TikZ: Intersection point with a double-line path

Question

When calculating the intersection point(s) between a line and another double-line path, TikZ normally returns the intersection at the middle of the double-line path. The question here is how to get the intersection with the outer line of the path. I believe, we can shift the point by a value .5\pgflinewidth + .5\pgfinnerlinewidth, but I'm using this inside a macro which should check first if the path is double or not, then, it can do the correction. The code currently is like this:

\documentclass[tikz,border=1mm]{standalone}
\usetikzlibrary{intersections}
\begin{document}

\begin{tikzpicture}
\node (rect) [name path=rect,draw,double,ultra thick,double distance=3pt, rounded corners,minimum size=1cm]{};
\draw[name path=line] (rect.center)--(.7,.7);
\path[name intersections={of= rect and line}];
\node at (intersection-1) [circle,fill=blue,inner sep=.5pt]{};
\end{tikzpicture}

\end{document}

I appreciate your advice.

Comment on @Augustin's answer:

This should be a comment, but posting the picture needs editing here. The answer of Augustin is only valid for the case of the line slope being 45 degrees, which is rarely the case. Try, for example,

...
\draw[name path=line,draw] (rect.center)--(.7,.1);
..

you get the following result:

I appreciate the trial, but I need a general solution. More importantly, I mentioned in my question that I can shift the point. What I need to accomplish is how to check if the path is double and how to get the keys for its innerlinewidth, total linewidth, ... etc (all the information you have is the path itself), to be able to do the correct shifting.

Answer 1

You can use the calc TikZ package to do the job:

\documentclass[tikz,border=1mm]{standalone}
\usetikzlibrary{intersections,calc}
\begin{document}

\begin{tikzpicture}
\def \borderSep {3pt} % Define the border separation as a constant
\node (rect) [name path=rect,draw,double,ultra thick,double distance=\borderSep, rounded   corners,minimum size=1cm]{};
\draw[name path=line,draw] (rect.center)--(.7,.7);
\path[name intersections = {of=rect and line, by={a}}];
% Offset the nodes by sqrt(2) * separation
\node at ($(a) + 1/1.41*(\borderSep,\borderSep)$) [circle,fill=blue,inner sep=.5pt]{};
\node at ($(a) - 1/1.41*(\borderSep,\borderSep)$) [circle,fill=blue,inner sep=.5pt]{};
\end{tikzpicture}

\end{document}

This is what you get:

Edit: More general solution:

\documentclass[tikz,border=1mm]{standalone}
\usetikzlibrary{intersections,calc}
\begin{document}

\begin{tikzpicture}
% If the rect has single border, set borderSep and borderThickness to 0pt
\def \borderSep {3pt}
\def \borderThickness {1.5pt}
\node (rect) [name path=rect,draw,double,ultra thick,double distance=\borderSep,rounded corners,minimum size=1cm]{};
\draw[name path=line,draw] (rect.center)--(.7,.1);

% Construct invisible rectangles at the positions of the borders
\node (rect) [name path=rectIn, rounded corners=6pt, minimum size=1cm+\borderSep+\borderThickness]{};
\node (rect) [name path=rectOut, rounded corners=2pt, minimum size=1cm-\borderSep-\borderThickness]{};

\path[name intersections = {of=rectIn and line, by={intIn}}];
\path[name intersections = {of=rectOut and line, by={intOut}}];
\node at (intIn) [circle,fill=blue,inner sep=.5pt]{};
\node at (intOut) [circle,fill=blue,inner sep=.5pt]{};
\end{tikzpicture}

\end{document}

Now this works even in the general case. Note that if you want more fine-grained control you need to edit (e.g. using a global variable) the radii of the rectIn's and rectOut's rounded corners.

Answer 2

Here is a mathematical way that uses \dimexpr where needed to be unit-independed (works with pt, or cm or whatever).

It works only for line (added with \myline command but it can take parameters as a real tikz line). The line can start from any point and stop to any other, but had to intersects with double path.

Also the distance of double path parts has to be defined in \DoubleDist variable. The code I suppose can be more general and work for ultra thick (but haven't yet include such parameter and I don't know if can be added without one more definition of new parameter).

Finally, the shape (circle) on the intersections is better to be chosen from the user but I was tired to do this too. (Anyone who can understand the code can do it himself I suppose).

Code:

\documentclass[tikz,border=1mm]{standalone}
\usetikzlibrary{intersections}
\usetikzlibrary{calc}
\begin{document}

\def\DoubleDist{4.1 pt}


%\Usage \myline(x1,y1)(x2,y2)[parameters]=\draw[parameters] (x1,y1)--(x2,y2); +keep needed numbers
\makeatletter
\def\myline{\@ifnextchar({\readFirstOPoint}{\node at (0,0){Error in line 1};}}
\def\readFirstOPoint(#1,#2){
\gdef\lineXStart{#1}
\gdef\lineYStart{#2}
\@ifnextchar(
{\readSecondPoint}
{\node at (0,0){Error in line 2};}
}
\def\readSecondPoint(#1,#2){
\gdef\lineXStop{#1}
\gdef\lineYStop{#2}
\readParametersAndDraw
}
\def\readParametersAndDraw
{\@ifnextchar[{\Storeparam}{\gdef\LineParam{\empty}\ExecuteLine}}
\def\Storeparam[#1]
{
\gdef\LineParam{[#1]}
\ExecuteLine
}
\def\ExecuteLine
{
\draw\LineParam (\lineXStart,\lineYStart)--(\lineXStop,\lineYStop);
}
\makeatother


% Will be used to shift the point
\newlength{\xsh}
\newlength{\ysh}

% Finding double path intersections. Usage \FindIndersections(path)
\makeatletter
\def\FindIndersections{
\@ifnextchar({\ReadIndersection}{\node at (0,0){Error in readind indersection}}
}
\def\ReadIndersection(#1){
\pgfmathsetmacro\XShiftFactor{(\lineXStop-\lineXStart)/sqrt((\lineXStart-\lineXStop)^2+(\lineYStart-\lineYStop)^2)}
\pgfmathsetmacro\YShiftFactor{(\lineYStop-\lineYStart)/sqrt((\lineXStart-\lineXStop)^2+(\lineYStart-\lineYStop)^2)}
\setlength{\xsh}{\dimexpr\XShiftFactor\dimexpr\dimexpr\DoubleDist/2\relax+\pgflinewidth\relax\relax}
\setlength{\ysh}{\dimexpr\YShiftFactor\dimexpr\dimexpr\DoubleDist/2\relax+\pgflinewidth\relax\relax}
\draw[fill=blue] ($(#1)-(\the\xsh ,\the\ysh)$) circle (1pt);
\draw[fill=blue] ($(#1)+(\the\xsh, \the\ysh)$) circle (1pt);
}
\makeatother

\begin{tikzpicture}
\node (rect) [name path=rect,draw,double,double distance=\DoubleDist, rounded corners,minimum size=30 pt]{};
\myline(0.2,0)(0.8,0.3)[brown,name path=line]
\path[name intersections={of= rect and line}];
\FindIndersections(intersection-1)
\end{tikzpicture}

\end{document}

Output:

With some complicated shapes as a cloud the intersection does not find the real middle and so my way fails too:

code:

\begin{tikzpicture}
\node (rect) [name path=rect,draw,draw, cloud,,double,double distance=\DoubleDist,minimum size=1.3 cm]{};
\myline(0.2,0)(-0.7,-0.4)[brown,name path=line]
\path[name intersections={of= rect and line}];
\draw[fill=red] (intersection-1) circle (1pt);
\FindIndersections(intersection-1)
\end{tikzpicture} 

(with tikzlibrary shapes).

Result:

Answer 3

\documentclass[tikz,border=1mm]{standalone}
\usetikzlibrary{intersections,fit}
\begin{document}

\begin{tikzpicture}
\node (rect) [name path=rect,draw,double,ultra thick,double distance=3pt, rounded corners,minimum size=1cm]{};
\draw[name path=line] (rect.center)--(.7,.7);
\path[name intersections={of= rect and line}];
\node at (intersection-1) [circle,fill=blue,inner sep=.5pt]{};
\end{tikzpicture}

\begin{tikzpicture}
\node (inner-rect) [name path=inner-rect,draw,ultra thick,
minimum size=1cm-4.5pt,inner sep=0pt,rounded corners=1.5pt]{};
\node (outer-rect) [name path=outer-rect,draw,ultra thick,
minimum size=1cm+4.5pt,inner sep=0pt,rounded corners=4.5pt]{};
\foreach \X [count=\Y] in {45,90,210,-45}
{\draw[name path=line-\Y] (inner-rect.center)--(\X:0.8);
\path[name intersections={of=inner-rect and line-\Y}]
node at (intersection-1) [circle,fill=blue,inner sep=.5pt]{};
\path[name intersections={of=outer-rect and line-\Y}]
node at (intersection-1) [circle,fill=red,inner sep=.5pt]{};}
\end{tikzpicture}
\end{document}