[Tex/LaTex] How to draw path of contour integral enclosing imaginary axis

decorationsnodestikz-pgf

I have practically no experience with Tikz but was able to piece together this diagram of a contour integral enclosing the imaginary axis.

It was produced with this code.

\documentclass[tikz,svgnames]{standalone}

\usepackage{mathtools}
\DeclareMathOperator{\im}{Im}
\DeclareMathOperator{\re}{Re}


\begin{document}
\begin{tikzpicture}[thick]
    % Axes:
    \draw [->] (-5,0) -- (5,0) node [above left]  {$\re(p_0)$};
    \draw [->] (0,-4.7) -- (0,4.7) node [below left = -1pt] {$\im(p_0)$};

    % Axes labels:
    \foreach \n in {-4,...,-1,1,2,...,4}{%
        \draw[fill] (0,\n) circle (1pt) node [right] {$i \omega_{_{\n}}$};
    }
    \draw[fill] (0,0) circle (1pt) node [above right] {0};

    % Contour line
    \draw[DarkBlue]
      (1,-4) -> (1,4) node [below right] {$C$} arc (0:180:1) (-1,4) -- (-1,-4) arc (180:360:1);

    \draw[fill] (3,2) circle (1pt) node [pin={above:poles of $h(p_0)$}] {};
    \draw[fill] (2,-2) circle (1pt) node [pin={above right:poles of $h(p_0)$}] {};

\end{tikzpicture}
\end{document}

There are a few things I'm still struggling with.

I would like the two half arcs at the top and bottom to be dashed but the vertical lines connecting them to remain solid.
The two pins labelling dots outside the contour with poles of h(p0) should be just one pin with lines pointing to both dots.
I'd like Im(p0) to be further removed from the imaginary axis but connected by a thin line just like the pins.
The contour should be decorated by a few arrows pointing in the counterclockwise direction.

Best Answer

Like this?

\documentclass[tikz,svgnames,border=3mm]{standalone}
\usetikzlibrary{decorations.markings, positioning}
\usepackage{mathtools}
\DeclareMathOperator{\im}{Im}
\DeclareMathOperator{\re}{Re}

\begin{document}
\begin{tikzpicture}[thick,
decoration={
markings,% switch on markings
mark=at position .75 with {\arrow{>}}}
                    ]
    % Axes:
    \draw [->] (-5,0) -- (5,0) node [above left]  {$\re(p_0)$};
    \draw [->] (0,-4.7) -- (0,4.7) node [below left = -1pt and 11mm] {$\im(p_0)$};

    % Axes labels:
    \foreach \n in {-4,...,-1,1,2,...,4}{%
        \draw[fill] (0,\n) circle (1pt) node [right] {$i \omega_{_{\n}}$};
    }
    \draw[fill] (0,0) circle (1pt) node [above right] {0};

% Contour line
\draw[DarkBlue,postaction={decorate}]   ( 1,-4) -- ( 1, 4) node [below right] {$C$};
\draw[DarkBlue,postaction={decorate}]   (-1, 4) -- (-1,-4);
\draw[DarkBlue,dashed]                  (1,4) arc (0:180:1) (-1,4)  (-1,-4) arc (180:360:1);

\draw[fill] (3, 2) circle (1pt) node[below right=2mm and 9mm] (h0) {poles of $h(p_0)$} 
            (2,-2) circle (1pt);
\draw[thin, shorten >=1mm] (h0.west) --  (3,2) (h0.south west) -- (2,-2);
\end{tikzpicture}
\end{document}

Addendum: let consider first OP comments regarding imaginary axis label:

\documentclass[tikz,svgnames,border=3mm]{standalone}
\usetikzlibrary{decorations.markings, positioning}
\usepackage{mathtools}
\DeclareMathOperator{\im}{Im}
\DeclareMathOperator{\re}{Re}

\begin{document}
\begin{tikzpicture}[thick,
decoration={
markings,% switch on markings
mark=at position .75 with {\arrow{>}}},
every pin/.append style = {pin distance=11mm, pin edge={<-,black}}% added
                    ]
% Axes:
\draw [->] (-5,0) -- (5,0) node [above left]  {$\re(p_0)$};
\draw [->] (0,-4.7) -- (0,4.7) node [below left, pin=left: $\im(p_0)$] {};% changed
% Axes labels:
\foreach \n in {-4,...,-1,1,2,...,4}{%
    \draw[fill] (0,\n) circle (1pt) node [right] {$i \omega_{_{\n}}$};
}
\draw[fill] (0,0) circle (1pt) node [above right] {0};
% Contour line
\draw[DarkBlue,postaction={decorate}]   ( 1,-4) -- ( 1, 4) node [below right] {$C$};
\draw[DarkBlue,postaction={decorate}]   (-1, 4) -- (-1,-4);
\draw[DarkBlue,dashed]                  (1,4) arc (0:180:1) (-1,4)
                                        (-1,-4) arc (180:360:1);

\draw[fill] (3, 2) circle (1pt) node[below right=2mm and 9mm] (h0) {poles of $h(p_0)$}
            (2,-2) circle (1pt);
\draw[thin, shorten >=1mm] (h0.west) --  (3,2) (h0.south west) -- (2,-2);
\end{tikzpicture}
\end{document}

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[Tex/LaTex] Connecting an arced path in TikZ

Do you mean some thing like this?

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{through,shapes}

\begin{document}
\begin{tikzpicture}
    % coordinaten
    \coordinate (m) at (0,4,0);
    % assen
    \draw (0,0,0) -- (0,4,0); % z
    \draw (0,0,0) -- (4,0,0); % x
    \draw (0,0,0) -- (0,0,4.65); % y
    % sfeer
    \draw (4,0,0) arc (0:116.5:4cm and -2cm);
    \draw (4,0,0) arc (0:90:4cm and 4cm);
    \draw (0,4,0) arc (90:206.5:2cm and 4cm);
    \node[draw,circle through={(m)}] (c) at (0,0,0) {};
    % fotosfeer
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    \draw (3.875,0,0) arc (0:90:3.875cm and 3.875cm);
    \draw (0,3.875,0) arc (90:205.8:1.875cm and 3.875cm);
    %fill
    \draw[fill=blue] (0,0,0) --(0,3.875,0) arc (90:205.8:1.875cm and 3.875cm) --(0,0,0) -- (3.875,0,0)  arc (0:90:3.875cm and 3.875cm) -- (0,0,0) -- (3.875,0,0) arc (0:115.8:3.875cm and -1.875cm)--  cycle;
    % convenctie zone
    \draw (2,0,0) arc (0:116.5:2cm and -1cm);
    \draw (2,0,0) arc (0:90:2cm and 2cm);
    \draw (0,2,0) arc (90:206.5:1cm and 2cm);
    %fill
    \draw[fill=red] (0,0,0) -- (0,2,0) arc (90:206.5:1cm and 2cm) --(0,0,0) -- (2,0,0)  arc (0:90:2cm and 2cm) -- (0,0,0) -- (2,0,0) arc (0:116.5:2cm and -1cm)--  cycle;
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    \draw (1,0,0) arc (0:116.5:1cm and -0.5cm);
    \draw (1,0,0) arc (0:90:1cm and 1cm);
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    %fill
    \draw[fill=green] (0,0,0) -- (0,1,0) arc (90:206.5:0.5cm and 1cm) --(0,0,0) -- (1,0,0)  arc (0:90:1cm and 1cm) -- (0,0,0) -- (1,0,0) arc (0:116.5:1cm and -0.5cm)--  cycle;

\end{tikzpicture}
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enter image description here

TikZ-PGF – How to Precisely Set the Position of Text Along a Path

For A:

Put the node right after to[out=90,in=90] like

\draw [<->] (data) to[out=90,in=90]node [pos=.5, above, sloped] (TextNode) {TCP} (app) ;

For B, do this:

\draw[<->,postaction={decorate,decoration={text along path,raise=1ex,text align=center,text={TCP}}}]   (data) to[out=90,in=90] (app);

Full code:

\documentclass{article}
%\usepackage{fontspec}
\usepackage{tikz}
\usetikzlibrary{positioning,decorations.text}


\begin{document}
\begin{tikzpicture}[node distance=2cm]
    \node (data) {Data};
    \node [right=of data] (app) {App};
    % Lines
    \draw [<->] (data) -- (app) node [pos=.5, above, sloped] (TextNode) {TCP}; % works fine
    \draw [<->] (data) to[out=90,in=90]node [pos=.5, above, sloped] (TextNode) {TCP} (app) ; % does not work
\end{tikzpicture}
\begin{tikzpicture}[node distance=2cm]
    \node (data) {Data};
    \node [right=of data] (app) {App};
    % Lines    
    \draw[<->,postaction={decorate,decoration={text along path,raise=1ex,text align=center,text={TCP}}}]   (data) to[out=90,in=90] (app); % does not work (causes error)
\end{tikzpicture}
\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] Connecting an arced path in TikZ

TikZ-PGF – How to Precisely Set the Position of Text Along a Path

Related Question