of symbols and family three for extensible characters. The \TEX\
distribution comes with matching fonts. Now, when one enters a formula like this:

\starttyping
y = \sqrt{x^2 + 4}
\stoptyping

the \type {x} and \type {y} are math italics (family 1), \type {1} and \type {2}
are upright (family 0), the \type {+} is a symbol (family 2) and the radical
comes from family 3 as it can differ in size. The letters are actually from the
math {\it italic} alphabet and there can be other alphabets: bold, bold italic,
blackboard, script, etc. For these one defines additional families or when one
runs out of families symbolic names can be used to map to the non alphabetic
\ASCII\ slots.

In \CONTEXT\ right from when we started with \LUATEX\ the multiple families were
dropped in favor of just one. \footnote {This is not entirely true because we
also have one for bold, and two for r2l regular and bold, but these are dealt
with in a special way: all definitions use family zero.} Because \UNICODE\ has a
concept of math alphabets (unfortunately with holes) we use \UNICODE\ \OPENTYPE\
fonts as well as (certainly before there was anything else than Cambria) virtual
(runtime) assemblies of traditional \TYPEONE\ fonts.

In this and following chapters we only discuss the \OPENTYPE\ fonts because that
is what we normally deal with. One complication there is that, although Cambria
set a clear standard, the fonts that evolved in the \TEX\ ecosystem are to a
large extend modelled after the traditional \TEX\ fonts. Fonts that originate
from elsewhere are a mix of both models. And it is this curious mix of approaches
that forces us to adapt the machinery and|/|or the fonts to our needs. For a long
time \CONTEXT\ assumed some consistency and although there were mechanisms in
place to deal with these (often not) subtle differences, in the long run that was
not what we wanted. So, when these fonts became more and more frozen we decided
to go for a more individual long term \quote {fix them runtime} solution.

A result is that in \LMTX\ we use a similar approach as in \MKIV\ but instead of
trying to fix the fonts automatically (driven by pseudo features), we now
delegate that to the font goodie mechanism where we can also fine tune more
easily per font: runtime tweaks. The basics are the same but it is a bit easier
that way, also because in the worst case one can program a specific tweak without
side effects for the rest.

\startplacefigure[title={Italics Sample 2}]
    \externalfigure
        [math-fonts-italics-002.tex]
        [width=\textwidth]
\stopplacefigure

The tweak that deals with italics (and other shapes) is:

\starttabulate[|T|||]
\NC tweak \NC \type {dimensions} \NC \NC \NR
\NC list  \NC table \NC a hash with treatments \NC \NR
\stoptabulate

\stopsection

\startsection[title={Primes}]

% \ctxlua{nodes.tasks.disableaction("math","noads.handlers.fixscripts")}
% \ctxlua{nodes.tasks.enableaction("math","noads.handlers.fixscripts")}

Primes are implemented in a curious way. In traditional \TEX\ they are treated as
superscripts which is often achieved by making the single quote into an active
character (in math mode) that takes care of this. The dimensions of a prime are
such that it comes at the right spot (according to the designers wish). However,
in \UNICODE\ the same symbol is used for minutes in text mode and because there
are no duplicates in \UNICODE, it is that already superscripted symbol that we
see show up in fonts. There is (for some reason) no dedicated single prime slot
(and one can argue that minutes and primes are really different things and if
not, why then does greek and latin don't share more).

In \CONTEXT\ we don't want to mess with active characters and even more, we want
proper symbols for the multiple primes. At the same time we need to handle
following superscripts as well as cases where a subscript is used as index to a
nucleus where the whole is then primed. This is implemented in a combination of
\TEX, \LUA\ and normalized prime symbols.

\startplacefigure[title={Primes Sample 1}]
    \externalfigure
        [math-fonts-primes-001.tex]
        [width=\textwidth]
\stopplacefigure

Fixing primes boils down to fixing dimensions and repositioning the shape.
Optionally the multiples can be emulated and a smaller size can be chosen. It's
also a matter of taste and primes are often not the best designed symbols.

The specification is:

\starttabulate[|T|||]
\NC tweak   \NC \type {fixprimes} \NC \NC \NR
\NC factor  \NC number  \NC fraction of the accent base height that the prime shifts up \NC \NR
\NC smaller \NC boolean \NC when \type {true}, replace multiples \NC \NR
\NC scale   \NC number  \NC the glyph scale \NC \NR
\NC fake    \NC number  \NC when set, fake multiples and use this width 0.75 \NC \NR
\NC keep    \NC boolean \NC keep text size prime as it is \NC \NR
\stoptabulate

In \MKIV\ we remap primes but in \LMTX\ we adapt the regular slots. As a
consequence we sacrifice the text size minutes. The \type {keep} option will
leave the text size variant as it is.

Keep in mind that primes are processed depending on what precedes and follows so
you cannot really test a character by just calling it: when there is something in
front it will become a superscripted prime.

\stopsection

\startsection[title={Scripts}]

This tweak will add superscript characters for plus and minus. The main reason
for them being supplied is that we need them to indicate an explicit (minus)
sign in calculator math examples.

\startplacefigure[title={Scripts Sample 1}]
    \externalfigure
        [math-fonts-scripts-001.tex]
        [width=\textwidth]
\stopplacefigure

The specification is:

\starttabulate[|T|||]
\NC tweak \NC \type {addscripts} \NC \NC \NR
\NC scale \NC number \NC the scale of the scripted character \NC \NR
\stoptabulate

Keep in mind that these scripts are processed depending on what precedes so you
cannot really test a character by just calling it.

\stopsection

\startsection[title={Radicals}]

The traditional \TEX\ engine is made in conjunction with the Computer Modern
Fonts and there the radical symbol sits below the baseline so that the height
indicates the rule thickness. In \OPENTYPE\ fonts this is a variable. The Latin
Modern Math font inherits this somewhat strange position property but we can fix
that with this tweak:

\startplacefigure[title={Radicals Sample 1}]
    \externalfigure
        [math-fonts-radicals-001.tex]
        [width=\textwidth]
\stopplacefigure

There are no options:

\starttabulate[|T|||]
\NC tweak \NC \type {fixradicals} \NC \NC \NR
\stoptabulate

\stopsection

\startsection[title={Accents}]

We cannot yet tweak accents, but here is an example:

\startplacefigure[title={Accents Sample 1}]
    \externalfigure
        [math-fonts-accents-001.tex]
        [width=\textwidth]
\stopplacefigure

\stopsection

\startsection[title={Spacing}]

There are \UNICODE\ characters for various spaces and this option defines them
when they are not present. It is up to the macro package to make sure that the
non breakable spaces are treated as such. In this document we get:

\def\ShowSpacing#1#2%
  {\NC \ruledhbox{\showmakeup[glue]\showstruts\strut\char"#1\strut}\NC#2\NC\NR}

\starttabulate[|w(1.5em)|T|]
    \ShowSpacing{00A0}{nbsp}
    \ShowSpacing{2000}{enquad}
    \ShowSpacing{2001}{emquad}
    \ShowSpacing{2002}{enspace}
    \ShowSpacing{2003}{emspace}
    \ShowSpacing{2004}{threeperemspace}
    \ShowSpacing{2005}{fourperemspace}
    \ShowSpacing{2006}{sixperemspace}
    \ShowSpacing{2007}{figurespace}
    \ShowSpacing{2008}{punctuationspace}
    \ShowSpacing{2009}{breakablethinspace}
    \ShowSpacing{200A}{hairspace}
    \ShowSpacing{200B}{zerowidthspace}
    \ShowSpacing{202F}{narrownobreakspace}
    \ShowSpacing{205F}{maththinspace}
\stoptabulate

There are no options:

\starttabulate[|T|||]
\NC tweak \NC \type {checkspacing} \NC \NC \NR
\stoptabulate

\stopsection

\startsection[title=Parameters]

An \OPENTYPE\ math fonts has a lot of parameters and because the engine let you
set them for every style (regular and cramped) you can exercise a lot of control.
A difference with traditional math is that we only have one cramped parameter:
\typ {SuperscriptShiftUpCramped}.

\startbuffer
\startoverlay
    {\ruledhbox{$\strut \red  \displaystyle        x^2_1 x^2 x_1$}}
    {\ruledhbox{$\strut \blue \crampeddisplaystyle x^2_1 x^2 x_1$}}
\stopoverlay
\stopbuffer

\typebuffer

Only the superscript is affected (in some miraculous way):

\startlinecorrection
    \scale[height=3cm]{\switchtobodyfont[pagella]\getbuffer}
\stoplinecorrection

\stopsection

\stopchapter

\stopcomponent