Unidad de coordenadas en pt aunque por defecto es cm en TikZ

Question

Como sabemos, en TikZ, si la unidad no se menciona en las coordenadas en TikZ, se toma cmde forma predeterminada.

Cuando extraje las coordenadas, esperaba que la unidad fuera cm. Pero TikZ muestra la unidad en la coordenada como pt.

¿Cómo determina TikZ la unidad de medida en una coordenada si no se especifica ninguna unidad?

MWE:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{calc}
\usetikzlibrary{positioning}
\tikzset{zigzag/.style={decorate,decoration=zigzag}}
\begin{document}

\newdimen\XCoord
\newdimen\YCoord
\newcommand*{\ExtractCoordinate}[1]{\path (#1); \pgfgetlastxy{\XCoord}{\YCoord};}

\begin{tikzpicture}
  \coordinate (c) at (0,-2);
  \coordinate (d) at (4,-2);
  \coordinate (e) at (2,-4);
  \draw[thick,red,zigzag,postaction={
    decoration={
        markings,
        mark=at position 0.7 with { \coordinate (x); },
        mark=at position 0.5 with { \coordinate (singularity); },
    },
    decorate
  }] (-2,0) coordinate(a) -- (2,0) coordinate(b);

  \draw[thick,fill=blue!20] (c) -- (b) -- (d) -- (e) -- cycle;
  \draw[thick,postaction={
    decoration={
        markings,
        mark = at position 0.7 with \coordinate (y);
    },
    decorate
  }] (a) -- (c);
  \draw[thick,red,dashed] (x) -- (y);

  \node[above = 10ex of singularity,red] (sn) {singularity};
  \draw[red,->] (sn) -- ($(singularity)+(0,1)$);
  \ExtractCoordinate{x};
  \node[above] at (\XCoord,\YCoord) {(\XCoord,\YCoord)};
\end{tikzpicture}

\end{document} 

Answer 1

Siempre puedes convertir todo, desde pt a cm o viceversa, multiplicando por la proporción 1pt/1cmo su inversa. (Si eso no es lo que buscas, estaré encantado de eliminar la publicación).

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{calc}
\usetikzlibrary{positioning}
\tikzset{zigzag/.style={decorate,decoration=zigzag}}
\begin{document}

\newdimen\XCoord
\newdimen\YCoord
\newcommand*{\ExtractCoordinate}[1]{\path (#1); \pgfgetlastxy{\XCoord}{\YCoord};}

\begin{tikzpicture}
  \coordinate (c) at (0,-2);
  \coordinate (d) at (4,-2);
  \coordinate (e) at (2,-4);
  \draw[thick,red,zigzag,postaction={
    decoration={
        markings,
        mark=at position 0.7 with { \coordinate (x); },
        mark=at position 0.5 with { \coordinate (singularity); },
    },
    decorate
  }] (-2,0) coordinate(a) -- (2,0) coordinate(b);

  \draw[thick,fill=blue!20] (c) -- (b) -- (d) -- (e) -- cycle;
  \draw[thick,postaction={
    decoration={
        markings,
        mark = at position 0.7 with \coordinate (y);
    },
    decorate
  }] (a) -- (c);
  \draw[thick,red,dashed] (x) -- (y);

  \node[above = 10ex of singularity,red] (sn) {singularity};
  \draw[red,->] (sn) -- ($(singularity)+(0,1)$);
  \ExtractCoordinate{x};
  \node[above] at (\XCoord,\YCoord) {%
  (\pgfmathparse{\XCoord*1pt/1cm}\pgfmathprintnumber{\pgfmathresult}\,cm,%
  \pgfmathparse{\YCoord*1pt/1cm}\pgfmathprintnumber[fixed,precision=2]{\pgfmathresult}\,cm)};
\end{tikzpicture}
\end{document}