path: root/fonts/stix2-otf/Math-features.tex

\cleardoublepage

\pdfbookmark[0]{Substitutions}{pdf.features}

\makeatletter
\let\UCS@mincodepoint\@empty
\let\UCS@maxcodepoint\@empty
\def\UCS@blockname{OpenType Language Systems and Features}
\makeatother

\begingroup

\UCStextfont

\newfontface{\stixmath}{STIX Two Math}

\parskip\smallskipamount

\section{OpenType Language Systems and Features}

See
the \href{https://docs.microsoft.com/en-us/typography/opentype/spec/featurelist}{OpenType
Specification} for a description of the following features.

\smallskip

\def\tablestrut{\rule[-3pt]{0pt}{13pt}}
\parindent 0pt
\begin{tabular}{@{}|ll*{4}{c}|@{}}
\multicolumn{1}{l}{Script}&\multicolumn{1}{l}{Language}&ccmp&dtls&flac&\multicolumn{1}{c}{ssty}\\[2pt]
\hline
\tablestrut math
& \textsc{default}&$\checkmark$&$\checkmark$&$\checkmark$&$\checkmark$\\
\hline
\end{tabular}

\smallskip

\section{Character Variants}

\begin{tabular}{@{}lll@{${}\to{}$}lll@{}}
cv01
     & U+019B
     & \UCSchartfont\char"019B
     & \UCSchartfont\addfontfeature{CharacterVariant=1}\char"019B
     & LATIN SMALL LETTER LAMBDA WITH STROKE\\
cv02
     & U+0264
     & \UCSchartfont\char"0264
     & \UCSchartfont\addfontfeature{CharacterVariant=2}\char"0264
     & LATIN SMALL LETTER RAMS HORN\\
cv03
     & U+2205
     & \UCSchartfont\char"2205
     & \UCSchartfont\addfontfeature{CharacterVariant=3}\char"2205
     & EMPTY SET\\
cv04
     & U+2216
     & \UCSchartfont\char"2216
     & \UCSchartfont\addfontfeature{CharacterVariant=4}\char"2216
     & SET MINUS
\end{tabular}

\smallskip

\textbf{Note}: The default shape of the empty set symbol has not been
     changed to preserve backwards compatibility.

\section{Stylistic Sets}

Version~1 of the STIX fonts contained a number of variant forms that
are preserved in STIX Two as OpenType Layout stylistic set
substitutions.  There are a limited number of such features available,
so while an effort has been made to group like substitutions together,
there is inevitably a ‘grab-bag’ feature (ss20) containing
miscellaneous variants.  Sets 8 and~9 are included for compatibility
with the XITS fonts.  The current repertoire may be extended in the
future if there is sufficient interest.

\raggedcolumns

\begin{multicols}{3}

\raggedright

\subsection{Stylistic Set 1 <ss01>}

\emph{Substitute roundhand for chancery Script Alphanumeric Symbols.}

\begin{ssubs}{01}
\U+1D49C\\  % A
\U+212C\\   % B
\U+1D49E\\  % C
\U+1D49F\\  % D
\U+2130\\   % E
\U+2131\\   % F
\U+1D4A2\\  % G
\U+210B\\   % H
\U+2110\\   % I
\U+1D4A5\\  % J
\U+1D4A6\\  % K
\U+2112\\   % L
\U+2133\\   % M
\U+1D4A9\\  % N
\U+1D4AA\\  % O
\U+1D4AB\\  % P
\U+1D4AC\\  % Q
\U+211B\\   % R
\U+1D4AE\\  % S
\U+1D4AF\\  % T
\U+1D4B0\\  % U
\U+1D4B1\\  % V
\U+1D4B2\\  % W
\U+1D4B3\\  % X
\U+1D4B4\\  % Y
\U+1D4B5\\  % Z
\end{ssubs}

\def\D+#1\\{%
    #1
    &\stixmath\XeTeXglyph\XeTeXglyphindex"u#1.dotless"
    &\stixmath\addfontfeature{StylisticSet=1}\XeTeXglyph\XeTeXglyphindex"u#1.dotless"\\}

\begin{ssubs}{01}
\U+1D4B6\\  % a
\U+1D4B7\\  % b
\U+1D4B8\\  % c
\U+1D4B9\\  % d
\U+212F\\   % e
\U+1D4BB\\  % f
\U+210A\\   % g
\U+1D4BD\\  % h
\U+1D4BE\\  % i
% \D+1D4BE\\  % i.dotless
\U+1D4BF\\  % j
% \D+1D4BF\\  % j.dotless
\U+1D4C0\\  % k
\U+1D4C1\\  % l
\U+1D4C2\\  % m
\U+1D4C3\\  % n
\U+2134\\   % o
\U+1D4C5\\  % p
\U+1D4C6\\  % q
\U+1D4C7\\  % r
\U+1D4C8\\  % s
\U+1D4C9\\  % t
\U+1D4CA\\  % u
\U+1D4CB\\  % v
\U+1D4CC\\  % w
\U+1D4CD\\  % x
\U+1D4CE\\  % y
\U+1D4CF\\  % z
\end{ssubs}

\begin{ssubs}{01}
\U+1D4D0\\  % A
\U+1D4D1\\  % B
\U+1D4D2\\  % C
\U+1D4D3\\  % D
\U+1D4D4\\  % E
\U+1D4D5\\  % F
\U+1D4D6\\  % G
\U+1D4D7\\  % H
\U+1D4D8\\  % I
\U+1D4D9\\  % J
\U+1D4DA\\  % K
\U+1D4DB\\  % L
\U+1D4DC\\  % M
\U+1D4DD\\  % N
\U+1D4DE\\  % O
\U+1D4DF\\  % P
\U+1D4E0\\  % Q
\U+1D4E1\\  % R
\U+1D4E2\\  % S
\U+1D4E3\\  % T
\U+1D4E4\\  % U
\U+1D4E5\\  % V
\U+1D4E6\\  % W
\U+1D4E7\\  % X
\U+1D4E8\\  % Y
\U+1D4E9\\  % Z
\end{ssubs}

\subsection{Stylistic Set 1 <ss01> (continued)}

\begin{ssubs}{02}
\U+1D4EA\\  % a
\U+1D4EB\\  % b
\U+1D4EC\\  % c
\U+1D4ED\\  % d
\U+1D4EE\\  % e
\U+1D4EF\\  % f
\U+1D4F0\\  % g
\U+1D4F1\\  % h
\U+1D4F2\\  % i
% \D+1D4F2\\  % i.dotless
\U+1D4F3\\  % j
% \D+1D4F3\\  % j.dotless
\U+1D4F4\\  % k
\U+1D4F5\\  % l
\U+1D4F6\\  % m
\U+1D4F7\\  % n
\U+1D4F8\\  % o
\U+1D4F9\\  % p
\U+1D4FA\\  % q
\U+1D4FB\\  % r
\U+1D4FC\\  % s
\U+1D4FD\\  % t
\U+1D4FE\\  % u
\U+1D4FF\\  % v
\U+1D500\\  % w
\U+1D501\\  % x
\U+1D502\\  % y
\U+1D503\\  % z
\end{ssubs}

\subsection{Stylistic Set 2 <ss02>}

\emph{Variants of selected math italic lowercase letters.}

\begin{ssubs}{02}
\U+1D454\\
\U+1D462\\
\U+1D463\\
\U+1D464\\
\U+1D467\\
\U+1D488\\
\U+1D628\\
\U+1D65C\\
\end{ssubs}

\subsection{Stylistic Set 3 <ss03>}

\emph{Variants of characters with cross-bars.}

\begin{ssubs}{03}
\U+019B\\
\U+210F\\
\end{ssubs}

\columnbreak

\subsection{Stylistic Set 4 <ss04>}

\emph{Larger, lower variants of prime, minute, second, etc.}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=4}\char"#1\\}

\begin{ssubs}{04}
\U+2032\\
\U+2033\\
\U+2034\\
\U+2035\\
\U+2036\\
\U+2037\\
\U+2057\\
\end{ssubs}

\subsection{Stylistic Set 5 <ss05>}

\emph{Shorter variants of selected arrows.}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=5}\char"#1\\}

\begin{ssubs}{05}
\U+2190\\
\U+2191\\
\U+2192\\
\U+2193\\
\U+21D1\\
\U+21D3\\
\U+21E0\\
\U+21E2\\
\end{ssubs}

\subsection{Stylistic Set 6 <ss06>}

\emph{Narrower or shorter variants of assorted symbols.}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=6}\char"#1\\}

\begin{ssubs}{06}
\U+2208\\
\U+220B\\
\U+2223\\
\U+2224\\
\U+2225\\
\U+2226\\
\U+2AEE\\
\end{ssubs}

\subsection{Stylistic Set 7 <ss07>}

\emph{Smaller versions of various operators.}

\textbf{Note}: In version 2.0.0, the transformation
       {\UCSchartfont\char"2205 ${}\to{}$
         \addfontfeature{CharacterVariant=3}\char"2205} was
       erroneously included in this stylistic set.  That
       transformation has been moved to cv03.

\smallskip

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=7}\char"#1\\}

\begin{ssubs}[1.2]{07}
\U+2140\\
\U+220F\\
\U+2210\\
\U+2211\\
\U+221A\\
\U+221B\\
\U+221C\\
\end{ssubs}

\subsection{Stylistic Set 8 <ss08>}

\emph{(XITS compatibility) Upright forms of integrals, including size
         variants (not shown).}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=8}\char"#1\\}

\begin{ssubs}[1.1]{08}
\U+222B\\
\U+222C\\
\U+222D\\
\U+222E\\
\U+222F\\
\U+2230\\
\U+2231\\
\U+2232\\
\U+2233\\
\U+2A0B\\
\U+2A0C\\
\U+2A0D\\
\U+2A0E\\
\U+2A0F\\
\U+2A10\\
\U+2A11\\
\U+2A12\\
\U+2A13\\
\U+2A14\\
\U+2A15\\
\U+2A16\\
\U+2A17\\
\U+2A18\\
\U+2A19\\
\U+2A1A\\
\U+2A1B\\
\U+2A1C\\
\end{ssubs}

\newpage

\subsection{Stylistic Set 9 <ss09>}

\emph{(XITS compatibility) Vertical slash variants of
some negated symbols.}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=9}\char"#1\\}

\begin{ssubs}[1.1]{09}
\U+0338\\
\U+2209\\
\U+220C\\
\U+2241\\
\U+2244\\
\U+2246\\
\U+2247\\
\U+2249\\
\U+2260\\
\U+2262\\
\U+2268\\
\U+2269\\
\U+226D\\
\U+226E\\
\U+226F\\
\U+2270\\
\U+2271\\
\U+2274\\
\U+2275\\
\U+2278\\
\U+2279\\
\U+2280\\
\U+2281\\
\U+2284\\
\U+2285\\
\U+2288\\
\U+2289\\
\U+22E0\\
\U+22E1\\
\U+22EC\\
\U+22ED\\
\end{ssubs}

\columnbreak

\subsection{Stylistic Set 10 <ss10>}

\emph{Slanted variants of selected greater/lesser relations.}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=10}\char"#1\\}

\begin{ssubs}[1.1]{10}
\U+2272\\
\U+2273\\
\U+22DA\\
\U+22DB\\
\U+2A9D\\
\U+2A9E\\
\U+2AAC\\
\U+2AAD\\
\end{ssubs}

\subsection{Stylistic Set 11 <ss11>}

\emph{Variant negated sub/superset relations.}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=11}\char"#1\\}

\begin{ssubs}[1.2]{11}
\U+228A\\
\U+228B\\
\U+2ACB\\
\U+2ACC\\
\end{ssubs}

\subsection{Stylistic Set 12 <ss12>}

\emph{Low-modulation, `sans serif'-like variants.}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=12}\char"#1\\}

\begin{ssubs}{12}
\U+221D\\
\U+2322\\
\U+2323\\
\end{ssubs}

\subsection{Stylistic Set 13 <ss13>}

\emph{Horizontally-flipped sine-wave symbol.}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=13}\char"#1\\}

\begin{ssubs}{13}
\U+223F\\
\end{ssubs}

\columnbreak

\subsection{Stylistic Set 14 <ss14>}

\emph{Taller versions of two symbols.}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=14}\char"#1\\}

\begin{ssubs}{14}
\U+2A3C\\
\U+2A3D\\
\end{ssubs}

\subsection{Stylistic Set 15 <ss15>}

\emph{Slab-serif variants.}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=15}\char"#1\\}

\begin{ssubs}{15}
\U+2229\\
\U+222A\\
\U+2293\\
\U+2294\\
\end{ssubs}

\subsection{Stylistic Set 16 <ss16>}

\emph{Variant circled operators (note inconsistent sets).}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=16}\char"#1\\}

\begin{ssubs}{16}
\U+2295\\
\U+2297\\
\U+229C\\
\end{ssubs}

\subsection{Stylistic Set 20 <ss20>}

\emph{Miscellaneous variants.}

\def\U+#1\\{#1&\stixmath\char"#1&\stixmath\addfontfeature{StylisticSet=20}\char"#1\\}

\begin{ssubs}{20}
\U+223E\\
\U+224C\\
\U+2423\\
\U+25A9\\
\end{ssubs}

\end{multicols}

\clearpage

\section{Mathematical Standardized Variants}

Standardized Variants are described in section 22.5 of the
\href{https://www.unicode.org/versions/Unicode12.0.0/ch22.pdf#G23168}{Unicode
12.0 Core Specification} and in the
\href{https://www.unicode.org/Public/12.0.0/ucd/StandardizedVariants.txt}{StandardizedVariants.txt}
file in the Unicode Character Database.

As noted below, most of the Standardized Variants are also accessible
via Character Variants or Stylistic Sets.

\medskip

\tracinglostchars=0

\begingroup

\def\arraystretch{1.2}

\newcommand{\variant}[2][]{U+#2&U+FE00 &\stixmath\char"#2&\stixmath\char"#2︀&#1\\}

\begin{tabular}{@{}l@{\,}ll@{${}\to{}$}l@{\qquad}l@{}}
\variant{0030}% short diagonal stroke form; # DIGIT ZERO
\variant[cv03]{2205}% zero with long diagonal stroke overlay form; # EMPTY SET
\variant[ss15]{2229}% with serifs; # INTERSECTION
\variant[ss15]{222A}% with serifs; # UNION
\variant[ss09]{2268}% with vertical stroke; # LESS-THAN BUT NOT EQUAL TO
\variant[ss09]{2269}% with vertical stroke; # GREATER-THAN BUT NOT EQUAL TO
\variant[ss10]{2272}% following the slant of the lower leg; # LESS-THAN OR EQUIVALENT TO
\variant[ss10]{2273}% following the slant of the lower leg; # GREATER-THAN OR EQUIVALENT TO
\variant[ss11]{228A}% with stroke through bottom members; # SUBSET OF WITH NOT EQUAL TO
\variant[ss11]{228B}% with stroke through bottom members; # SUPERSET OF WITH NOT EQUAL TO
\variant[ss15]{2293}% with serifs; # SQUARE CAP
\variant[ss15]{2294}% with serifs; # SQUARE CUP

\variant[ss16]{2295}% with white rim; # CIRCLED PLUS
\variant[ss16]{2297}% with white rim; # CIRCLED TIMES
\variant[ss16]{229C}% with equal sign touching the circle; # CIRCLED EQUALS

\variant[ss10]{22DA}% with slanted equal; # LESS-THAN EQUAL TO OR GREATER-THAN
\variant[ss10]{22DB}% with slanted equal; # GREATER-THAN EQUAL TO OR LESS-THAN
\variant[ss14]{2A3C}% tall variant with narrow foot; # INTERIOR PRODUCT
\variant[ss14]{2A3D}% tall variant with narrow foot; # RIGHTHAND INTERIOR PRODUCT
\variant[ss10]{2A9D}% with similar following the slant of the upper leg; # SIMILAR OR LESS-THAN
\variant[ss10]{2A9E}% with similar following the slant of the upper leg; # SIMILAR OR GREATER-THAN
\variant[ss10]{2AAC}% with slanted equal; # SMALLER THAN OR EQUAL TO
\variant[ss10]{2AAD}% with slanted equal; # LARGER THAN OR EQUAL TO
\variant[ss11]{2ACB}% with stroke through bottom members; # SUBSET OF ABOVE NOT EQUAL TO
\variant[ss11]{2ACC}% with stroke through bottom members; # SUPERSET OF ABOVE NOT EQUAL TO
\end{tabular}

\endgroup

\endgroup

\endinput