Is there a way to draw the rest of a path by mirroring the existing part?

Question

Here is a simple path, which has a symmetry:

\begin{document}
\begin{tikzpicture}
\draw[thick] (0,0) -- ++(-9,0) -- ++(5,3) -- ++(2,7) -- ++(2,0);

\draw[green,thick] (0,10) -- ++(2,0) -- ++(2,-7) -- ++(5,-3) -- ++(-9,0);
\end{tikzpicture}
\end{document}

Now instead of drawing the green part manually, would it be possible to just say -- mirror cycle or similar and draw it automatically? I know there are ways as explained in Can we mirror a part in tikz ("axial symmetry", "reflection")? but there the path is not continous and it requires an extra environment, where the path is copied, so there is no reduction in maintanence, when the path changes.

Answer 1

It can be done with spath3

\documentclass[tikz, border=1cm]{standalone}
\usetikzlibrary{spath3}
\begin{document}
\begin{tikzpicture}
\path[spath/save=apath] (0, 0) -- ++(-9, 0) -- ++(5, 3) -- ++(2, 7) -- ++(2, 0);
\draw[thick, fill=green, spath/use=apath] [spath/transform={apath}{xscale=-1}, spath/use={apath, reverse, move, weld}] -- cycle;
\end{tikzpicture}
\end{document}

Answer 2

The mirror axis is at x = 0, thus a simple macro with the sign as parameter is a simple solution. Because of the color change, a continuous solution is not possible anyway:

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
  \draw[thick]
    (0, 0) -- ++(-9, 0) -- ++(5, 3) -- ++(2, 7) -- ++(2, 0)
  ;
  \draw[green, thick]
    (0, 10) -- ++(2, 0) -- ++(2, -7) -- ++(5, -3) -- ++(-9, 0)
  ;
\end{tikzpicture}
\end{document}

A continuous solution is more complicate. For example, the mirrored points can be calculated and stored in a list in reverse order:

\documentclass[tikz]{standalone}

\newdimen\myX

\makeatletter
\newcommand*{\myInit}[1]{%
  #1%
  \pgfextra{%
    \global\myX\pgf@x
    \global\let\myList\@empty
  }%
}
\newcommand*{\myNext}[1]{%
  -- #1%
  \pgfextra{%
    \xdef\myList{%
      --(\the\dimexpr2\myX-\pgf@x\relax,\the\pgf@y)%
      \myList
    }%
  }%
}
\makeatother

\begin{document}
\begin{tikzpicture}
  \draw[thick, fill=lightgray]
    \myInit{(0, 0)}
    \myNext{++(-9, 0)}
    \myNext{++(5, 3)}
    \myNext{++(2, 7)}
    \myList
    -- cycle
  ;
\end{tikzpicture}
\end{document}

Answer 3

To illustrate handy path operations in Asymptote: reverse, xscale, etc.

// copy to http://asymptote.ualberta.ca/ and click Run
unitsize(1cm);
path Lpath=(0,0)--(-9,0)--(-4,3)--(-2,10)--(0,10);   // the left path
path Rpath=xscale(-1)*Lpath;                         // the right path is symmetric with the left to axis x=0   
path mypath=Lpath--reverse(Rpath)--cycle;            // the whole (closed) path
fill(mypath,lightgreen);                            // filling the whole path
draw(Lpath,red+2pt);                                // draw the left path    
draw(Rpath,blue+2pt);                               // draw the right path

shipout(bbox(5mm,invisible));                       // make the boundary bigger

Update A more appropriate for the whole path is using & connector, as suggested by @NguyenVanChi1998

path mypath=Lpath & reverse(Rpath) & cycle;