Misplaced path using -| or |- with decoration (e.g. snake)

Question

If I draw a path with the -|(horizontal-first-then-vertical) or |- (vertical-first-then-horizontal) commands and decorate the path with the snake-morphing operation, the latter half of the path is misplaced.

Here is an example:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}

\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}
\path[draw=red,  ->]                              (0,0) -| (5,5);
\path[draw=black,->,decorate,decoration={snake}]  (0,0) -| (5,5);
\end{tikzpicture}
\caption{Wrong}
\end{figure}
\begin{figure}
\centering
\begin{tikzpicture}
\path[draw=red,  ->]                              (0,0) -| (5,5);
\path[draw=blue,->,decorate,decoration={snake}]   (5,0) -- (5,5);
\end{tikzpicture}
\caption{Correct}
\end{figure}
\end{document}

In this special case the (black) vertical part has an offset by the same amount as the amplitude of the snake, i.e. the black sine curve is not centered around the red vertical path. The second figure shows how the sine curve is actually expected to look like (cp. blue curve).

The amount of displacement varies with the actual values of the coordinates and it happens to look really ugly in combination with the arrow head, because the arrow remains centered at the correct position.

How do I fix this?

Answer 1

Here is a way to resolve it. It is based on tobias closed zigzag, where neither closed nor zigzag are important. What is, however, important is that the local extrema get shifted in tangent space, see this picture. Result:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}

\begin{document}


\pgfdeclaredecoration{centered zigzag}{initial}{
\state{initial}[
        width=+0pt,
        next state=big down,
        persistent precomputation={
            \pgfmathsetmacro{\myint}{int(\pgfdecoratedinputsegmentlength/\pgfdecorationsegmentlength)}
            \ifodd\myint
             \pgfmathsetmacro\matchinglength{
             \pgfdecoratedinputsegmentlength / int(1+\pgfdecoratedinputsegmentlength/\pgfdecorationsegmentlength)}
            \else
             \pgfmathsetmacro\matchinglength{
             \pgfdecoratedinputsegmentlength / int(\pgfdecoratedinputsegmentlength/\pgfdecorationsegmentlength)}
            \fi
            \setlength{\pgfdecorationsegmentlength}{\matchinglength pt}
            \pgfmathsetmacro{\myint}{int(\pgfdecoratedinputsegmentlength/\pgfdecorationsegmentlength)}
        }] {
        \pgfcoordinate{zigzag-cycle-start}{\pgfqpoint{0pt}{-\pgfdecorationsegmentamplitude}}
        \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
        }
  \state{big down}[switch if less than=+.5\pgfdecorationsegmentlength to center finish,
                   width=+.5\pgfdecorationsegmentlength,
                   next state=big up]
  {
    \pgfpathlineto{\pgfqpoint{0pt}{-\pgfdecorationsegmentamplitude}}
  }
  \state{big up}[switch if less than=+.5\pgfdecorationsegmentlength to center finish,
                 width=+.5\pgfdecorationsegmentlength,
                 next state=big down]
  {
    \pgfpathlineto{\pgfqpoint{0pt}{\pgfdecorationsegmentamplitude}}
  }
  \state{center finish}[width=0pt, next state=final]{
   % this state is unecessary at the moment
  }
  \state{final}
  {
  }
}
\begin{figure}
\centering
\begin{tikzpicture}
\path[draw=red,  ->]                              (0,0) -| (5,5);
\path[draw=blue,->,decorate,rounded corners,decoration={
            centered zigzag,
            segment length=10pt,
            amplitude=2mm
        }] (0,0) -| (5,5);
\end{tikzpicture}
\caption{Centered zigzag with rounded corners.}
\end{figure}
\end{document}