Embedding equation labels inside figures/graphics?

Question

One thing I would really like to do (for the purposes of a thesis) is to embed equation references/tags inside images, so that I can reference the equations outside of the image.

To give you an idea, I would like to achieve something like the following:

However, I would like the equation numbers to be dynamic, that is, to change depending on the other equations in the document in which the graphic is embedded. I used GeoGebra to create this picture, but unfortunately I don't think this supports equation references (even though it is possible to export the picutre in TiKZ format, I think).

I have been told that it is much better practice for my thesis to create diagrams which summarise the equations being solved, but the downside of this is that the referencing is not necessarily straightforward. For example, I would like to be able to refer to the equations inside the graphic, rather than saying "Equation (1) from Figure XX".

Has anyone figured out a way to do this? If so, what strategy did you use?

Answer 1

1. Export to tikz:

The resulting code is an absolute horror. But it does compile to what was displayed (there might be some edge cases).

\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\definecolor{zzttqq}{rgb}{0.6,0.2,0}
\definecolor{qqqqff}{rgb}{0,0,1}
\definecolor{cqcqcq}{rgb}{0.75,0.75,0.75}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\draw [color=cqcqcq,dash pattern=on 1pt off 1pt, xstep=1.0cm,ystep=1.0cm] (0,-10) grid (10,0);
\draw[->,color=black] (0,0) -- (10,0);
\foreach \x in {,1,2,3,4,5,6,7,8,9}
\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};
\draw[->,color=black] (0,-10) -- (0,0);
\foreach \y in {-10,-9,-8,-7,-6,-5,-4,-3,-2,-1}
\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {\footnotesize $\y$};
\draw[color=black] (0pt,-10pt) node[right] {\footnotesize $0$};
\clip(0,-10) rectangle (10,0);
\fill[line width=1.2pt,color=zzttqq,fill=zzttqq,fill opacity=0.1] (9.2,-2.18) -- (2.56,-2.12) -- (5.08,-5.16) -- cycle;
\draw [line width=1.2pt,color=zzttqq] (9.2,-2.18)-- (2.56,-2.12);
\draw [line width=1.2pt,color=zzttqq] (2.56,-2.12)-- (5.08,-5.16);
\draw [line width=1.2pt,color=zzttqq] (5.08,-5.16)-- (9.2,-2.18);
\begin{scriptsize}
\fill [color=qqqqff] (9.2,-2.18) circle (1.5pt);
\draw[color=qqqqff] (9.36,-1.92) node {$A$};
\fill [color=qqqqff] (2.56,-2.12) circle (1.5pt);
\draw[color=qqqqff] (2.72,-1.86) node {$B$};
\fill [color=qqqqff] (5.08,-5.16) circle (1.5pt);
\draw[color=qqqqff] (5.24,-4.9) node {$C$};
\draw[color=zzttqq] (7.4,-3.78) node {$b$};
\end{scriptsize}
\end{tikzpicture}
\end{document}

2. add a node and the desired equation.

\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
    
    \definecolor{zzttqq}{rgb}{0.6,0.2,0}
    \definecolor{qqqqff}{rgb}{0,0,1}
    \definecolor{cqcqcq}{rgb}{0.75,0.75,0.75}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
    \draw [color=cqcqcq,dash pattern=on 1pt off 1pt, xstep=1.0cm,ystep=1.0cm] (0,-10) grid (10,0);
    \draw[->,color=black] (0,0) -- (10,0);
    \foreach \x in {,1,2,3,4,5,6,7,8,9}
    \draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};
    \draw[->,color=black] (0,-10) -- (0,0);
    \foreach \y in {-10,-9,-8,-7,-6,-5,-4,-3,-2,-1}
    \draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {\footnotesize $\y$};
    \draw[color=black] (0pt,-10pt) node[right] {\footnotesize $0$};
    \clip(0,-10) rectangle (10,0);
    \fill[line width=1.2pt,color=zzttqq,fill=zzttqq,fill opacity=0.1] (9.2,-2.18) -- (2.56,-2.12) -- (5.08,-5.16) -- cycle;
    \draw [line width=1.2pt,color=zzttqq] (9.2,-2.18)-- (2.56,-2.12);
    \draw [line width=1.2pt,color=zzttqq] (2.56,-2.12)-- (5.08,-5.16);
    \draw [line width=1.2pt,color=zzttqq] (5.08,-5.16)-- (9.2,-2.18);
    \begin{scriptsize}
    \fill [color=qqqqff] (9.2,-2.18) circle (1.5pt);
    \draw[color=qqqqff] (9.36,-1.92) node {$A$};
    \fill [color=qqqqff] (2.56,-2.12) circle (1.5pt);
    \draw[color=qqqqff] (2.72,-1.86) node {$B$};
    \fill [color=qqqqff] (5.08,-5.16) circle (1.5pt);
    \draw[color=qqqqff] (5.24,-4.9) node {$C$};
    \draw[color=zzttqq] (7.4,-3.78) node {$b$};
    \end{scriptsize}
    
    % adding some reference to some equation
    \node at (8,-5){Applying equation \ref{eq-2}};
\end{tikzpicture}
    
    According to the right Pythagorean theorem:
\begin{equation}\label{eq-1}
    a^2 + b^2 = c^2
\end{equation}
    
According to the wrong Pythagorean theorem:
    \begin{equation}\label{eq-2}
    a + b = c
\end{equation}
\end{document}

Result:

EDIT:

Request: write the equation but don't display it, yet keep it referenced.

Answer: use the textpos package and wrap your equation in a textblock environment:

%\usepackage{textpos} <--- in the preambule
According to the wrong Pythagorean theorem:
\begin{textblock}{width}(X_offset, Y_offset)
\begin{equation}\label{eq-2}
    a + b = c
\end{equation}
\end{textblock}

You can use (X_offset, Y_offset) to "yeet" the equation out of the paper, for e.g. (10,10).

Result:

The equation can't be found in the pdf, but it is written in the LaTeX source.

Answer 2

I am a bit confused about the other answer but going on

embed equation references/tags inside images, so that I can reference the equations outside of the image

Yes, this is possible but not that straight forward.

The numbered displaymath environments need a line width which is easily achieved in TikZ by setting a text width but you need to choose a sensible text width on your own. This will also place the equation number inside the node.

I've added a node with aligned in the example below where \tagoutside produces another column where the equation number is set left-aligned (as in your picture but not as with amsmath usually).

The \rlap and the measurements inside it make sure that the equation number is actually outside the node but this has the side effect that the equation numbers are also outside of the bounding box of the TikZ picture.

There probably is a more sophisticated solution with a tikzmark approach but for simple equations (and a simple rectangular node) this might be enough.

Code

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{shadows}
\makeatletter
\newcommand*\tagoutside[1]{
  &\kern-\alignsep@
    \rlap{% no math content → no mathrlap necessary
      \pgfmathsetlength\pgfutil@tempdima
        {\pgfkeysvalueof{/pgf/inner xsep}+(\pgfkeysvalueof{/pgf/outer xsep})}%
      \kern\pgfutil@tempdima
      \refstepcounter{equation}\label{#1}%
      \quad\tagform@\theequation
    }%
}
\makeatother

\begin{document}
Some formulas:
\begin{align}
    c^2 &= a^2 + b^2 \label{tri} \\
    E   &= mc^2      \label{albert}
\end{align}

Now a tikzpicture (inside a float):
\begin{figure}
\centering
\begin{tikzpicture}
\node[text width=3cm, draw, drop shadow, fill=white] {
  \vspace{-\topskip}
  \begin{align}
    c^2 &= a^2 + b^2 \label{tikz-tri} \\
    E   &= mc^2      \label{tikz-albert}
  \end{align}
};
\node[draw, drop shadow, fill=white] at (4,0) {$
  \begin{aligned}
    c^2 &= a^2 + b^2 \tagoutside{tikzed-tri} \\
    E   &= mc^2      \tagoutside{tikzed-albert}
  \end{aligned}$};
\end{tikzpicture}
\end{figure}

Now another set of formulas:
\begin{align}
    c^2 &= a^2 + b^2 \label{tri*} \\
    E   &= mc^2      \label{albert*}
\end{align}

Equations
\eqref{tri}        \eqref{albert}
\eqref{tikz-tri}   \eqref{tikz-albert}
\eqref{tikzed-tri} \eqref{tikzed-albert}
\eqref{tri*}       \eqref{albert*}
\end{document}

Output