How make TikZ arrow tips match arrows with TeX Gyre Termes Math font?

Question

How can I (globally in the document, I hope) change the shape of TikZ arrowheads (including those in tikzcd environments) so match the arrowheads from the TeX Gyre Terms Math font (using XeLaTeX)?

The style Straight Barb almost matches, but the ends of the barbs are different: in TeX Gyre Termes Math, the ends of the barbs are horizontal, whereas in TikZ Straight Barb heads, the ends of the bars are perpendicular to the body of the barb.

\documentclass[12pt]{article}
\usepackage[left=2.5in,right=2.5in]{geometry}
\usepackage{tikz-cd}
\usetikzlibrary{arrows.meta,decorations.markings}
\tikzset{
  >={Straight Barb[scale=0.8]},
  commutative diagrams/arrow style=tikz
}
\usepackage{fontspec}
\usepackage{unicode-math}
\setmainfont{TeX Gyre Termes}[Scale=1.0]
\defaultfontfeatures{Scale=MatchLowercase, Ligatures=TeX}
\setmathfont{TeX Gyre Termes Math}
\begin{document}
\large
\begin{equation}    % eq 1
  A \longrightarrow B \rightarrow C
\end{equation}
%
\begin{equation}    % eq 2
  \begin{tikzcd}
    A \arrow[r,thick] {$f$} & B
  \end{tikzcd}
\end{equation}
\end{document}

Related: How make TikZ arrow tips match tips of newtxmath font's arrows?

Answer 1

The official solution is the math font option of tikz-cd.

\documentclass{article}
\usepackage{unicode-math}
\setmathfont{texgyrepagella-math.otf}
\usepackage{tikz,tikz-cd}
\tikzcdset{arrow style={math font}}
\pgfmathdeclarefunction{axis_height}{0}{\begingroup\pgfmathreturn.25em\endgroup}
\pgfmathdeclarefunction{rule_thickness}{0}{\begingroup\pgfmathreturn.06em\endgroup}
% credit to https://tex.stackexchange.com/questions/420034/tikzcdsetarrow-style-math-font-breaks-the-rendering-of-arrows
\begin{document}
\large
\begin{equation}    % eq 1
  A \longrightarrow B \rightarrow C
\end{equation}
%
\begin{equation}    % eq 2
  \begin{tikzcd}
    A \arrow[r] {$f$} & B
  \end{tikzcd}
\end{equation}
\end{document}

Answer 2

Try this:

\documentclass{article}
\usepackage{tikz-cd}
\usetikzlibrary{arrows.meta,decorations.markings}
\makeatletter
% based on the definition of arrow tip "Straight Barb"
\pgfdeclarearrow{
  name = TeX Gyre Termes Math,
  defaults = {
    %%% <<< begin of change
    length = +3.5pt 2,
    %%% <<< end of change
    width'  = +0pt 2,
    line width = +0pt 1 1,
  },
  setup code = {
    % Compute front miter length:
    \pgfmathdivide@{\pgf@sys@tonumber\pgfarrowlength}{\pgf@sys@tonumber\pgfarrowwidth}%
    \let\pgf@temp@quot\pgfmathresult%
    \pgf@x\pgfmathresult pt%
    \pgf@x\pgfmathresult\pgf@x%
    \pgf@x4\pgf@x%
    \advance\pgf@x by1pt%
    \pgfmathsqrt@{\pgf@sys@tonumber\pgf@x}%
    \pgf@xc\pgfmathresult\pgfarrowlinewidth% xc is front miter
    \pgf@xc.5\pgf@xc
    \pgf@xa\pgf@temp@quot\pgfarrowlinewidth% xa is extra harpoon miter
    % Set ends
    \ifpgfarrowroundjoin
      \pgfarrowssettipend{\pgfarrowlength\advance\pgf@x by.5\pgfarrowlinewidth}
    \else
      \pgfarrowssettipend{\pgfarrowlength\advance\pgf@x by\pgf@xc\ifpgfarrowharpoon\advance\pgf@x by\pgf@xa\fi}
    \fi
    \pgfarrowssetvisualbackend{\pgfarrowlength\advance\pgf@x by.5\pgfarrowlinewidth}
    \pgfarrowssetbackend{-.5\pgfarrowlinewidth}
    % harpoon miter correction
    \ifpgfarrowreversed
      \pgfarrowssetlineend{\pgfarrowlength\ifpgfarrowharpoon\advance\pgf@x by.5\pgfarrowlinewidth\fi}
    \else
      \pgfarrowssetlineend{\pgfarrowlength\advance\pgf@x by-.5\pgfarrowlinewidth}
    \fi
    % The hull:
    \ifpgfarrowroundjoin
      \pgfarrowshullpoint{\pgfarrowlength\advance\pgf@x by.5\pgfarrowlinewidth}{\ifpgfarrowharpoon-.5\pgfarrowlinewidth\else0pt\fi}%
    \else%
      \ifpgfarrowharpoon
        \pgfarrowshullpoint{\pgfarrowlength\advance\pgf@x by\pgf@xc\advance\pgf@x by\pgf@xa}{-.5\pgfarrowlinewidth}%
      \else
        \pgfarrowshullpoint{\pgfarrowlength\advance\pgf@x by\pgf@xc\advance\pgf@x by\pgf@xa}{0pt}%
      \fi%
    \fi
    \pgfarrowsupperhullpoint{.5\pgfarrowlinewidth}{.5\pgfarrowwidth\advance\pgf@y by.5\pgfarrowlinewidth}%
    \pgfarrowsupperhullpoint{-.5\pgfarrowlinewidth}{.5\pgfarrowwidth\advance\pgf@y by.5\pgfarrowlinewidth}%
    \ifpgfarrowharpoon
      \pgfarrowshullpoint{-.5\pgfarrowlinewidth}{-.5\pgfarrowlinewidth}%
    \fi
    % The following are needed in the code:
    \pgfarrowssavethe\pgfarrowlinewidth
    \pgfarrowssavethe\pgfarrowlength
    \pgfarrowssavethe\pgfarrowwidth
  },
  drawing code = {
    \pgfsetdash{}{+0pt}
    \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi
    \ifpgfarrowroundcap\pgfsetroundcap\else\pgfsetbuttcap\fi
    \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi
    \pgfpathmoveto{\pgfqpoint{0pt}{.5\pgfarrowwidth}}
    \pgfpathlineto{\pgfqpoint{\pgfarrowlength}{0pt}}
    \ifpgfarrowharpoon
      \pgfpathlineto{\pgfqpoint{\pgfarrowlength\advance\pgf@x by\ifpgfarrowreversed\else-\fi\pgfarrowlinewidth}{0pt}}
    \else
      \pgfpathlineto{\pgfqpoint{0pt}{-.5\pgfarrowwidth}}
    \fi
    \pgfusepathqstroke
    %%% <<< begin of change
    % draw two white lines
    \begin{pgfscope}
      % \pgfsetstrokecolor{red}\pgfsetstrokeopacity{0.5} % just for test
      \pgfsetstrokecolor{white}
      \pgfmathsincos{atan2(2\pgfarrowlength,\pgfarrowwidth)}
      \pgfmathreciprocal{\pgfmathresulty}
      \pgf@xa=\pgfmathresult\pgflinewidth
      \pgf@ya=\pgfmathresultx pt
      \pgf@ya=.5\pgf@ya
      \pgf@ya=\dimexpr.5\pgfarrowwidth-\pgf@sys@tonumber\pgf@ya\pgflinewidth+.5\pgflinewidth\relax
      % let w = arrow width, l = arrow length, x = line width, 
      % and tan(.) = w/(2l)
      % top line = (-sin(.)  x/2, w/2 + (1-cos(.)) * x/2) -- +(sin(.) * x/2, 0pt),
      %   where -x/2 < -sin(.) * x/2 < 0
      \pgfpathmoveto{\pgfqpoint{-.5\pgfarrowlinewidth}{\pgf@ya}}
      \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
      \ifpgfarrowharpoon
      \else
        \pgfpathmoveto{\pgfqpoint{-.5\pgfarrowlinewidth}{-\pgf@ya}}
        \pgfpathlineto{\pgfqpoint{\pgf@xa}{-\pgf@ya}}
      \fi
      \pgfusepathqstroke
    \end{pgfscope}
    %%% <<< end of change
  },
  parameters = {
    \the\pgfarrowlinewidth,%
    \the\pgfarrowlength,%
    \the\pgfarrowwidth,%
    \ifpgfarrowharpoon h\fi%
    \ifpgfarrowroundjoin j\fi%
    \ifpgfarrowroundcap c\fi%
  },
}
\makeatother
\tikzset{
  >={TeX Gyre Termes Math[scale=.8]}
}
\tikzcdset{
  arrow style=tikz,
  every arrow/.append style={line width=1.2pt}
}
\usepackage{fontspec}
\usepackage{unicode-math}
\setmainfont{TeX Gyre Termes}[Scale=1.0]
\defaultfontfeatures{Scale=MatchLowercase, Ligatures=TeX}
\setmathfont{TeX Gyre Termes Math}
\begin{document}
\Huge
\begin{equation}    % eq 1
  A \longrightarrow B \rightarrow C
\end{equation}
%
\begin{equation}    % eq 2
  \begin{tikzcd}
    A \arrow[r, "f"] & B
  \end{tikzcd}
\end{equation}
\end{document}