Crossing paths in TikZ without intersection

Question

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

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}

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}

Answer 1

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

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.

Answer 2

I was going to say that this is just what the knots TikZ library is for, except that in testing it then I found that it didn't cope well with rounded corners. Fortunately, it was a quick fix (which is now on CTAN).

\documentclass[border=5pt]{standalone}
%\url{http://tex.stackexchange.com/q/115923/86}
\usepackage{tikz}
\usetikzlibrary{knots}  

\begin{document}

\begin{tikzpicture} 
\begin{knot}[
  consider self intersections=true,
  flip crossing=1,
]
\strand[rounded corners=10pt,line width=4pt,red]
    (0,2.5) -- (1.5,2.5) -- (1.5,0.5) -- (0.5,0.5)-- (0.5,1.5) -- (3,1.5);
\end{knot}
\draw (0,0) grid[step=1] (3,3);
\end{tikzpicture}
\end{document}

The underlying mechanism is similar to that in Frédéric's answer: to use the double option to draw the overlying line. However, rather than drawing the path in segments what this method does is to redraw the upper part in the vicinity of the intersection. This means that the rest of the path is drawn "whole" and so has no artefacts on the joins.