The Shape of Code

Ever since I discovered that it’s sometimes possible to extract the x/y values of the points/circles/diamonds appearing in a graph, within a pdf, I have been trying to automate the process.

Within a pdf there are two ways of encoding an image, such as the one below. The information can be specified using a graphics image format (e.g., jpeg, png, or svg), or it can be specified using a sequence of pdf’s internal virtual machine instructions.

After spotting an interesting graph containing data points, when reading a paper, the quickest way to find out whether the image is embedded in the pdf as an image file (the most common case) is to run pdfcpu (using the options extract -m image). If the graph is not contained in the image files extracted by pdfcpu, it may have been created using internal pdf commands (or be a format not yet support by pdfcpu).

Until recently, finding the sequence of internal pdf instructions used to visualise a particular graph was a tedious process. A few months ago, I discovered the tool pdfsyntax, which has an option to convert the pdf internals into a html page containing links between the various components (making it easy to go to a particular page and view the contents). However, pdfsyntax is still new, i.e., it regularly fails to convert a pdf file.

As distributed, pdf files are compressed. They can be converted to readable form using the command qpdf –stream-data=uncompress (images remain in their respective binary format). To locate the instructions that generate a graph, I search for a sequence of 3-4 characters appearing close to the graph in the displayed text (it is difficult to predict how words will be split for layout purposes, within a pdf). The instructions that generate the graph may appear later in the uncompressed file, with a named reference to these instructions appearing around this text (i.e., a pdf function call). LLM’s are great at describing the behavior of sequences of pdf instructions.

Why not grep uncompressed pdf files to find those containing the instructions used to generate graphs?

Surprisingly, apps that produce pdf files use a myriad of different instruction sequences to draw circles, diamonds, pluses, etc. While there is a pdf instruction to draw a circle, the most common technique uses four Bézier curves to draw each quadrant of a circle; a colored circle might be drawn by filling a specified area with a chosen color. The plus (+) symbol is sometimes drawn as a vertical line followed by a horizontal line (or the other order), and sometimes all the vertical lines are drawn followed by all the horizontal lines. Diamonds are created using four angled lines.

Fewer combinations of instructions are used to draw the values associated with the axis ticks, e.g., 10, 20, 30, etc.

The output from my script that searches pdf files for possible extractable data lists the line numbers of possible data points and possible tick labels, along with the totals for each. A graph will usually contain many points and 10+ labels. Lower totals usually suggest incidental matches.

If an appropriate instruction sequence is found, it is copied to a file, and a bespoke awk script (usually an edited version of a previous script) extracts the numeric values within the reference frame of the graph axis bounds. This extraction process first calculates the x/y coordinates of the center of the circle/diamond/plus, in the pdf frame, then calculates the x/y coordinates of the axis tick marks, in the pdf frame, then maps the x/y data points to the axis frame.

I’m not expecting the extraction of numeric values to have any degree of automation anytime soon. But then, this problem would make a great challenge for LLM coding apps…

When a graph is specified using an image format, WebPlotDigitizer is the extraction tool of choice.