Position things in the middle between a node and an arrow tip

Question

Say I want to draw something like a flow chart, that is nodes connected by arrows that sometimes merge. This would be a typical pattern:

I used the following code to create this small example:

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning,calc,arrows.meta}

\begin{document}
  \begin{tikzpicture}
    \node[draw] (a) {A};
    \node[draw,right=of a] (b) {B};
    \node[draw,below=5mm of b] (c) {C};

    \path[-{LaTeX[]}] (b) edge (c);
    \draw (a) |- ($(b)!0.5!(c)$);
  \end{tikzpicture}
\end{document}

Now the line from A hits the one between B and C precisely at its middle point. Given the arrow tip, however, this is not the visually most pleasant position. We'd want it to hit the middle point between the end of the arrow tip and B.

Short of tinkering with magic constants, how can we do this using TikZ?

Answer 1

Here's a first pass which adjusts automatically for the current line width but not for the kind of arrow tip. It also requires modification if the direction direction/angle of the path differs or if the arrow points in the opposite direction, for example.

\documentclass[tikz,border=10pt,multi]{standalone}
\usetikzlibrary{positioning,calc,arrows.meta}
\begin{document}
\begin{tikzpicture}
  [
    every node/.append style={draw},
    my adjustment/.store in=\arrowadjust,
    % by default, for this type of arrow tip, length=3pt 4.5 0.8 [ref. p. 185]
    arrow line/.style={%
      draw,
      -{LaTeX[]},
      my adjustment={.5*(3pt + 4.5*\pgflinewidth)}
    },
  ]
  \node (a) {A};
  \node [right=of a] (b) {B};
  \node [below=5mm of b] (c) {C};
  \path [arrow line] (a) |- ([yshift=\arrowadjust]$(b)!0.5!(c)$) (b) -- (c);
\end{tikzpicture}
\end{document}

You can find the values for the arrow(s) you are interested in in the file texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.meta.code.tex:

\pgfdeclarearrow{
  name = Latex,
  defaults = {
    length  = +3pt 4.5 .8,% +2.8pt 3 0.8,
    width' = +0pt .75,
    line width = +0pt 1 1,
  },

(LaTeX is an alias for Latex).