For anyone following this, it turns out I’m a total idiot… Elixir is handling tens of thousands of elements just fine, as I have just discovered with better benchmarking. Even if each element contains a number of totally not optimised polynomials implemented as structs.

It turns out that unlike what I previously reported, the problem is with typst. Problems start to happen when I try to compile typst files of > 20.000 lines with a large number of graphical objects. To be fair to typst, these files are probably much larger than anything anyone has tried to use typst on (I don’t know whether the critical part is the patching or the rendering, but I’m not that interested in finding out).

Because of this, I have decided to keep the core constraint-based architecture the same and drop typst. I’ll be try to use resvg (the rust svg rendering library, which also has Elixir bindings) for text rendering and measuring and to render SVGs into PNGs. I assume that resvg is probably better optimised than typst for rendering larger numbers of shapes.

The only thing I lose is math typesetting, but it turns out plots don’t use that much math typesetting. One can get by with unicode symbols, superscripts, subscripts and not much else.

Quartz (this library is no longer called playfair) can now draw line plots (by very inefficiently drawing line segments individually instead of using a normal path because I haven’t iomplemented paths yet).

Example here:

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Code:

defmodule Quartz.Benchmarks.LinePlot do
  use Dantzig.Polynomial.Operators
  require Quartz.Figure, as: Figure
  alias Quartz.Plot2D
  alias Quartz.Length

  def build_plot() do
    figure =
      Figure.new([width: Length.cm(8), height: Length.cm(6), debug: false], fn _fig ->
        [[bounds]] =
          Figure.bounds_for_plots_in_grid(
            nr_of_rows: 1,
            nr_of_columns: 1,
            padding: Length.pt(16)
          )

      x = for i <- 1..100, do: 0.01 * i
      y = for x_i <- x, do: x_i * 0.3 + (0.05 * :rand.uniform())

      data = %{x: x, y: y}

      _plot =
        Plot2D.new(id: "plot_A")
        |> Plot2D.set_bounds(bounds)
        |> Plot2D.line_plot("x", "y", data)
        # Use typst to explicitly style the title and labels ――――――――――――――――――――――――――――――――
        |> Plot2D.put_title("A. Line plot")
        |> Plot2D.put_axis_label("y", "Prediction: $f(x)$", text: [escape: false])
        |> Plot2D.put_axis_label("x", "Predictor: $x$", text: [escape: false])
        |> Plot2D.finalize()
      end)

    path = Path.join([__DIR__, "line_plot", "example.pdf"])
    Figure.render_to_pdf_file!(figure, path)
  end
end

Some more examples, this time for distribution plots.

KDE smoothing of the posterior distributions for a NUTS bayesian simulation, showing all 4 chains in the same plot:

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The same data plotted using boxplots (boxplots are not very configurable yet, but that is just a question of adding more options):

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Finally, the contour plot I’ve shown before, but with a much higher resolution now that we don’t depend on typst and can use the more performant (for this use case) resvg renderer (note that we can fake powers of integers with superscript unicode characters, although for more advanced things one really needs proper math typesetting):

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And no, Quartz still can’t rotate text, which messes up the case where the labels of the y-axis are longer, but it works fine for these short labels.