Length of curve in TikZ

Question

Is it possible to compute the length of a generic curve in TikZ?

An answer to this question would solve TikZ dashes and closed curves as follows: Let lc be the length of the curve and lp the desired length of the dash pattern. All we have to do is rescale the dash pattern to the length lc/round(lc/lp).

Answer 1

Improved version:

You can use a decoration and \pgfdecoratedpathlength:

The code:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\makeatletter
\tikzset{%
    measureme/.style={
    decoration={
        markings,
        mark=at position 1 with {\node[below,black,anchor=west] {My length is \pgfdecoratedpathlength};},
    },
    postaction=decorate
}
}
\makeatother
\begin{document}

\begin{tikzpicture}[line width=2pt]
\coordinate (A); 
\coordinate (B) at (20pt,0);
\draw[cyan,measureme] (A) -- (B);
\begin{scope}[yshift=-1cm]
\coordinate (A); 
\coordinate (B) at (20pt,0);
\draw[cyan,measureme] (A) arc[start angle=180,end angle=0,radius=10pt];
\end{scope}
\begin{scope}[yshift=-2.5cm]
\coordinate (A); 
\coordinate (B) at (20pt,0);
\draw[cyan,measureme] (A) .. controls(0.25,2) and (0.75,-2) .. (B);
\end{scope}
\begin{scope}[yshift=-5cm]
\coordinate (A); 
\coordinate (B) at (20pt,0);
\draw[cyan,measureme] (A) .. controls(0.25,7) and (0.75,-7) .. (B);
\end{scope}
\end{tikzpicture}

\end{document}

Initial version:

Here's an option using decorations and the distance from start key:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\makeatletter
\tikzset{%
    measureme/.style={
    decoration={
        markings,
        mark=at position -.01pt with {%
            \pgfkeysgetvalue{/pgf/decoration/mark info/distance from start}\@totallength
            \global\let\@totallength\@totallength
        },
        mark=at position 0 with {\node[black] {\@totallength};},
    },
    postaction=decorate
}
}
\makeatother
\begin{document}

\begin{tikzpicture}
\coordinate (A); 
\coordinate (B) at (20pt,0);
\draw[cyan,measureme] (A) -- (B);
\begin{scope}[xshift=3cm]
\coordinate (A); 
\coordinate (B) at (20pt,0);
\draw[cyan,measureme] (A) .. controls(0.25,2) and (0.75,-2) .. (B);
\end{scope}
\begin{scope}[xshift=6cm]
\coordinate (A); 
\coordinate (B) at (20pt,0);
\draw[cyan,measureme] (A) .. controls(0.25,7) and (0.75,-7) .. (B);
\end{scope}
\end{tikzpicture}

\end{document}