TikZ: Access coordinates of decorated paths?

Question

Is it possible to access the coordinates of the decoration of some paths? I draw two paths, e.g., with:

   \begin{figure}[t]
     \begin{tikzpicture}
       \draw [red,decorate,decoration={crosses, segment length=1.05cm,
           transform={shift only}}]
             {(4, 4) .. controls(6, 3.5) .. (8, 4)};
       \draw [red,decorate,decoration={crosses, segment length=1.05cm,
           transform={shift only}}]
             {(4, 4) .. controls(6, 4.5) .. (8, 4)};
    \end{tikzpicture}
   \end{figure}

Each of these paths contains some crosses I would like to connect with some arrows. If I could access the coordinates of the crosses, this would be quite simple. Is this somehow possible?

Answer 1

Here's one way to do it which works by modifying the crosses decoration to add a labelling to each cross. You have the option to specify the prefix of the labelling and the numerical index increments as the decoration places crosses.

\documentclass{article}
%\url{http://tex.stackexchange.com/q/65557/86}

\usepackage{tikz}
\usetikzlibrary{decorations.shapes}

\makeatletter
% crosses decoration

\pgfkeys{/pgf/decoration/label cross name/.initial=cross}
\newcount\pgf@lblcross@index

\pgfdeclaredecoration{labelled crosses}{init}
{
  \state{init}[width=+0pt,next state=crosses,persistent
precomputation={
  \pgfkeysgetvalue{/pgf/decoration/label cross name}{\pgf@lblcross}
  \global\pgf@lblcross@index=0\relax
    \pgfmathparse{\pgfkeysvalueof{/pgf/decoration/shape start
width}/2}
    \edef\pgf@lib@dec@ssw{\pgfmathresult pt}
    \pgfmathparse{\pgfkeysvalueof{/pgf/decoration/shape start
height}/2}
    \edef\pgf@lib@dec@ssh{\pgfmathresult pt}
  }]{}  
  \state{crosses}[switch if less than=+\pgfdecorationsegmentlength to
last,
                  width=+\pgfdecorationsegmentlength]
  {
    \pgfcoordinate{\pgf@lblcross-\the\pgf@lblcross@index}{\pgfpointorigin}
    \global\advance\pgf@lblcross@index by 1\relax
    \pgfpathmoveto{\pgfqpoint{-\pgf@lib@dec@ssw}{\pgf@lib@dec@ssh}}
    \pgfpathlineto{\pgfqpoint{\pgf@lib@dec@ssw}{-\pgf@lib@dec@ssh}}
    \pgfpathmoveto{\pgfqpoint{-\pgf@lib@dec@ssw}{-\pgf@lib@dec@ssh}}
    \pgfpathlineto{\pgfqpoint{\pgf@lib@dec@ssw}{\pgf@lib@dec@ssh}}
  }
  \state{last}[width=+\pgfdecoratedremainingdistance]
  {
    \pgfcoordinate{\pgf@lblcross-\the\pgf@lblcross@index}{\pgfpointorigin}
    \global\advance\pgf@lblcross@index by 1\relax
    \pgfpathmoveto{\pgfqpoint{-\pgf@lib@dec@ssw}{\pgf@lib@dec@ssh}}
    \pgfpathlineto{\pgfqpoint{\pgf@lib@dec@ssw}{-\pgf@lib@dec@ssh}}
    \pgfpathmoveto{\pgfqpoint{-\pgf@lib@dec@ssw}{-\pgf@lib@dec@ssh}}
    \pgfpathlineto{\pgfqpoint{\pgf@lib@dec@ssw}{\pgf@lib@dec@ssh}}
  }
  \state{final}{
    \pgfpathmoveto{\pgfpointdecoratedpathlast}
  }
}

\makeatother

\begin{document}
\begin{tikzpicture}
       \draw [postaction={draw=red,decorate},decoration={labelled
crosses, label cross name=A, segment length=1.05cm,
           transform={shift only}}]
             {(4, 4) .. controls(6, 3.5) .. (8, 4)};
       \draw [postaction={draw=red,decorate},decoration={labelled
crosses, label cross name=B, segment length=1.05cm,
           transform={shift only}}]
             {(4, 4) .. controls(6, 4.5) .. (8, 4)};
             \draw[->,green,dashed] (A-1) to[bend right] (B-2);
             \draw[->,green,dashed] (A-3) to[bend left] (B-3);
    \end{tikzpicture}
\end{document}

This produces:

(Actually, it doesn't but only because after generating the real picture I decided that it was too small to see what was going on so I scaled it up, but I couldn't be bothered to change the code above.)