[Tex/LaTex] Curved Arrows in Tikz

tikz-arrowstikz-pgf

I am new in Tikz and have searched but not found what I am looking for (which should be a particularly simple).

I have a commutative diagram in which I am illustrating diagram chasing. I would like a curved arrow from B to C' but I need it to go around the outside of the diagram, curving around B'. Similarly, I need a curved arrow from B to C' but curving around C. I have been unable to move the arrows outside of inside of the diagram. What is the simple way of specifying this?

Moreover, is there a general way of telling Tikz how to add curves to your arrows, i.e. if I wanted to do the same thing as above but then make the arrow 'wavy' the whole way from B to C' or specify an arbitrary path of curved and loops from one node to the next?

\[
\begin{tikzpicture}
\matrix (m) [matrix of math nodes, row sep=3em,
column sep=3em, text height=1.5ex, text depth=0.25ex]
{ B & C  \\
B' & C' \\ };
\path[->]
(m-1-1) edge node[above] {$g$} (m-1-2)
         edge node[left] {$\beta$} (m-2-1)
         edge [bend left=30] (m-2-2)
         edge [bend right=15] (m-2-2);
\path[->]
(m-1-2) edge node[right] {$\gamma$} (m-2-2);
\path[->]
(m-2-1)  edge node[below] {$g'$} (m-2-2);
\end{tikzpicture}
\]

Best Answer

This is a possible solution, use of looseness=xx and bend left=xx, For the wavy line and arrow, here a style called snake it is defined,

enter image description here

Code

\usepackage[margin=1in]{geometry}
\usepackage{amsmath}% http://ctan.org/pkg/stackrel
\usepackage{tikz,siunitx}
\usetikzlibrary{matrix,positioning,calc}
\usetikzlibrary{decorations.pathmorphing}
\tikzset{snake it/.style={-stealth,
decoration={snake, 
    amplitude = .4mm,
    segment length = 2mm,
    post length=0.9mm},decorate}}
\begin{document}

\[
\begin{tikzpicture}
\matrix (m) [matrix of nodes, row sep=3em,
column sep=3em, text height=1.5ex, text depth=0.25ex]
{ B & C  \\
$B'$ & $C'$ \\ };
\path[->]
(m-1-1) edge node[above] {$g$} (m-1-2)
         edge node[left] {$\beta$} (m-2-1)
         edge [bend left=90,looseness=2,snake it] (m-2-2)
         edge [bend right=90,looseness=2] (m-2-2);
\path[->]
(m-1-2) edge node[right] {$\gamma$} (m-2-2);
\path[->]
(m-2-1)  edge node[below] {$g'$} (m-2-2);
\end{tikzpicture}
\]
\end{document}

Related Solutions

[Tex/LaTex] How to have one straight arrows surrounded by two curved arrows (TikZ)

you can create a node at each end of the lines and then connect these nodes. by adjusting the minimum size of node you can improve aesthetics.

(sorry for my google english)


\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,positioning,fit,petri,calc,shadows}

\begin{document}

\begin{tikzpicture}[
    parent/.style={%
        rounded corners,
        thick,
        draw=red!75,
        fill=red!20,
        thick,
        inner ysep=2pt,
        inner xsep=2pt,
        minimum width = 4cm,
        minimum height = 1.5cm,
        align=center
    },
    child/.style={%
        rounded corners,
        thick,
        draw=blue!90,
        fill=blue!35,
        thick,
        inner ysep=2pt,
        inner xsep=2pt,
        minimum width = 4cm,
        minimum height = 1.5cm,
        align=center
    },
    grandchild/.style={%
        rounded corners,
        thick,
        draw=green!90,
        fill=green!35,
        thick,
        inner ysep=2pt,
        inner xsep=2pt,
        minimum width = 4cm,
        minimum height = 1.5cm,
        align=center
    },
    line/.style={%
        semithick,
        ->,
        shorten >=1pt,
        >=stealth'
    },
    call/.style={%
        blue,
        semithick,
        ->,
        shorten >=1pt,
        >=stealth'
    },
    return/.style={%
        red,
        semithick,
        ->,
        shorten >=1pt,
        >=stealth'
    }]
    \node[child] (child) {Child};
    \node[parent] at (-6,3) (parent 1) {Node 1\\I have manually\\connected this one};
    \node[parent] at (0,3) (parent 2) {Node 2\\I have manually\\connected this one};
    \node[parent] at (6,3) (parent 3) {Node 3\\I have manually\\connected this one};
    \node[parent] at (-6,-3) (grandchild 1) {Node 4\\I have manually\\connected this one};
    \node[parent] at (0,-3) (grandchild 2) {Node 5\\I have NOT manually\\connacted this one};
    \node[parent] at (6,-3) (grandchild 3) {Node 6\\I have NOT manually\\connacted this one};

    %draw three lines from each parent to each child
    \draw [line] (parent 1.south east)node[above left](p1){} -- (child.north west)node[below right](c1){};
    \draw [line] (parent 2.south)node[above](p2){} -- (child.north)node[below](c2){};
    \draw [line] (parent 3.south west)node[above right](p3){} -- (child.north east) node[below left](c3){};

    %draw three lines from each parent to each child
    \draw [line] (grandchild 1.north east)node[below left,minimum size=2em](p4){} -- (child.south west)node[above right,minimum size=2em](c4){};
    \draw [line] (grandchild 2.north)node[below,minimum size=2em](p5){} -- (child.south)node[above,minimum size=2em](c5){};
    \draw [line] (grandchild 3.north west)node[below right](p6){} -- (child.south east)node[above left](c6){};


\foreach \nn in{1,2,3,4,5,6}{
    \draw [call] (p\nn) to [bend right=15] (c\nn);
    \draw [return] (c\nn) to [bend right=15] (p\nn);
    }

\end{tikzpicture}

\end{document}!

the result

[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

Best Answer

Related Solutions

[Tex/LaTex] How to have one straight arrows surrounded by two curved arrows (TikZ)

[Tex/LaTex] Natural transformation arrow with TikZ

Related Question