Add another level of compass anchors to standard TikZ nodes with TikZ 3.0

Question

I am new to StackExchange and I cannot ask for clarification in the comments, so I had to open a new question for this. I am interested how the accepted answer to Add more anchors to standard TikZ nodes with TikZ 3.0 works.

The answer provided code for additional compass anchors towards the west (north north west, west north west, west south west, south south west). I was able to add equivalent anchors on the east side. Now I would like to add another level of anchors on the compass (e.g. between north north west and west, north north west and north west, or west north west and north west).

Unfortunately, I do not understand how the code in the accepted answer of the original question works and I cannot find an explanation, so I find myself unable to deduct the correct code required to get another level of compass anchors.

Answer 1

From bottom to top,

• \pgf@x and \pgf@y are dimension registers internally used by pgf.
• \pgf@xa and \pgf@ya are dimension registers for pgf developers/users to store dimensions temporarily.
• \pgf@process{<code>} executes <code> in a scope \begingroup ... \endgroup and then updates \pgf@x and \pgf@y to their values globally. So normally <code> assigns new values to \pgf@x and \pgf@y, and keeps any other changes locally.
• \anchor{<name>}{<code>} defines a new node anchor at position \pgf@x and \pgf@y, in which \pgf@x and \pgf@y are set by <code>.

Each of the above commands/registers is documented in pgfmanual.

Using the introduction to commands/registers, let's understand how north north west works.

  \anchor{north north west}{%
    \pgf@process{\southwest}%  % \pgf@x = x_sw, \pgf@y = y_sw
    \pgf@xa=1.5\pgf@x%         % \pgf@x = x_sw, \pgf@y = y_sw, \pgf@xa = 1.5x_sw
    \pgf@process{\northeast}%  % \pgf@x = x_ne, \pgf@y = y_ne, \pgf@xa = 1.5x_sw
    \pgf@x.5\pgf@x%            % \pgf@x = .5x_ne, \pgf@y = y_ne, \pgf@xa = 1.5x_sw
    \advance\pgf@x by \pgf@xa% % \pgf@x = .5x_ne+1.5x_sw, \pgf@y = y_ne, \pgf@xa = 1.5x_sw
    \pgf@x=.5\pgf@x%           % \pgf@x = .25x_ne+.75x_sw, \pgf@y = y_ne, \pgf@xa = 1.5x_sw
  }%                           % return \pgf@x, \pgf@y

So basically north north west assigns

x = 1/4 * x_ne + 3/4 * x_sw
y =       y_ne

A new anchor at the midpoint of north west and north north west will have coordiates

x = 1/8 * x_ne + 7/8 * x_sw
y =       y_ne

So it can be defined by

  \anchor{1 north 7/8 west}{%
    \pgf@process{\southwest}%
    \pgf@xa=3.5\pgf@x%
    \pgf@process{\northeast}%
    \pgf@x.5\pgf@x%
    \advance\pgf@x by \pgf@xa%
    \pgf@x=.25\pgf@x%
  }%

---

Alternatively, you can use coordinate calculations to emulate these anchors:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[nodes={circle, draw, inner sep=2pt, fill}]
  \draw[local bounding box=a] (0, 0) rectangle (5, 3);
\draw
    node at (a.north) {}
    node at (a.north west) {}
    node[blue] at ($(a.north west)!0.5!(a.north)$) {}
    node[red]  at ($(a.north west)!0.25!(a.north)$) {};
\end{tikzpicture}
\end{document}