[Tex/LaTex] Plotting loops: trajectories and directions

arrowsloopstikz-pgf

Plotting loops: trajectories have directions.
How to plot the following figures using tikz

enter image description here

1st I start to plot the 2nd fig using the code

 \begin{tikzpicture}
 \draw (3,2) ellipse (.5cm and .25cm);
\draw (2.9,1.9) to [controls=+(90:1) and +(90:1)] (3,2);
\end{tikzpicture}

To plot the last fig, I have used.

\begin{tikzpicture}
    \draw  (.5,0) .. controls (3,3) and (-1,3) .. (1.5,0);
\end{tikzpicture}

But unable to plt the outer and inside curves and the arrows.
Using Hobby I wrote

\begin{tikzpicture}[use Hobby shortcut]
 \draw  (-.3 ,1).. (0, 0) .. ( 1.2 , 0 ) .. ( 0 , 0 ) .. (-.3 ,-1);
 \draw  (.45, 0) .. ( .9 , 0 ) .. ( .6 , 0 ) .. ( .7 , -0.01);
\draw  (-.15, 1.2).. (-.01, .2) ..(.01, .22).. (.6, .1) .. ( 1.3 , 0 ) .. ( 0 , -.1 ) .. (-.3 ,-1.2);
\end{tikzpicture}

But problem for the outer curve persists. What to do?

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{hobby,decorations.markings}

\begin{document}
\begin{tikzpicture}[
  use Hobby shortcut,
  vec1/.style={
    decorate,
    decoration={
      markings,      % v-- can fine-tune arrow position and rotation
      mark=at position 0.1 with {\arrow[rotate=5]{stealth}},
    }
  },
  vec2/.style={
    decorate,
    decoration={
      markings,      % v-- here again---fine-tune as needed
      mark=at position 0.080 with {\arrow{stealth}},
      mark=at position 0.206 with {\arrow{stealth reversed}},
      mark=at position 0.800 with {\arrow{stealth reversed}},
      mark=at position 0.930 with {\arrow{stealth}},
    }
  },
]
  % filled points
  %\fill (0,0) circle (1pt);
  %\fill (2,0) circle (1pt);
     \draw (0.4, 0) .. (0.8, 0.3) .. (1.0, 0) .. (0.4, 0);
    \draw  (-.3 ,1).. (0, 0) .. ( 1.2 , 0 )
     \draw  (-.3 ,-1).. (0, 0) .. ( 1.2 , 0 ) .. ( 0 , 0 ) ;
     \draw   (.5, 0) .. ( .8 , 0 ) .. ( .6 , 0 ) .. ( .7 , -0.012);
     \draw (-.1, 1)..(-.08, .7)..(-.05, .4)..( .1 , .4 )..( .7 , .6 )..( 1.4 , 0 )..( .7 , -.6 )..( .2 , -.4 )..(-.1,-.5)..(-.11 ,-.8);
    \end{tikzpicture}
\end{document}

Best Answer

Here's a solution using hobby for the third image. This should be enough to get you started on the other two.

Code

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{hobby,decorations.markings}

\begin{document}
\begin{tikzpicture}[
  use Hobby shortcut,
  vec1/.style={
    decorate,
    decoration={
      markings,      % v-- can fine-tune arrow position and rotation
      mark=at position 0.1 with {\arrow[rotate=5]{stealth}},
    }
  },
  vec2/.style={
    decorate,
    decoration={
      markings,      % v-- here again---fine-tune as needed
      mark=at position 0.080 with {\arrow{stealth}},
      mark=at position 0.206 with {\arrow{stealth reversed}},
      mark=at position 0.800 with {\arrow{stealth reversed}},
      mark=at position 0.930 with {\arrow{stealth}},
    }
  },
]
  % filled points
  \fill (0,0) circle (1pt);
  \fill (2,0) circle (1pt);

  % inner loop
  \draw[postaction=vec1] (-0.6,0.1) .. (0,0.4) .. (0.4,0) .. 
    (0,-0.4) .. (-0.25,-0.25) .. (-0.1,0.1);

  % middle crossing loop
  \draw[postaction=vec2] (3,-1) .. (2,0) .. (0,0.93) .. 
    (-0.93,0) .. (0,-0.93) .. (2,0) .. (3,1);

  % outer loop
  \draw[-stealth] (2.75,-1) .. (2,-0.75) .. (1.25,-1) .. (0,-1.25) .. 
    (-1.25,0) .. (0,1.25) .. (1.25,1) .. (2,0.75) .. (2.75,1);
\end{tikzpicture}
\end{document}

Output

enter image description here

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