[Tex/LaTex] Crossing paths in TikZ without intersection

intersectionspgf-decorationstikz-pgf

Once again, I'm preparing a new logic puzzle; Resuko to be precise.

enter image description here

For the race track, I would like to have a symbolized bridge/underbridge -|-. I searched this site, but only found this question: Intersection of 2 lines not really connected in TikZ

The answers there seem to indicate that there is no automatic solution for full paths. I'm quite sure, i have seen this, but maybe with PSTricks. Any ideas?

Edit:

Unfortunately, Frédéric's solution does not work after integration into logicpuzzle.sty. Some path construction must be supported, like trackpath in the following MWE:

\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}  
\makeatletter
\tikzstyle{bridge path}=[rounded corners=10pt,decorate,decoration={show path construction,
lineto code={
    \draw [white,line width = 4pt,double=red,double distance=4pt]
            (\tikzinputsegmentfirst) -- (\tikzinputsegmentlast);},
curveto code={
      \draw [red,line width = 4pt] (\tikzinputsegmentfirst) .. controls
        (\tikzinputsegmentsupporta) and (\tikzinputsegmentsupportb)
        ..(\tikzinputsegmentlast);
            }}]  
\newcommand*\trackpath[3]%
{%
  (#1.5,#2.5)%
  \foreach \LP@direction in {#3}%
  {%
    \ifnum\LP@direction=1%
    --++(-1,-1)%
    \fi%
    \ifnum\LP@direction=2%
    --++(0,-1)%
    \fi%
    \ifnum\LP@direction=3%
    --++(1,-1)%
    \fi%
    \ifnum\LP@direction=4%
    --++(-1,0)%
    \fi%
    \ifnum\LP@direction=6%
    --++(1,0)%
    \fi%
    \ifnum\LP@direction=7%
    --++(-1,1)%
    \fi%
    \ifnum\LP@direction=8%
    --++(0,1)%
    \fi%
    \ifnum\LP@direction=9%
    --++(1,1)%
    \fi%
  };%
}%
%
\newcommand*\track[1]{
  \draw[bridge path] #1;
}
\makeatother
\begin{document}
\begin{tikzpicture} 
\track{\trackpath{0}{2}{6,2,2,4,8,6,6}}
\draw (0,0) grid[step=1] (3,3);
\end{tikzpicture}
\end{document}

MWE

Then, the decoration doesn't work any longer. 🙁 It works with a TikZ path, \trackpath seems to trigger the problem.

Any idea what's going wrong?

Edit2:

With Frédéric's idea to change the way how the path is constructed, we have a final solution:

\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}  
\makeatletter
\tikzstyle{bridge path}=[rounded corners=10pt,decorate,decoration={show path construction,
lineto code={
    \draw [white,line width = 4pt,double=red,double distance=4pt]
            (\tikzinputsegmentfirst) -- (\tikzinputsegmentlast);},
curveto code={
      \draw [red,line width = 4pt] (\tikzinputsegmentfirst) .. controls
        (\tikzinputsegmentsupporta) and (\tikzinputsegmentsupportb)
        ..(\tikzinputsegmentlast);
            }}]  
\newcommand*\trackpath[3]%
{%
  (#1.5,#2.5)%
  \foreach \LP@dir/\LP@length in {#3}%
  {%
    \ifnum\LP@dir=2%
    --++(0,-\LP@length)%
    \fi%
    \ifnum\LP@dir=4%
    --++(-\LP@length,0)%
    \fi%
    \ifnum\LP@dir=6%
    --++(\LP@length,0)%
    \fi%
    \ifnum\LP@dir=8%
    --++(0,\LP@length)%
    \fi%
  };%
}%
%
\newcommand*\track[1]{
  \draw[bridge path] #1;
}
\makeatother
\begin{document}
\begin{tikzpicture} 
\track{\trackpath{0}{2}{6/1,2/2,4/1,8/1,6/2}}
\draw (0,0) grid[step=1] (3,3);
\end{tikzpicture}
\end{document}

enter image description here

Best Answer

The basic idea is to use a double line, with a white border. The problem is the default way tikz draws this is to draw the path completely a first time (the white border) and then completely a second time. The way around this is to use a decoration, more specifically the "show path construction" decoration. This decorates the path piecewise.

The code is 

\documentclass[border=5pt]{standalone}

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

\tikzstyle{bridge path}=[rounded corners=10pt,decorate,decoration={show path construction,
lineto code={
    \draw [white,line width = 4pt,double=red,double distance=4pt]
            (\tikzinputsegmentfirst) -- (\tikzinputsegmentlast);},
curveto code={
      \draw [red,line width = 4pt] (\tikzinputsegmentfirst) .. controls
        (\tikzinputsegmentsupporta) and (\tikzinputsegmentsupportb)
        ..(\tikzinputsegmentlast);
            }}]  

\begin{document}

\begin{tikzpicture} 

\draw[bridge path] 
    (0,2.5) -- (1.5,2.5) -- (1.5,0.5) -- (0.5,0.5)-- (0.5,1.5) -- (3,1.5);

\draw (0,0) grid[step=1] (3,3);

\end{tikzpicture}


\end{document}

The result is

enter image description here

Comment on Josef's comment that the code does not survive the integration into his style. From what I can tell, the problem occurs when one of the coordinates of the specified path is also one of the intersection points. I don't know why this occurs. As a quick fix, I would change the way the path is specified in Josef's edit: I would not say move left/right/up/down, but rather the give the coordinates of where the path curves (the corners). Maybe Andrew's code works better.

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