[Tex/LaTex] Parallel arrows between nodes of varying size

tikz-pgf

I am using this solution to the question TikZ parallel Edges between Nodes to draw figures with parallel arrows next to edges.

Minimal working example

\documentclass[tikz]{standalone}

\usetikzlibrary{calc}

\tikzset{
  % store of parameters
  parallel distance/.store in=\paradist,
  parallel shorten/.store in=\parashorten,
  parallel label distance/.store in=\paralabdist,
  % default values
  parallel distance=1mm, % distance of parallel arrows from link
  parallel shorten=0mm, % to shorten parallel arrows
  parallel label distance=2.5mm, % distance of label from link
  % main style
  edge with values/.style args={#1 and #2}{
    to path={
      \pgfextra{
        \pgfinterruptpath
        % middle point
        \coordinate (m) at ($(\tikztostart)!.5!(\tikztotarget)$);
        % from-to arrow
        \draw[-stealth,shorten >=\parashorten,shorten <=\parashorten]
        ($(\tikztostart)!\paradist!-90:(\tikztotarget)$)
        --
        ($(\tikztotarget)!\paradist!90:(\tikztostart)$)
        % middle of from-to arrow
        coordinate[pos=.5](m from);
        % label of from-to arrow
        \node[font=\tiny] at ($(m)!\paralabdist!(m from)$){#1};
        % to-from arrow
        \draw[-stealth,shorten >=\parashorten,shorten <=\parashorten]
        ($(\tikztotarget)!\paradist!-90:(\tikztostart)$)
        --
        ($(\tikztostart)!\paradist!90:(\tikztotarget)$)
        % middle of to-from arrow
        coordinate[pos=.5](m to);
        % label of to-from arrow
        \node[font=\tiny] at ($(m)!\paralabdist!(m to)$){#2};
        \endpgfinterruptpath
      }
         (\tikztostart) -- (\tikztotarget)
    },
  },
}

\begin{document}
\begin{tikzpicture}
    %the decorating arrows start at the center of the nodes
    \draw node[draw] (a) {large node}
        ++(3,0) node[draw] (b) {other node}
        edge[edge with values=a and b] (a);
    %if node sizes are about equal, it can be fixed by shortening both ends
    \draw (0,-1) node[draw] (a2) {large node}
        ++(3,0) node[draw] (b2) {other node}
        edge[parallel shorten=1cm,edge with values=a and b] (a2);
    %if the error is asymmetric this won't work
    \draw (0,-2) node[draw] (a3) {large node}
        ++(3,0) node[draw] (b3) {n}
        edge[parallel shorten=1cm,edge with values=a and b] (a3);
\end{tikzpicture}
\end{document}

This produces the following output:

Problem description

The problem is that the decorating arrows begin at the center of the nodes, and not at the border. I could manually fix this by specifying both shorten > and shorten < for each edge, but this would be cumbersome.

I am looking for a solution that draws the decorating arrows at correct spots.

Note that letting the edges start/end at specified anchors is not an option, since I am using diagonal edges, too.

My analysis

The problem appears to be caused by the fact that within to path, the macros \tikztostart and \tikztotarget resolve to either the nodes (?) or the center of the nodes. If you use them asis, tikz's smart handling works and the line you draw starts at the border of the node.
This happens in the final (\tikztostart) -- (\tikztotarget).

But as soon as, e.g., \tikztostart is wrapped in a calculation ($(\tikztostart)$), the path begins at the node center and not on the border of the node.

If there was a way to get the "smart" endpoints of the path within to path, then the problem could easily be solved.

Of course I'm also open to another equivalent solution.

I'm aware of Connect Tikz nodes via two parallel arrows, but this is not applicable, since I also require styling the two arrows differently (different colors). So I'm looking for code that really draws two additional arrows parallel to an edge, like the one above.

Example of my application using my answer below

Best Answer

I found out a way of getting the coordinates on the border of the involved shapes by using

\pgfmathanglebetweenpoints{\pgfpointanchor{\tikztostart}{center}}{\pgfpointanchor{\tikztotarget}{center}}

Now shorten is not necessary anymore to get a good result.

Full working solution

\documentclass[tikz]{standalone}

\usetikzlibrary{calc}

\tikzset{
  % store of parameters
  parallel distance/.store in=\paradist,
  parallel shorten/.store in=\parashorten,
  parallel label distance/.store in=\paralabdist,
  % default values
  parallel distance=1mm, % distance of parallel arrows from link
  parallel shorten=0mm, % to shorten parallel arrows
  parallel label distance=2.5mm, % distance of label from link
  % main style
  edge with values/.style args={#1 and #2}{
    to path={
      \pgfextra{
        \pgfinterruptpath
        \pgfmathanglebetweenpoints{\pgfpointanchor{\tikztostart}{center}}{\pgfpointanchor{\tikztotarget}{center}}
        \coordinate (start) at (\tikztostart.\pgfmathresult);
        \pgfmathanglebetweenpoints{\pgfpointanchor{\tikztotarget}{center}}{\pgfpointanchor{\tikztostart}{center}}
        \coordinate (target) at (\tikztotarget.\pgfmathresult);
        % middle point
        \coordinate (m) at ($(start)!.5!(target)$);
        % from-to arrow
        \draw[-stealth,shorten >=\parashorten,shorten <=\parashorten]
        ($(start)!\paradist!-90:(target)$)
        --
        ($(target)!\paradist!90:(start)$)
        % middle of from-to arrow
        coordinate[pos=.5](m from);
        % label of from-to arrow
        \node[font=\tiny] at ($(m)!\paralabdist!(m from)$){#1};
        % to-from arrow
        \draw[-stealth,shorten >=\parashorten,shorten <=\parashorten]
        ($(target)!\paradist!-90:(start)$)
        --
        ($(start)!\paradist!90:(target)$)
        % middle of to-from arrow
        coordinate[pos=.5](m to);
        % label of to-from arrow
        \node[font=\tiny] at ($(m)!\paralabdist!(m to)$){#2};
        \endpgfinterruptpath
      }
         (\tikztostart) -- (\tikztotarget)
    },
  },
}

\begin{document}
\begin{tikzpicture}
    %the decorating arrows start at the center of the nodes
    \draw node[draw] (a) {large node}
        ++(3,0) node[draw] (b) {other node}
        edge[edge with values=a and b] (a);
    %if node sizes are about equal, it can be fixed by shortening both ends
    \draw (0,-1) node[draw] (a2) {large node}
        ++(3,0) node[draw] (b2) {other node}
        edge[edge with values=a and b] (a2);
    %if the error is asymmetric this won't work
    \draw (0,-2) node[draw] (a3) {large node}
        ++(3,0) node[draw] (b3) {n}
        edge[edge with values=a and b] (a3);
\end{tikzpicture}
\end{document}

Related Solutions

[Tex/LaTex] How to draw labeled parallel arrows in commutative diagram with TikZ

Here are your labeled lines.

There are other ways to shift nodes but IMO the transform canvas is the most direct, so you are doing fine for that aspect.

To label a line, you can add a node command at the end of the line specification. The label may be placed above or below and you can specify where along the line with keywords such as midway or the more general pos=<fraction along line>. I also shifted the diagonal lines so that they may both be seen (since one was dashed).

I added a macro to simplify the shifting of the diagonal lines.

\documentclass[border=5pt]{standalone}

\usepackage{amsmath,amssymb}

\usepackage{tikz}
\usetikzlibrary{calc}


\begin{document}

\begin{tikzpicture}[node distance=2.8cm, auto]

\pgfmathsetmacro{\shift}{0.3ex}

\node (P) {$\mathfrak{P}=\bigoplus_{i\in I}\mathfrak{P_{i}}$};
\node(Q)[right of=P] {$\mathfrak{P_{j}}$};
\node (B) [below of=P] {$\mathfrak{B}$};
\node (C) [right of=B] {$\mathfrak{C}$};

\draw[transform canvas={yshift=0.5ex},->] (P) --(Q) node[above,midway] {\tiny top};
\draw[transform canvas={yshift=-0.5ex},->](Q) -- (P) node[below,midway] {\tiny bottom}; 
\draw[->](Q) to node {$a$}(C);
\draw[->] (P) to node[swap] {$\pi_{j}$} (B);
\draw[->,dashed] (B) to node {$\psi$} (C);

\draw[->,transform canvas={xshift=-\shift,yshift=\shift}](Q) to node {$a$}(B);
\draw[->, dashed,transform canvas={xshift=\shift,yshift=-\shift}] (Q) to node[swap] {$g$} (B);

\end{tikzpicture}

\end{document}

enter image description here

[Tex/LaTex] Natural transformation arrow with TikZ

As percusse mentions in his comment, the tikz-cd package offers you a convenient set of macros to draw commutative diagrams; here's a little example:

\documentclass{article} 
\usepackage{tikz-cd}

\begin{document}

\begin{tikzcd}[column sep=huge]
\textbf{CRing}
  \arrow[bend left=50]{r}[name=U,label=above:$\scriptstyle\mathrm{GL}_n$]{}
  \arrow[bend right=50]{r}[name=D,label=below:$\scriptstyle U$]{} &
\textbf{Grp}
  \arrow[shorten <=10pt,shorten >=10pt,Rightarrow,to path={(U) -- node[label=right:$\det$] {} (D)}]{}
\end{tikzcd}

\end{document}

enter image description here

Since originally the question asked for a TikZ solution using a matrix of nodes, here's a "pure" TikZ possible solution:

\documentclass{article} 
\usepackage{tikz}
\usetikzlibrary{matrix,arrows}

\begin{document}

\begin{tikzpicture}
\matrix[matrix of nodes,column sep=2cm] (cd)
{
   \textbf{CRing} & \textbf{Grp} \\
};
\draw[->] (cd-1-1) to[bend left=50] node[label=above:$\scriptstyle\mathrm{GL}_n$] (U) {} (cd-1-2);
\draw[->] (cd-1-1) to[bend right=50,name=D] node[label=below:$\scriptstyle U$] (V) {} (cd-1-2);
\draw[double,double equal sign distance,-implies,shorten >=10pt,shorten <=10pt] 
  (U) -- node[label=right:$\det$] {} (V);
\end{tikzpicture}

\end{document}

enter image description here

An answer to the edit to the original question, showing two possibilities (a curved double arrow, and a straight one):

\documentclass{article} 
\usepackage{tikz}
\usetikzlibrary{matrix,arrows}

\begin{document}

\begin{tikzpicture}[description/.style={fill=white,inner sep=2pt}]
    \matrix (m) [matrix of math nodes, row sep=3em,
    column sep=2.0em, text height=1.5ex, text depth=0.25ex]
    { \mathcal{D} & & \mathcal{J} \\
      \mathcal{C} & & \\ };
    \path[->,font=\scriptsize]
    (m-1-1) edge[loop left] node[auto] (fg) {$ F \circ G $} (m-1-1)
    (m-1-1.20) edge node[auto] {$ G $} (m-1-3.160)
    (m-1-3.200) edge node[auto] {$ F $} (m-1-1.340)
    (m-1-1) edge node[left] (h) {$ H $} (m-2-1);
    \draw[double,double equal sign distance,-implies] (fg.290) -- (h.150);    
\end{tikzpicture}

\begin{tikzpicture}[description/.style={fill=white,inner sep=2pt}]
    \matrix (m) [matrix of math nodes, row sep=3em,
    column sep=2.0em, text height=1.5ex, text depth=0.25ex]
    { \mathcal{D} & & \mathcal{J} \\
      \mathcal{C} & & \\ };
    \path[->,font=\scriptsize]
    (m-1-1) edge[loop left] node[auto] (fg) {$ F \circ G $} (m-1-1)
    (m-1-1.20) edge node[auto] {$ G $} (m-1-3.160)
    (m-1-3.200) edge node[auto] {$ F $} (m-1-1.340)
    (m-1-1) edge node[left] (h) {$ H $} (m-2-1);
    \draw[double,double equal sign distance,-implies] (fg.290) to[out=-90,in=180] (h.180);    
\end{tikzpicture}

\end{document}

enter image description here

And here's the corresponding code using tikz-cd:

\documentclass{article} 
\usepackage{tikz-cd}

\begin{document}

\begin{tikzcd}[column sep=huge,row sep=huge]
\mathcal{D}
  \arrow[loop left]{}[name=fg]{F \circ G}
  \rar[start anchor=30, end anchor=151]{G}
  \arrow{d}[name=h,swap]{H} & 
\mathcal{J}\lar[start anchor=196, end anchor=-14]{F} \\
\mathcal{C}
\arrow[shorten >=4pt,Rightarrow,to path={(fg.290) -- (h.175)}]{}
\end{tikzcd}

\begin{tikzcd}[column sep=huge,row sep=huge]
\mathcal{D}
  \arrow[loop left]{}[name=fg]{F \circ G}
  \rar[start anchor=30, end anchor=151]{G}
  \arrow{d}[swap,name=h]{H} & 
\mathcal{J}\lar[start anchor=196, end anchor=-14]{F} \\
\mathcal{C}
\arrow[shorten >=3pt,Rightarrow,to path={(fg.290) to[out=-90,in=180] (h)}]{}
\end{tikzcd}

\end{document}

enter image description here

To add a label to the double arrow (as requested in a comment), you can use an additional node; here's an example using both approaches (the first one using tikz-cd and the second one using "pure" TikZ):

\documentclass{article} 
\usepackage{tikz-cd}
\usepackage{tikz}
\usetikzlibrary{matrix,arrows}

\begin{document}

\begin{tikzcd}[column sep=huge,row sep=huge]
\mathcal{D}
  \arrow[loop left]{}[name=fg]{F \circ G}
  \rar[start anchor=30, end anchor=151]{G}
  \arrow{d}[swap,name=h]{H} & 
\mathcal{J}\lar[start anchor=196, end anchor=-14]{F} \\
\mathcal{C}
\arrow[shorten >=1pt,Rightarrow,to path={(fg.290) to[out=-90,in=180] node[xshift=-3.5mm] {$\tau$} (h)}]{}
\end{tikzcd}

\begin{tikzpicture}[description/.style={fill=white,inner sep=2pt}]
    \matrix (m) [matrix of math nodes, row sep=3em,
    column sep=2.0em, text height=1.5ex, text depth=0.25ex]
    { \mathcal{D} & & \mathcal{J} \\
      \mathcal{C} & & \\ };
    \path[->,font=\scriptsize]
    (m-1-1) edge[loop left] node[auto] (fg) {$ F \circ G $} (m-1-1)
    (m-1-1.20) edge node[auto] {$ G $} (m-1-3.160)
    (m-1-3.200) edge node[auto] {$ F $} (m-1-1.340)
    (m-1-1) edge node[left] (h) {$ H $} (m-2-1);
    \draw[double,double equal sign distance,-implies] (fg.290) to[out=-90,in=180] node[xshift=-3.5mm] {$\tau$} (h.180);    
\end{tikzpicture}

\end{document}

enter image description here

Minimal working example

Problem description

My analysis

Example of my application using my answer below

Best Answer

Full working solution

Related Solutions

[Tex/LaTex] How to draw labeled parallel arrows in commutative diagram with TikZ

[Tex/LaTex] Natural transformation arrow with TikZ

Related Question