% !TeX program = lualatex
% !TeX encoding = UTF-8
\documentclass[fleqn,slidestop,professionalfonts]{beamer}
%\usepackage{graphicx}
\usepackage{fontspec}
\usepackage{unicode-math}
\listfiles

\unimathsetup{vargreek-shape=TeX,math-style=ISO,bold-style=ISO}

\setromanfont[Ligatures=TeX,Scale=0.92]{Lucida Bright}
\setsansfont[Ligatures=TeX,Scale=0.92]{Lucida Bright}
\setmonofont[Ligatures=TeX,Scale=0.80]{Lucida Sans Typewriter}
\setmathfont[Scale=0.92]{Lucida Math}

\def\TeX{T\kern-.15em\lower.5ex\hbox{E}\kern-.05emX\@}
\def\LaTeX{La\kern-.1em\TeX\@}

\DeclareRobustCommand\XeTeX{Xe\kern-.1em\TeX\@}
\DeclareRobustCommand\LuaTeX{Lua\kern-.1em\TeX\@}
\DeclareRobustCommand\XeLaTeX{Xe\kern-.05em\LaTeX\@}
\DeclareRobustCommand\LuaLaTeX{Lua\kern-.05em\LaTeX\@}
\DeclareRobustCommand\CONTEXT{Con\kern-.1em\TeX t\@}

\def\UC{Unicode}
\def\OT{Open\-Type}
\def\TL{\TeX\ Live}

% some markup
\def\acro#1{{\small #1}}
\def\pkg#1{{\small\texttt{#1}}}
\def\cs#1{{\small\texttt{\char`\\#1}}}

\def\LatinUpper{ABC XYZ}
\def\LatinLower{abc xyz}
\def\LatinSample{\LatinUpper\;\LatinLower}

\def\GreekUpper{\Alpha\Beta\Gamma \Xi\Psi\Omega}
\def\GreekLower{\alpha\beta\gamma \xi\psi\omega}
\def\GreekSample{\GreekUpper\;\GreekLower}

\def\GreekUpperAll{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta\Iota\Kappa\Lambda\Mu\Nu\Xi\Omicron\Pi\Rho\Sigma\Tau\Upsilon\Phi\Xi\Psi\Omega\nabla}
\def\GreekLowerAll{\alpha\beta\gamma\delta\varepsilon\zeta\eta\theta\iota\kappa\lambda\mu\nu\xi\omicron\pi\rho\varsigma\sigma\tau\upsilon\phi\xi\psi\omega\epsilon\vartheta\varkappa\varphi\varrho\varpi}
\def\GreekLowerAlmostAll{\alpha\beta\gamma\delta\varepsilon\zeta\eta\theta\iota\kappa\lambda\mu\nu\xi\omicron\pi\rho\varsigma\sigma\tau\upsilon\phi\xi\psi\omega\epsilon\vartheta\varphi\varrho\varpi}

\mode<presentation>
{
  \usetheme{Singapore}
  \setbeamercovered{transparent}
}

% If you wish to uncover everything in a step-wise fashion,
% uncomment the following command: 
%\beamerdefaultoverlayspecification{<+->}

\begin{document}

\title{\OT\ math font development:\\
  Progress and Challenges}

\author[Ulrik Vieth]
{Ulrik Vieth\\ Stuttgart, Germany}

\date
{5th International \CONTEXT\ Meeting,\\
  Bassenge-Boirs, Belgium, 2011}

\begin{frame}
  \titlepage
\end{frame}

\begin{frame}
  \frametitle{Overview of this talk}
  \vspace*{\baselineskip}
  \begin{itemize}
  \item Review of Technology
    \begin{itemize}
    \item What is \UC\ math? What is \OT\ math?
    \item What is the basis for \OT\ math fonts?
    \end{itemize}
  \item Progress in font development
    \begin{itemize}
    \item What are the choices of \OT\ math fonts?
    \item What are the latest font developments?
    \end{itemize}
  \item Challenges in font development
    \begin{itemize}
    \item Completeness of math symbols
    \item Completeness of math alphabets
    \item Design issues: Choosing matching fonts
    \item Design issues: How should certain fonts look like?
    \item Technical issues: Glyph metrics
    \end{itemize}
  \end{itemize}
\end{frame}


\section{Technology Review}
\subsection*{}

\begin{frame}
  \frametitle{What is \UC\ math?}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item What is \UC?
    \begin{itemize}
    \item encoding standard for (input) characters and symbols
    \end{itemize}
  \item What is \UC\ math?
    \begin{itemize}
    \item addition of math symbols and alphabets to \UC\
    \end{itemize}
  \item What does \UC\ math provide?
    \begin{itemize}
    \item hundreds of math symbols added to slots U+2xxx 
    \item dozens of math alphabets added to slots U+1Dxxx
    \\[\smallskipamount]
    \item size variants of math symbols are  \emph{not} encoded:\\
 	different size, same symbol $\Rightarrow$ same meaning
    \\[\smallskipamount]
    \item font variants of math alphabets \emph{are} encoded:\\
 	different font, same letter $\Rightarrow$ different meaning
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{What is \OT\ math?}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item What is \OT?
    \begin{itemize}
    \item font technology for (output) glyphs and symbols
    \end{itemize}
  \item What is \OT\ math?
    \begin{itemize}
    \item addition of MATH table to \OT\ font format
    \end{itemize}
  \item What does \OT\ math provide?
    \begin{itemize}
    \item global font metrics for spacing of math formulas
    \item glyph metrics for positioning of math accents
    \item lookups for horizontal/vertical variants (sizes)
    \item lookups for horizontal/vertical constructions
    \\[\smallskipamount]
    \item base glyphs addressed by \UC\ slots
    \item variants (sizes) addressed through lookups
    \item constructions addressed through lookups
    \\[\smallskipamount]
    \item alternates addressed through stylistic sets
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{What is the basis for \OT\ math fonts?}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item the \OT\ math specification 
    \begin{itemize}
    \item developed by the MS Typography team
    \item unpublished, but available on request
    \end{itemize}
  \item the reference font: Cambria Math
    \begin{itemize}
    \item developed by a contractor (Tiro Typeworks)
    \item widely available, viewable with FontForge
    \end{itemize}
  \item the reference implementation: MS Office 2007, 2010
    \begin{itemize}
    \item developed by the MS Office team
    \item completely closed, covered by patents
    \end{itemize}
  \item a full implementation: \LuaTeX
    \begin{itemize}
    \item implements an \OT\ math engine in \TeX
    \end{itemize}
  \item a partial implementation: \XeTeX
    \begin{itemize}
    \item uses a \TeX\ engine with \OT\ parameters
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{What are the problems of this basis?}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item the \OT\ math specification 
    \begin{itemize}
    \item may be vague or not clear enough in some areas
    \item may be unavailable to most font developers
    \end{itemize}
  \item the reference font: Cambria Math
    \begin{itemize}
    \item may include bugs, e.g. incorrect glyphs or parameters
    \end{itemize}
  \item the reference implementation: MS Office 2007, 2010
    \begin{itemize}
    \item may not fully adhere to the specification
    \item may include undocumented workarounds
    \end{itemize}
  \item a full implementation: \LuaTeX
    \begin{itemize}
    \item has to figure out how the reference really works
    \item has to work around bugs in reference fonts
    \end{itemize}
  \item a partial implementation: \XeTeX
    \begin{itemize}
    \item will behave different from the reference anyway
    \end{itemize}
  \end{itemize}
\end{frame}


\section{Progress in font development}
\subsection*{}

\begin{frame}
  \frametitle{Progress in font development}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item What are the choices of  \OT\ math fonts?
  \item What are the latest developments?
  \item Which typefaces are already supported?
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Choices for \OT\ math fonts}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item \OT\ math fonts already available/released
    \begin{itemize}
    \item Cambria Math, since 2007
    \item Asana Math, since 2008
    \item XITS Math, since 2010
    \item Latin Modern Math BETA, since 2011
    \end{itemize}
  \item \OT\ math fonts near completion
    \begin{itemize}
    \item Lucida Math, November 2011
    \item Minion Math, October 2011
    \end{itemize}
  \item \OT\ math fonts under development
    \begin{itemize}
    \item Neo Euler, since 2009 (unfinished)
    \item Maxwell Math (announced)
    \item TeX Gyre Math (planned)
    \end{itemize}
  \item most math fonts are from the same few developers
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{\OT\ math fonts by developers}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item Ross Mills, Tiro Typeworks
    \begin{itemize}
    \item Cambria Math
    \item Maxwell Math
    \end{itemize}
  \item Khaled Hosny, Egypt
    \begin{itemize}
    \item XITS Math
    \item Neo Euler (with DANTE, HZ)
    \item Lucida Math (with TUG, B\&H)
    \end{itemize}
  \item GUST e-foundry, Poland
    \begin{itemize}
    \item Latin Modern Math
    \item TeX Gyre Math
    \end{itemize}
  \item individual developers
    \begin{itemize}
    \item Asana Math (Apostolos Syropoulos)
    \item Minion Math (Johannes Küster)
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{\OT\ math fonts by typefaces}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item traditional \TeX\ fonts
    \begin{itemize}
    \item Latin Modern + LM Math
    \item whatever + Neo Euler
    \end{itemize}
  \item standard PostScript fonts
    \begin{itemize}
    \item Times + XITS Math
    \item Palatino + Asana Math
    \item TeX Gyre + TG Math
    \end{itemize}
  \item commercial fonts
    \begin{itemize}
    \item Lucida Bright + Lucida Math
    \item Minion Pro + Minion Math
    \end{itemize}
  \item new font designs
    \begin{itemize}
    \item Cambria + Cambria Math
    \item Maxwell + Maxwell Math
    \end{itemize}
  \end{itemize}
\end{frame}

\subsection*{}

\setmathfont{Cambria Math}

\begin{frame}
  \frametitle{Overview of math alphabets (Cambria Math)}
  \vspace*{0.5\baselineskip}
  \begin{footnotesize}
  \begin{tabular}{@{}p{5pc}p{7pc}p{7pc}p{2pc}@{}}
  \cs{mathup}		& $\mathup{\LatinSample}$		& $\mathup{\GreekSample} $	& $\mathup {0123}$ \\
  \cs{mathit}		& $\mathit{\LatinSample}$		& $\mathit{\GreekSample} $		& \\
  \cs{mathbfup}		& $\mathbfup{\LatinSample}$	& $\mathbfup{\GreekSample}$ 	& $\mathbfup{0123}$ \\
  \cs{mathbfit}		& $\mathbfit{\LatinSample}$ 	& $\mathbfit{\GreekSample}$ 	& 
  \\[\smallskipamount]
  \cs{mathsfup}		& $\mathsfup{\LatinSample}$	& \mbox{(not assigned)}		& $\mathsfup{0123}$ \\
  \cs{mathsfit}		& $\mathsfit{\LatinSample}$		& \mbox{(not assigned)}		& \\
  \cs{mathbfsfup} 	& $\mathbfsfup{\LatinSample}$	& \mbox{(missing)}\;\mbox{(missing)}	& $\mathbfsfup{0123}$ \\
  \cs{mathbfsfit} 		& $\mathbfsfit{\LatinSample}$	& \mbox{(missing)}\;\mbox{(missing)}	& 
  \\[\smallskipamount]
  \cs{mathscr}		& $\mathscr{\LatinSample}$		& & \\
  \cs{mathbfscr}		& $\mathbfscr{\LatinSample}$ 	& &
  \\[\smallskipamount]
  \cs{mathfrak}		& $\mathfrak{\LatinSample}$	& & \\
  \cs{mathbffrak} 	& $\mathbffrak{\LatinSample}$ 	& & 
  \\[\smallskipamount]
  \cs{mathbb}		& $\mathbb{\LatinSample}$ 		& 						& $\mathbb{0123}$ \\
  \end{tabular}
  \end{footnotesize}
\end{frame}

\setmathfont{Asana Math}

\begin{frame}
  \frametitle{Overview of math alphabets (Asana Math)}
  \vspace*{0.5\baselineskip}
  \begin{footnotesize}
  \begin{tabular}{@{}p{5pc}p{7pc}p{7pc}p{2pc}@{}}
  \cs{mathup}		& $\mathup{\LatinSample}$		& $\mathup{\GreekSample} $	& $\mathup {0123}$ \\
  \cs{mathit}		& $\mathit{\LatinSample}$		& $\mathit{\GreekSample} $		& \\
  \cs{mathbfup}		& $\mathbfup{\LatinSample}$	& $\mathbfup{\GreekSample}$ 	& $\mathbfup{0123}$ \\
  \cs{mathbfit}		& $\mathbfit{\LatinSample}$ 	& $\mathbfit{\GreekSample}$ 	& 
  \\[\smallskipamount]
  \cs{mathsfup}		& $\mathsfup{\LatinSample}$	& \mbox{(not assigned)}		& $\mathsfup{0123}$ \\
  \cs{mathsfit}		& $\mathsfit{\LatinSample}$		& \mbox{(not assigned)}		& \\
  \cs{mathbfsfup} 	& $\mathbfsfup{\LatinSample}$	& $\mathbfsfup{\GreekSample}$	& $\mathbfsfup{0123}$ \\
  \cs{mathbfsfit} 		& $\mathbfsfit{\LatinSample}$	& $\mathbfsfit{\GreekSample}$ 	& 
  \\[\smallskipamount]
  \cs{mathscr}		& $\mathscr{\LatinSample}$		& & \\
  \cs{mathbfscr}		& $\mathbfscr{\LatinSample}$ 	& &
  \\[\smallskipamount]
  \cs{mathfrak}		& $\mathfrak{\LatinSample}$	& & \\
  \cs{mathbffrak} 	& $\mathbffrak{\LatinSample}$ 	& & 
  \\[\smallskipamount]
  \cs{mathbb}		& $\mathbb{\LatinSample}$ 		& 						& $\mathbb{0123}$ \\
  \end{tabular}
  \end{footnotesize}
\end{frame}

\setmathfont{XITS Math}
\setmathfont[range={\mathcal,\mathbfcal},StylisticSet=1]{XITS Math}

\begin{frame}
  \frametitle{Overview of math alphabets (XITS Math)}
  \vspace*{0.5\baselineskip}
  \begin{footnotesize}
  \begin{tabular}{@{}p{5pc}p{7pc}p{7pc}p{2pc}@{}}
  \cs{mathup}		& $\mathup{\LatinSample}$		& $\mathup{\GreekSample} $	& $\mathup {0123}$ \\
  \cs{mathit}		& $\mathit{\LatinSample}$		& $\mathit{\GreekSample} $		& \\
  \cs{mathbfup}		& $\mathbfup{\LatinSample}$	& $\mathbfup{\GreekSample}$ 	& $\mathbfup{0123}$ \\
  \cs{mathbfit}		& $\mathbfit{\LatinSample}$ 	& $\mathbfit{\GreekSample}$ 	& 
  \\[\smallskipamount]
  \cs{mathsfup}		& $\mathsfup{\LatinSample}$	& \mbox{(not assigned)}		& $\mathsfup{0123}$ \\
  \cs{mathsfit}		& $\mathsfit{\LatinSample}$		& \mbox{(not assigned)}		& \\
  \cs{mathbfsfup} 	& $\mathbfsfup{\LatinSample}$	& $\mathbfsfup{\GreekSample}$	& $\mathbfsfup{0123}$ \\
  \cs{mathbfsfit} 		& $\mathbfsfit{\LatinSample}$	& $\mathbfsfit{\GreekSample}$ 	& 
  \\[\smallskipamount]
  \cs{mathscr}		& $\mathscr{\LatinSample}$		& & \\
  \cs{mathbfscr}		& $\mathbfscr{\LatinSample}$ 	& & \\
  \cs{mathcal}		& $\mathcal{\LatinUpper}$  		& & \\
  \cs{mathbfcal}		& $\mathbfcal{\LatinUpper}$ 	& &
  \\[\smallskipamount]
  \cs{mathfrak}		& $\mathfrak{\LatinSample}$	& & \\
  \cs{mathbffrak} 	& $\mathbffrak{\LatinSample}$ 	& & 
  \\[\smallskipamount]
  \cs{mathbb}		& $\mathbb{\LatinSample}$ 		& 						& $\mathbb{0123}$ \\
  \end{tabular}
  \end{footnotesize}
\end{frame}

\setmathfont[Scale=0.92]{Lucida Math}
\setmathfont[range={\mathcal,\mathbfcal},Scale=0.92,StylisticSet=4]{Lucida Math}

\begin{frame}
  \frametitle{Overview of math alphabets (Lucida Math)}
  \vspace*{0.5\baselineskip}
  \begin{footnotesize}
  \begin{tabular}{@{}p{5pc}p{7pc}p{7pc}p{2pc}@{}}
  \cs{mathup}		& $\mathup{\LatinSample}$		& $\mathup{\GreekSample} $	& $\mathup {0123}$ \\
  \cs{mathit}		& $\mathit{\LatinSample}$		& $\mathit{\GreekSample} $		& \\
  \cs{mathbfup}		& $\mathbfup{\LatinSample}$	& $\mathbfup{\GreekSample}$ 	& $\mathbfup{0123}$ \\
  \cs{mathbfit}		& $\mathbfit{\LatinSample}$ 	& $\mathbfit{\GreekSample}$ 	& 
  \\[\smallskipamount]
  \cs{mathsfup}		& $\mathsfup{\LatinSample}$	& \mbox{(not assigned)}		& $\mathsfup{0123}$ \\
  \cs{mathsfit}		& $\mathsfit{\LatinSample}$		& \mbox{(not assigned)}		& \\
  \cs{mathbfsfup} 	& $\mathbfsfup{\LatinSample}$	& $\mathbfsfup{\GreekSample}$	& $\mathbfsfup{0123}$ \\
  \cs{mathbfsfit} 		& $\mathbfsfit{\LatinSample}$	& $\mathbfsfit{\GreekSample}$ 	& 
  \\[\smallskipamount]
  \cs{mathscr}		& $\mathscr{\LatinSample}$		& & \\
  \cs{mathbfscr}		& $\mathbfscr{\LatinUpper}$\;\mbox{(missing)} 	& & \\
  \cs{mathcal}		& $\mathcal{\LatinUpper}$  		& & \\
  \cs{mathbfcal}		& $\mathbfcal{\LatinUpper}$ 	& &
  \\[\smallskipamount]
  \cs{mathfrak}		& $\mathfrak{\LatinSample}$	& & \\
  \cs{mathbffrak} 	& \mbox{(missing)}\;\mbox{(missing)}			& & 
  \\[\smallskipamount]
  \cs{mathbb}		& $\mathbb{\LatinUpper}$\;\mbox{(missing)} & 				& \mbox{(missing)}  \\
  \end{tabular}
  \end{footnotesize}
\end{frame}

\setmathfont{Latin Modern Math}

\begin{frame}
  \frametitle{Overview of math alphabets (LM Math)}
  \vspace*{0.5\baselineskip}
  \begin{footnotesize}
  \begin{tabular}{@{}p{5pc}p{7pc}p{8pc}p{2pc}@{}}
  \cs{mathup}		& $\mathup{\LatinSample}$		& $\mathup{\GreekSample} $	& $\mathup {0123}$ \\
  \cs{mathit}		& $\mathit{\LatinSample}$		& $\mathit{\GreekSample} $		& \\
  \cs{mathbfup}		& $\mathbfup{\LatinSample}$	& $\mathbfup{\GreekSample}$ 	& $\mathbfup{0123}$ \\
  \cs{mathbfit}		& $\mathbfit{\LatinSample}$ 	& $\mathbfit{\GreekSample}$ 	& 
  \\[\smallskipamount]
  \cs{mathsfup}		& $\mathsfup{\LatinSample}$	& \mbox{(not assigned)}		& $\mathsfup{0123}$ \\
  \cs{mathsfit}		& $\mathsfit{\LatinSample}$		& \mbox{(not assigned)}		& \\
  \cs{mathbfsfup} 	& $\mathbfsfup{\LatinSample}$	& $\mathbfsfup{\GreekUpper}$\;\mbox{(missing)}	& $\mathbfsfup{0123}$ \\
  \cs{mathbfsfit} 		& $\mathbfsfit{\LatinSample}$	& $\mathbfsfit{\GreekUpper}$\;\mbox{(missing)} 	& 
  \\[\smallskipamount]
  \cs{mathscr}		& $\mathscr{\LatinUpper}$\;\mbox{(missing)} 	& & \\
  \cs{mathbfscr}		& $\mathbfscr{\LatinUpper}$\;\mbox{(missing)} 	& &
  \\[\smallskipamount]
  \cs{mathfrak}		& $\mathfrak{\LatinSample}$	& & \\
  \cs{mathbffrak} 	& $\mathbffrak{\LatinSample}$	& & 
  \\[\smallskipamount]
  \cs{mathbb}		& $\mathbb{\LatinSample}$ 		& 						& $\mathbb{0123}$ \\
  \end{tabular}
  \end{footnotesize}
\end{frame}

\setmathfont{Neo Euler}

\begin{frame}
  \frametitle{Overview of math alphabets (Neo Euler)}
  \vspace*{0.5\baselineskip}
  \begin{footnotesize}
  \begin{tabular}{@{}p{5pc}p{7pc}p{8pc}p{2pc}@{}}
  \cs{mathup}		& $\mathup{\LatinSample}$		& $\mathup{\GreekSample} $	& $\mathup {0123}$ \\
  \cs{mathbfup}		& $\mathbfup{\LatinSample}$	& $\mathbfup{\GreekSample}$ 	& $\mathbfup{0123}$
  \\[\smallskipamount]
  \cs{mathscr}		& $\mathscr{\LatinUpper}$\;\mbox{(missing)} 	& & \\
  \cs{mathbfscr}		& $\mathbfscr{\LatinUpper}$\;\mbox{(missing)} 	& &
  \\[\smallskipamount]
  \cs{mathfrak}		& $\mathfrak{\LatinSample}$	& & \\
  \cs{mathbffrak} 	& $\mathbffrak{\LatinSample}$	& & \\
  \end{tabular}
  \end{footnotesize}
\end{frame}

\section{Challenges in font development}
\subsection*{}

\begin{frame}
  \frametitle{Challenges in font development}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item Completeness
    \begin{itemize}
    \item Completeness of math symbols
    \item Completeness of math alphabets
    \end{itemize}
  \item Design Issues
    \begin{itemize}
    \item How to choose matching fonts?
    \item How should certain fonts look like?
    \end{itemize}
  \item Technical Issues
    \begin{itemize}
    \item Glyph metrics in \OT\ vs. \TeX
    \item Handling of bold math fonts
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Completeness of math symbols (I)}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item \UC\ math defines hundreds of math symbols
  \item \OT\ math fonts can choose what to implement
    \begin{itemize}
    \item most fonts do not supply all math symbols
    \item most fonts have some missing math symbols
    \item each font has different range of math symbols
    \item all fonts have common subset (traditional \TeX)
    \end{itemize}
  \item How complete are current fonts?
    \begin{itemize}
    \item most complete: XITS (derived from STIX) 
    \item somewhat complete: Asana, Cambria, Lucida
    \item least complete: Latin Modern, Neo Euler
    \end{itemize}
  \item How much incompleteness can be tolerated?
    \begin{itemize}
    \item it may depend on your usage of math fonts
    \item it may depend on the field (math, physics, etc)
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Completeness of math symbols (II)}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item \TeX\ traditionally uses several macro constructions
  \item \OT\ math fonts need replacements for macros
    \begin{itemize}
    \item triple dots (\cs{ldots}, \cs{cdots}, \cs{ddots}, etc)
    \item double and triple integrals, primes, backprimes
    \item negated symbols, stacked symbols
    \item constructed arrows with hooks and tails
    \item long arrows (including extensible versions)
    \item wide accents (including extensible versions)
    \item over- and underbraces (incl. extensible versions)
    \end{itemize}
  \item \OT\ math fonts provide new semantics
    \begin{itemize}
    \item horizontal variants (e.g. multiple sizes)
    \item horizontal constructions (e.g. extensible versions)
    \end{itemize}
  \end{itemize}
\end{frame}

 \subsection*{}

\begin{frame}
  \frametitle{Completeness of math alphabets}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item Serif (main text)
    \begin{itemize}
    \item Latin/Greek: 4 shapes (regular, italic, bold, bold italic)
    \item Numerals: 2 shapes (regular, bold), no italics
    \end{itemize}
  \item Sans Serif
    \begin{itemize}
    \item Latin/Greek: 4/2 shapes (regular, italic, bold, bold italic)
    \item Numerals: 2 shapes (regular, bold), no italics
    \end{itemize}
  \item Script (Calligraphic)
    \begin{itemize}
    \item Latin (uc + lc): 2 shapes (regular, bold), no Numerals
    \end{itemize}
  \item Fraktur (Blackletter)
    \begin{itemize}
    \item Latin (uc + lc): 2 shapes (regular, bold), no Numerals
    \end{itemize}
  \item Blackboard Bold (Openface)
    \begin{itemize}
    \item Latin (uc + lc), Numerals: 1 shape (regular)
    \end{itemize}
   \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Completeness of math alphabets}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item \UC\ math defines dozens of math alphabets
  \item \OT\ fonts can choose what to implement
  \item many fonts have some missing math alphabets
    \begin{itemize}
    \item bold sans-serif Greek (upright + italic)
    \item lowercase Script, bold Script, bold Fraktur
    \item lowercase BBold, numerals BBold
    \end{itemize}
  \item some fonts may provide additional alphabets
    \begin{itemize}
    \item alternate Script or Calligraphic
    \item alternate italic and bold italic
    \end{itemize}
  \item How much incompleteness can be tolerated?
    \begin{itemize}
    \item it may depend on your usage of math fonts
    \item it may depend on the field (math, physics, etc)
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Math alphabets: bold sans-serif Greek}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item What about bold sans-serif?
    \begin{itemize}
    \item Do you need a bold sans-serif math alphabet?
    \item Do you need it a lot or just a few times?
    \item Do you need Greek as well or will just Latin do?
    \item Do you need lowercase Greek or will uppercase do?  
    \item Do you mind substituting another font, if necessary?
    \end{itemize}
  \item What is available in current fonts?
    \begin{itemize}
    \item XITS, Asana, Lucida have complete bold sans alphabets
    \item Cambria is missing bold sans Greek, has only Latin
    \item Latin Modern is missing lowercase bold sans Greek
    \item Neo Euler has no sans-serif whatsoever
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Math alphabets: Script or Calligraphic}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item What about Script or Calligraphic?
    \begin{itemize}
    \item Do you need a Script or Calligraphic math alphabet?
    \item Do you need both or will any one of them do?
    \item Do you need bold Script as well or will regular do?  
    \item Do you need lowercase Script or will uppercase do?  
    \item Do you mind substituting another font, if necessary?
    \end{itemize}
  \item What is available in current fonts?
    \begin{itemize}
    \item Cambria, Asana, XITS have complete Script alphabets
    \item XITS, Lucida have alternate Calligraphic as well
    \item Lucida is missing lowercase bold Script
    \item Latin Modern, Neo Euler are missing lowercase Script
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Math alphabets: Blackboard Bold}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item What about Blackboard Bold?
    \begin{itemize}
    \item Do you need a Blackboard Bold math alphabet?
    \item Do you need lowercase letters or will uppercase do?
    \item Do you need numerals as well or will letters do?
    \item Do you care how the the BBold font looks like?
    \item Do you mind substituting another font, if necessary?
    \end{itemize}
  \item What is available in current fonts?
    \begin{itemize}
    \item Cambria Asana, XITS, LM have complete BBold
    \item Lucida is missing lowercase and numerals BBold
    \item Neo Euler has no BBold whatsoever
    \end{itemize}
  \end{itemize}
\end{frame}


\subsection*{}

\begin{frame}
  \frametitle{Design issues: Choosing matching fonts}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item \UC\ math combines several math alphabets
  \item \OT\ math fonts need to choose matching fonts
    \begin{itemize}
    \item no problem for comprehensive families (LM, Lucida, etc)
    \item could be a design issue for most other font families
    \end{itemize}
  \item Choosing a matching sans-serif font:
    \begin{itemize}
    \item Which sans-serif font to go with Times, Palatino, Euler?
    \item Which fonts are available for inclusion?
    \item Which fonts contain a bold sans Greek alphabet?
    \item Is bold sans Greek distinguishable from bold serif?
    \end{itemize}
 \item Choosing a matching Script or Fraktur font:
    \begin{itemize}
    \item Which Script/Calligraphic or Fraktur fonts to use?
    \item Which fonts are available for inclusion?
    \end{itemize}
  \end{itemize}
\end{frame}



\begin{frame}
  \frametitle{Design issues: Greek alphabets}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item What about upright Greek (regular and bold)?
    \begin{itemize}
    \item How should an upright Greek alphabet look like?
    \item Is upright Greek different from unslanted Greek?
    \item Does unslanted Greek look strange or unbalanced?
    \item It may be necessary to review some glyph designs
    \setmathfont{Latin Modern Math}
    \item Example: 
	$\mathup{\gamma}$, $\mathup{\nu}$, $\mathup{\pi}$, $\mathup{\epsilon}$ in Latin Modern
    \end{itemize}
  \item Latin Modern Math
    \\[\smallskipamount]
    \setmathfont{Latin Modern Math}
    \begin{small}
    \begin{tabular}{@{}p{4pc}p{16pc}@{}}
    ~~~~\cs{mathup} 	& $\mathup{\GreekLowerAlmostAll}$	\\
    ~~~~\cs{mathit} 	& $\mathit{\GreekLowerAlmostAll}$ 
    \end{tabular}
    \end{small}
  \item Cambria Math
    \\[\smallskipamount]
    \setmathfont{Cambria Math}
    \begin{small}
    \begin{tabular}{@{}p{4pc}p{16pc}@{}}
    ~~~~\cs{mathup} 	& $\mathup{\GreekLowerAll}$	\\
    ~~~~\cs{mathit} 	& $\mathit{\GreekLowerAll}$ 
    \end{tabular}
    \end{small}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Design issues: Greek alphabets}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item What about bold sans-serif Greek (upright and italic)?
    \begin{itemize}
    \item How should a bold sans-serif Greek alphabet look like?
    \item What makes lowercase Greek serif or sans-serif?\\
      (e.g. uniform stroke thickness, hooks, tails, etc)
    \item Is bold sans Greek distinguishable from bold serif?
    \item It may depend on the font characteristics\\
      (e.g. constrast between thin and thick strokes)
    \end{itemize}
  \item Lucida Math
    \\[\smallskipamount]
    \setmathfont[Scale=0.88]{Lucida Math}
    \begin{small}
    \begin{tabular}{@{}p{6pc}p{16pc}@{}}
    ~~~~\cs{mathbfit} 	& $\mathbfit{\GreekLowerAll}$	\\
    ~~~~\cs{mathbfsfit} 	& $\mathbfsfit{\GreekLowerAll}$ 
    \end{tabular}
    \end{small}
  \item XITS Math
    \\[\smallskipamount]
    \setmathfont{XITS Math}
    \begin{small}
    \begin{tabular}{@{}p{6pc}p{16pc}@{}}
    ~~~~\cs{mathbfit} 	& $\mathbfit{\GreekLowerAll}$	\\ 
    ~~~~\cs{mathbfsfit} 	& $\mathbfsfit{\GreekLowerAll}$ 
    \end{tabular}
    \end{small}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Design issues: Script/Calligraphic}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item What about Script/Calligraphic?
    \begin{itemize}
    \item How should a Script/Calligraphic font look like?
    \item What do users expect for Script or Calligraphic?
    \item How is the font set up (spacing, alignment, etc)?
    \item Not every Script font is well-suited for math
    \end{itemize}
  \item Font Examples
    \begin{small}
    \begin{tabular}{@{}p{6pc}p{12pc}@{}}
    ~~~~Cambria Math & 
	\setmathfont{Cambria Math}
	$\mathscr{ABC XYZ\,abc xyz}$	\\
    ~~~~Asana Math & 
	\setmathfont[Scale=0.92]{Asana Math}
	$\mathscr{ABC XYZ\,abc xyz}$	\\
    ~~~~XITS Math & 
	\setmathfont{XITS Math}
	$\mathscr{ABC XYZ\,abc xyz}$	\\
    ~~~~Lucida Math & 
	\setmathfont[Scale=0.80]{Lucida Math}
	$\mathscr{ABC XYZ\,abc xyz}$	\\
    ~~~~LM Math & 
	\setmathfont{Latin Modern Math}
	$\mathscr{ABC XYZ}$	\\
    ~~~~Neo Euler & 
	\setmathfont{Neo Euler}
	$\mathscr{ABC XYZ}$ \\
    \end{tabular}
    \\[\smallskipamount]
    \begin{tabular}{@{}p{6pc}p{12pc}@{}}
    ~~~~XITS Math & 
	\setmathfont{XITS Math:+ss01}
	$\mathcal{ABC XYZ}$ (+ss01) \\
    ~~~~Lucida Math & 
	\setmathfont[Scale=0.92]{Lucida Math:+ss04}
	$\mathcal{ABC XYZ}$ (+ss04) \\
    \end{tabular}
    \end{small}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Design issues:  Fraktur}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item What about Fraktur (Blackletter)?
    \begin{itemize}
    \item How should a Fraktur math alphabet look like?
    \item What do users expect for Fraktur (Blackletter)?
    \item How is the font set up (spacing, alignment, etc)?
    \item Not every Blackletter font is well-suited for math
    \end{itemize}
  \item Font Examples
    \begin{small}
    \begin{tabular}{@{}p{6pc}p{12pc}@{}}
    ~~~~Cambria Math & 
	\setmathfont{Cambria Math}
	$\mathfrak{ABC XYZ\,abc xyz}$	\\
    ~~~~Asana Math & 
	\setmathfont{Asana Math}
	$\mathfrak{ABC XYZ\,abc xyz}$	\\
    ~~~~XITS Math & 
	\setmathfont[Scale=0.92]{XITS Math}
	$\mathfrak{ABC XYZ\,abc xyz}$	\\
    ~~~~Lucida Math & 
	\setmathfont[Scale=1.0]{Lucida Math}
	$\mathfrak{ABC XYZ\,abc xyz}$	\\
    ~~~~LM Math & 
	\setmathfont{Latin Modern Math}
	$\mathfrak{ABC XYZ\,abc xyz}$	\\
    ~~~~Neo Euler & 
	\setmathfont{Neo Euler}
	$\mathfrak{ABC XYZ\,abc xyz}$	\\
    \end{tabular}
    \end{small}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Design issues: Blackboard Bold}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item What about Blackboard Bold?
    \begin{itemize}
    \item How should a Blackboard Bold font look like?
    \item Do you prefer a serif or sans-serif style of BBold?
    \end{itemize}
  \item What is available in current fonts?
    \begin{itemize}
    \item Cambria, Asana have serif BBold design
    \item XITS, Lucida, LM have sans-serif BBold design
    \end{itemize}
  \item Font Examples
    \begin{small}
    \begin{tabular}{@{}p{6pc}p{12pc}@{}}
    ~~~~Cambria Math & 
	\setmathfont{Cambria Math}
	$\mathbb{ABC NOPQR XYZ\,abc xyz\,0123}$	\\
    ~~~~Asana Math & 
	\setmathfont[Scale=0.92]{Asana Math}
	$\mathbb{ABC NOPQR XYZ\,abc xyz\,0123}$	\\
    ~~~~XITS Math & 
	\setmathfont{XITS Math}
	$\mathbb{ABC NOPQR XYZ\,abc xyz\,0123}$	\\
    ~~~~Lucida Math & 
	\setmathfont[Scale=0.92]{Lucida Math}
	$\mathbb{ABC NOPQR XYZ}$ \\
    ~~~~LM Math & 
	\setmathfont{Latin Modern Math}
	$\mathbb{ABC NOPQR XYZ\,abc xyz\,0123}$	\\
    \end{tabular}
    \end{small}
  \end{itemize}
\end{frame}

\subsection*{}

\begin{frame}
  \frametitle{Technical issues: Glyph metrics (I)}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item \TeX\ traditionally uses special interpretation of metrics
    \begin{itemize}
    \item nominal width = offset of subscript
    \item italic correction = offset of superscript
    \item nominal width + italic correction = actual width
    \end{itemize}
  \item \OT\ math uses standard interpretation of metrics
    \begin{itemize}
    \item nominal width = actual width
    \item italic correction = usually ignored
    \item math kern = correction to script position
    \end{itemize}
  \item What about current engines?
    \begin{itemize}
    \item MS Office follows the \OT\ interpretation
    \item \LuaTeX\ follows the \OT\ interpretation
    \item \XeTeX\ follows traditional \TeX\ interpretation
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Technical issues: Glyph metrics (II)}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item \TeX\ math fonts need adjustments for \OT\ math
    \begin{itemize}
    \item new width = old width + italic correction
    \item math kern = adjustments to old script position
    \end{itemize}
  \item Why is that needed?
    \begin{itemize}
    \item italic correction is ignored in \OT\ math
    \item collisions with superscripts or other glyphs
    \end{itemize}   
  \item What about current fonts?
    \begin{itemize}
    \item Cambria was designed for \OT\ metrics
    \item Asana, XITS seem to work for \OT\ metrics
    \item Lucida, LM were designed for \TeX\ metrics
    \item Lucida has just switched to \OT\ metrics
    \item LM will have to follow eventually
    \item Neo Euler is not affected (upright design)
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}[fragile]
  \frametitle{Technical issues: What about bold math?}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item traditional (La)\TeX\ handling of bold math
    \begin{itemize}
    \item \cs{boldsymbol}, \cs{bm}\\
	font switch within math, e.g. markup of vectors, etc.
    \item \cs{boldmath}, \verb|\mathversion{bold}|\\
     	font switch outside math, e.g. headlines, emphasis, etc.
    \end{itemize}
  \item \OT\ handling of bold math switching
    \begin{itemize}
    \item math alphabet switches handled within one font
    \item font-switching to all-bold means loading new font
    \end{itemize}
  \item How to design bold versions of \OT\ math fonts?
    \begin{itemize}
    \item regular symbols should be replaced by bold symbols
    \item regular allphabets should be replaced by bold alphabets
    \item bold alphabets should be replaced by heavy (if available)
    \item large symbols may be missing in bold version
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Summary}
  \vspace*{0.5\baselineskip}
  \begin{itemize}
  \item \OT\ math fonts are making progress
    \begin{itemize}
    \item several new fonts will become available soon
    \item still more fonts are needed for other typefaces
    \end{itemize}
  \item \OT\ math fonts remain challenging
    \begin{itemize}
    \item development of math fonts is far from easy
    \item development of math fonts is a lot of work
    \item testing of math fonts will need more work
    \end{itemize}
  \item \OT\ math engines
    \begin{itemize}
    \item MS Office has defined the reference behaviour
    \item \LuaTeX\ closely follows the reference behaviour
    \item \XeTeX\ is incompatible and is falling behind
    \end{itemize}
  \end{itemize}
\end{frame}

\end{document}

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