[Tex/LaTex] Drawing Smooth Hyperbolic Curves in TikZ

plottikz-pgf

I am trying to draw the following picture with TikZ. However it doesn't seem possible to get the correct smoothness like in the picture.

enter image description here

Can anyone tell me how to achieve it. What I have tried so far is using parabola function and smooth plot.

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}

\draw [<->,thick] (0,5) node (yaxis) [above, text width=3.5cm,align=center] {$s_1$}
        |- (7,0) node (xaxis) [right] {$s_2$};

\coordinate (A) at (2.5,4.7);
\coordinate (B) at (2.80,2.0);
\coordinate (C) at (3.75,1.50);
\coordinate (D) at (6.7,0.75);

%\draw[thick] plot [smooth] coordinates{(A) (B) (C) (D)};
% \draw (2.5,4.7) parabola bend (2  .8,2) (6.7,0.75);
\draw  (6.7,1.00) parabola bend (3.5,0.95) (2.5,4.7) ;

\node [yshift=0.25cm] at (A) {$T = C$};
\node [xshift=0.65cm] at (D) {$c_1/\psi$};

\draw[dotted] (0,4.5) node[xshift=-8pt] {$n_1$} -- (6.5,4.5);
\draw[dotted] (6.5,4.5) -- (6.5,0) node[yshift=-8pt] {$n_2$};


%\draw[dotted] (0,0.9) node[xshift=-8pt] {$1$} -- (4.5,0.9);
\draw[dotted] (1.5,4.5) -- (1.5,0) node[yshift=-8pt] {$I_1/\psi$};

\node[text width=2.5cm,align=center] at (3,0.75) {Transfer domain \\ $T > C$};
\node[text width=4cm,align=center] at (4.75,3.5) {Computation domain \\ $T < C$};

\end{tikzpicture}
\end{document}

Best Answer

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}

\draw [<->,thick] (0,5) node (yaxis) [above, text width=3.5cm,align=center] {$s_1$}
        |- (7,0) node (xaxis) [right] {$s_2$};

\coordinate (A) at (2.5,4.7);
\coordinate (B) at (2.80,2.0);
\coordinate (C) at (3.75,1.50);
\coordinate (D) at (6.7,0.75);

%\draw[thick] plot [smooth] coordinates{(A) (B) (C) (D)};
% \draw (2.5,4.7) parabola bend (2  .8,2) (6.7,0.75);
\draw (6.7,1.00) .. controls (3,1.7) and (2.4,1.7) .. (2.5,4.7) ;

\node [yshift=0.25cm] at (A) {$T = C$};
\node [xshift=0.65cm] at (D) {$c_1/\psi$};

\draw[dotted] (0,4.5) node[xshift=-8pt] {$n_1$} -- (6.5,4.5);
\draw[dotted] (6.5,4.5) -- (6.5,0) node[yshift=-8pt] {$n_2$};


%\draw[dotted] (0,0.9) node[xshift=-8pt] {$1$} -- (4.5,0.9);
\draw[dotted] (1.5,4.5) -- (1.5,0) node[yshift=-8pt] {$I_1/\psi$};

\node[text width=2.5cm,align=center] at (3,0.75) {Transfer domain \\ $T > C$};
\node[text width=4cm,align=center] at (4.75,3.5) {Computation domain \\ $T < C$};

\end{tikzpicture}
\end{document}

enter image description here

Related Solutions

[Tex/LaTex] Drawing a hyperbolic trajectory

Here is a solution, without fancy drawing for the Earth, but which shows the varying solar radiation as the Earth travels along the hyperbolic orbit.

Note: an elliptical version is available here.

enter image description here

\documentclass{article}
\usepackage{tikz}
\begin{document}

\begin{center}
  \begin{tikzpicture}[scale=2]
    \pgfmathsetmacro{\e}{1.44022}               % eccentricity of the hyperbola
    \pgfmathsetmacro{\a}{1}
    \pgfmathsetmacro{\b}{\a*sqrt((\e)^2 - 1)}
    \pgfmathsetmacro{\c}{sqrt((\a)^2+(\b)^2}    % distance from centre to focus
    \pgfmathsetmacro{\Sunradius}{0.2}           % Sun radius
    \pgfmathsetmacro{\Earthradius}{0.05}        % Earth radius
    \pgfmathsetmacro{\thetamax}{1.5}

    \draw plot[domain = -\thetamax:\thetamax] ({\a*cosh(\x)}, {\b*sinh(\x)});
    \draw (\c,0) circle (1pt);

    \shade[%
        top color=yellow!70,%
        bottom color=red!70,%
        shading angle={45},%
    ] (\c,0) circle (\Sunradius);

    % This function computes the direction in which light hits the Earth.
    \pgfmathdeclarefunction{f}{1}{%
    \pgfmathparse{
      ((-\c+\a*cosh(#1))<0) * ( 180 + atan( \b*sinh(#1)/(-\c+\a*cosh(#1)) ) ) 
        +
      ((-\c+\a*cosh(#1))>=0) * ( atan( \b*sinh(#1)/(-\c+\a*cosh(#1)) ) ) 
    }
  }


  % This function computes the distance between Earth and the Sun,
  % which is used to calculate the varying radiation intensity on Earth.
  \pgfmathdeclarefunction{d}{1}{%
    \pgfmathparse{ sqrt((-\c+\a*cosh(#1))^2+(\b*sinh(#1))^2) }
  }

  \pgfmathtruncatemacro{\N}{8}  % an even number is best here
  \pgfmathsetmacro{\thetaoffset}{.15*\thetamax}
  \foreach \k in {0,1,...,\N}{
    \pgfmathsetmacro{\theta}{(\thetamax-\thetaoffset)*(2*\k/\N-1)}
      \pgfmathsetmacro{\radiation}{100*(1-\c)/d(\theta))^2}
      \colorlet{Earthlight}{yellow!\radiation!blue}
        \shade[
          top color=Earthlight,
          bottom color=blue,
          shading angle={90+f(\theta)},
        ] ({\a*cosh(\theta)}, {\b*sinh(\theta)}) circle (\Earthradius);

    }
    \end{tikzpicture}
\end{center}
\end{document}

EDIT: with a nice .png of the Earth at the focus instead.

enter image description here

The picture I used is adapted from the one posted there.

enter image description here

\documentclass{article}
\usepackage{tikz}
\begin{document}

\begin{center}
  \begin{tikzpicture}[scale=2]
    \pgfmathsetmacro{\e}{1.44022}               % eccentricity of the hyperbola
    \pgfmathsetmacro{\a}{1}
    \pgfmathsetmacro{\b}{\a*sqrt((\e)^2 - 1)}
    \pgfmathsetmacro{\c}{sqrt((\a)^2+(\b)^2}    % distance from centre to focus
    \pgfmathsetmacro{\Earthradius}{0.1}        % Earth radius
    \pgfmathsetmacro{\UFOradius}{.03}
    \pgfmathsetmacro{\thetamax}{1.2}

    \draw plot[domain = -\thetamax:\thetamax] ({\a*cosh(\x)}, {\b*sinh(\x)});

    \path (\c,0) node(a) {\includegraphics[width=.5cm]{earth.png}};

  \pgfmathtruncatemacro{\N}{8}  % an even number is best here
  \pgfmathsetmacro{\thetaoffset}{.05*\thetamax}
  \foreach \k in {0,1,...,\N}{
    \pgfmathsetmacro{\theta}{(\thetamax-\thetaoffset)*(2*\k/\N-1)}
        \shade[top color=black,bottom color=gray]
            ({\a*cosh(\theta)}, {\b*sinh(\theta)}) circle (\UFOradius);

    }
    \end{tikzpicture}
\end{center}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Drawing a hyperbolic trajectory

Related Question