Half circle node

Question

Some time ago I wanted to create a half-circle node and I used the solution below. However, this solution has one drawback that if you fill the node, the whole circle is filled, not only a half. Is it possible to make sure that only half of the node that is drawn is filled?

MWE:

\documentclass{minimal}
\usepackage{tikz}

\begin{document}

\makeatletter
\tikzset{arc style/.initial={}}
\pgfdeclareshape{half circle}{
  \inheritsavedanchors[from=circle]
  \inheritanchorborder[from=circle]

  \inheritanchor[from=circle]{center}
  \inheritanchor[from=circle]{south}
  \inheritanchor[from=circle]{west}
  \inheritanchor[from=circle]{north}
  \inheritanchor[from=circle]{east}

  \inheritbackgroundpath[from=circle]

  \beforebackgroundpath{
    \pgfkeys{/tikz/arc style/.get=\tmp}
    \expandafter\tikzset\expandafter{\tmp}
    \tikz@options

    \radius \pgf@xa=\pgf@x
    \centerpoint \pgf@xb=\pgf@x \pgf@yb=\pgf@y

    \advance\pgf@xb by \pgf@xa
    \pgfpathmoveto{\pgfpoint{\pgf@xb}{\pgf@yb}}
    \pgfpatharc{0}{-180}{\pgf@xa}

    \pgfusepath{draw}
  }
}
\makeatother

\begin{tikzpicture}

\fill[fill=black!10] (0,0) rectangle (6,4);
\node[half circle,inner sep=9pt] (a) at (2,2) {};
\node[half circle,inner sep=9pt,fill=white] (b) at (4,2) {};

\end{tikzpicture}

\end{document}

Answer 1

(Summing up comments.) While this doesn't answer the question of what is wrong with your node shape definition, you are re-inventing the wheel a bit, as the shapes.geometric library already defines a semicircle shape.

The default orientation of that shape is with the arc on top, but you can turn it the other way with shape border rotate=180. And the default anchor is center, which is in the interior of the half circle. To use the midpoint of the diameter as anchor, set anchor=chord center.

\documentclass[border=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\tikzset{
  half circle/.style={
      semicircle,
      shape border rotate=180,
      anchor=chord center,
      minimum size=5mm
      }
}
\begin{document}
\begin{tikzpicture}
    \node [half circle, draw=blue, fill=red] at (1,1) {};
    \fill (1,1) circle[radius=1pt];
\end{tikzpicture}
\end{document}