Converting equations to images

Question

I am looking to convert LaTeX equations to images in the pdf output. After searching around here I've found some sources to websites and software that can convert individual equations to images, but it would be really nice if I could run such a converter on an entire tex file and have it convert the equations to images automatically. It's tedious to manually convert every equation only to plug them back into the document as an image.

\subsection{Linear equation through a point given its gradient}
A very simple differential equation is to find a linear equation through a particular point $P(x_i,y_i)$ given its gradient $k_i$ (or more commonly used for lines, its slope).
\begin{equation}
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C
\end{equation}
Plug in the initial conditions to find the particular value of the constant of integration $C$.

Here's the default output where equations contain selectable text (in Acrobat Reader):

But I was wondering if it was possible to output a pdf where the equations are converted to images like this (in Acrobat Reader):

Note: Initially, I had asked a different question but then I decided to reword it significantly. As a result, the comments and answer aren't actually relevant to that older question anymore. I decided to re-post the revised version as a new question.

Answer 1

One possibility is to put each equation inside a tikzpicture and then use tikzexternalize to automatically convert each equation to png and include that png, similar to tikz external use png as default instead of pdf. The implementation below requires that you replace \begin{equation}\end{equation} with the new command \pngequation.

This needs to be compiled with -shell-escape. Note that the compiler to create the images is hardcoded, in this case pdflatex, which can be modified if you want another compiler.

Note that this is only a proof on concept. It is rather roundabout, very likely has limitations, problems and/or side effects, and is therefore not recommended - for most use cases there will be easier solutions as mentioned in the comments.

MWE:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{external}
\tikzexternalize
\tikzset{%
    % Add size information to the .dpth file (png is in density not size)
    /pgf/images/external info,
    % Use the png export AND the import
    use png/.style={png export,png import},
    png export/.style={
        external/system call=%
        {pdflatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource";%
         convert -density 300 -transparent white "\image.pdf" "\image.png"; rm -f "\image.pdf"},
    },
    png import/.code={%
        \tikzset{%
            /pgf/images/include external/.code={%
                % Here you can alter to whatever you want
                % \pgfexternalwidth is only available if /pgf/images/external info
                % is set
                \includegraphics%
                [width=\pgfexternalwidth,height=\pgfexternalheight]%
                {{##1}.png}%
            }%
        }%
    }%
}
\newcounter{pngeq}
\setcounter{pngeq}{0}
\newcommand{\pngequation}[1]{%
\tikzset{use png}
\begin{tikzpicture}
\node (eq) {
\hspace{-1.1\parindent}\begin{minipage}{\textwidth}%
\setcounter{equation}{\number\value{pngeq}}
\begin{equation}
#1
\end{equation}
\end{minipage}
};
\end{tikzpicture}%
\stepcounter{pngeq}
}
\begin{document}
\section{Linear equation through a point given its gradient}
A very simple differential equation is to find a linear equation through a particular point $P(x_i,y_i)$ given its gradient $k_i$ (or more commonly used for lines, its slope).
\pngequation{
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C
}
Plug in the initial conditions to find the particular value of the constant of integration $C$.
\pngequation{
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C'
}
\end{document}

Result:

---

For subequations you can extend the solution above along the same lines. First add an extra subequation counter that resets with the main counter:

\newcounter{pngsubeq}[pngeq]

Then define a command \pngsubequation that steps this counter and uses it in the numbering.

\newcommand{\pngsubequation}[1]{%
\tikzset{use png}
\ifnum\value{pngsubeq}=0\stepcounter{pngeq}\fi% first subequation, step main counter
\stepcounter{pngsubeq}
\begin{tikzpicture}
\node (eq) {
\hspace{-1.1\parindent}\begin{minipage}{\textwidth}%
\renewcommand{\theequation}{\arabic{pngeq}\alph{pngsubeq}}
\begin{equation}
#1
\end{equation}
\end{minipage}
};
\end{tikzpicture}%
}

To step the main counter for the subequations a hook can be added to the subequations environment:

\BeforeBeginEnvironment{subequations}{\stepcounter{pngeq}}

Then you can use \begin{subequations} with \pngsubeqation inside:

\begin{subequations}
\pngsubequation{...}
\pngsubequation{...}
\end{subequations}

Full code, with a feq sets of normal equations and subequations:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{external}
\tikzexternalize
\tikzset{%
    % Add size information to the .dpth file (png is in density not size)
    /pgf/images/external info,
    % Use the png export AND the import
    use png/.style={png export,png import},
    png export/.style={
        external/system call=%
        {pdflatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource";%
         convert -density 300 -transparent white "\image.pdf" "\image.png"; rm -f "\image.pdf"},
    },
    png import/.code={%
        \tikzset{%
            /pgf/images/include external/.code={%
                % Here you can alter to whatever you want
                % \pgfexternalwidth is only available if /pgf/images/external info
                % is set
                \includegraphics%
                [width=\pgfexternalwidth,height=\pgfexternalheight]%
                {{##1}.png}%
            }%
        }%
    }%
}
\newcounter{pngeq}
\setcounter{pngeq}{0}
\newcounter{pngsubeq}[pngeq]
\newcommand{\pngequation}[1]{%
\tikzset{use png}
\stepcounter{pngeq}
\begin{tikzpicture}
\node (eq) {
\hspace{-1.1\parindent}\begin{minipage}{\textwidth}%
\renewcommand{\theequation}{\arabic{pngeq}}
\begin{equation}
#1
\end{equation}
\end{minipage}
};
\end{tikzpicture}%
}
\BeforeBeginEnvironment{subequations}{\stepcounter{pngeq}}
\newcommand{\pngsubequation}[1]{%
\tikzset{use png}
\stepcounter{pngsubeq}
\begin{tikzpicture}
\node (eq) {
\hspace{-1.1\parindent}\begin{minipage}{\textwidth}%
\renewcommand{\theequation}{\arabic{pngeq}\alph{pngsubeq}}
\begin{equation}
#1
\end{equation}
\end{minipage}
};
\end{tikzpicture}%
}
\begin{document}
\section{Linear equation through a point given its gradient}
A very simple differential equation is to find a linear equation through a particular point $P(x_i,y_i)$ given its gradient $k_i$.
\pngequation{
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C
}
Plug in the initial conditions to find the particular value of the constant of integration $C$.
\pngequation{
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C'
}
A very simple differential equation is to find a linear equation through a particular point $P(x_i,y_i)$ given its gradient $k_i$.
\begin{subequations}
\pngsubequation{
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C
}
Plug in the initial conditions to find the particular value of the constant of integration $C$.
\pngsubequation{
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C'
}
\end{subequations}
A very simple differential equation is to find a linear equation through a particular point $P(x_i,y_i)$ given its gradient $k_i$.
\pngequation{
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C
}
Plug in the initial conditions to find the particular value of the constant of integration $C$.
\pngequation{
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C'
}
A very simple differential equation is to find a linear equation through a particular point $P(x_i,y_i)$ given its gradient $k_i$.
\begin{subequations}
\pngsubequation{
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C
}
Plug in the initial conditions to find the particular value of the constant of integration $C$.
\pngsubequation{
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C'
}
\end{subequations}
\end{document}
\tikzset{use png}
\begin{tikzpicture}
\node (eq) {
\hspace{-\parindent}\begin{minipage}{\textwidth}%
\begin{equation}
\frac{dy}{dx} = k_i \iff \int dy = \int k_i \cdot dx \iff y = k_i \cdot x + C
\end{equation}
\end{minipage}
};
\end{tikzpicture}

Result: