How to configure TikZ's angle radius option (of the angles library) so its default unit of measure conforms to the TikZ picture in which it is used?

Question

I fail to understand what the default unit of measure is for TikZ's angle radius option of the angles TikZ library. By "default unit of measure" I mean the one used when no unit is specified explicitly. For example, under "normal" circumstances TikZ will process the instruction \draw (0,0) -- (2,1); by drawing a rectangle 2cm in length and 1cm in height, because \draw's default unit of measure is 1cm, so when no unit is specified explicitly, the cm unit is used. This is true in general in TikZ, however the following LaTeX code demonstrates that this is not the case as far as the angle radius option is concerned.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{angles}
\begin{document}
\begin{tikzpicture}
   \coordinate (a) at (1,0);
   \coordinate (b) at (0,0);
   \coordinate (c) at (0,1);

   \draw (a) -- (b) -- (c);

   \draw pic [draw, angle radius = 1cm] {angle=a--b--c};

   \coordinate (d) at (3,0);
   \coordinate (e) at (2,0);
   \coordinate (f) at (2,1);

   \draw (d) -- (e) -- (f);

   \draw pic [draw, angle radius = 1] {angle=d--e--f};
\end{tikzpicture}
\end{document}

This produces (in Overleaf, using the 2022 LuaLatex engine)

For the left hand figure explicit units were specified, but for the right hand figure the units were not specified explicitly.

Why is the right hand figure different to the left hand one? Why wasn't cm taken as the default unit, as is the norm in TikZ pictures? Is this a bug in TikZ? How is it possible to configure TikZ in such a way that the angle radius option will use as its default unit of measure whatever unit is used by the TikZ picture in which the angle radius option occurs?

---

EDIT: I have opened a ticket about this issue in the PGF/TikZ bug tracker.

Answer 1

As noted in the comments already, 1 as unitless value passed to angle radius will be interpreted by the library as 1pt.

This is actually an interesting find, because the modern notation for circle and arc is very different in that the option radius that can be used for both (and probably looks quite similar to angle radius to the user) does not interpret 1 as 1pt but as 1 * <basic unit> which is 1cm by default. I think this is an unlucky inconsistency which is probably due to the different ways the angles library and the modern notation for circle and arc have developed. I personally think that it should become unified. (Of course, it might not be straght-forward to unify this behaviour, because the x and y base units may differ resulting in elliptical arcs, which is probably not wanted for the angles library. So somehow one would have to decide whether to use the x or the y base unit, or to accept that the arc for the angle pic can be elliptical.)

Anyways, you can extract the length of the basic x and y units easily unsing \pgfpointxy{1}{1} \pgfgetlastxy{\baseunitx}{\baseunity} for further use:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{angles}

\begin{document}
\begin{tikzpicture}
    \coordinate (a) at (1,0);
    \coordinate (b) at (0,0);
    \coordinate (c) at (0,1);
    
    \draw (a) -- (b) -- (c);
    
    \draw pic [draw, angle radius = 1cm] {angle=a--b--c};
    
    \coordinate (d) at (3,0);
    \coordinate (e) at (2,0);
    \coordinate (f) at (2,1);
    
    \draw (d) -- (e) -- (f);

    \pgfpointxy{1}{1}
    \pgfgetlastxy{\baseunitx}{\baseunity}

    \draw pic [draw, angle radius = {1 * \baseunitx}] {angle=d--e--f};
\end{tikzpicture}
\end{document}