15

I know how to draw a sine curve in TikZ and I know how to rotate it in the plane of the paper. I would now like to draw a sine curve that oscillates in the depth of the paper - to give the impression that the wave it illustrates oscillates in and out of the direction perpendicular to the paper.

It could be somehow similar to the blue curve in this picture:

enter image description here

Any suggestions on how this can be done in TikZ?

  • A simple 3d parametric should work: Just let the vertical axis be t, and then the other two are the usual x, sin x. – Peter Grill Jun 27 '12 at 20:12
  • Could you provide a small example? Thank you in advance. – user15272 Jun 27 '12 at 20:21
23

It is possible, but it does not neccessarily help understanding. The first is a rotation with constant angular velocity about the z-axis, which you probably get from the picture. But it gets quite incomprehendable from there: I wouldn't know what the second one is.

So I started experimenting. The next two explore the possibility to draw surfaces connecting to the xy-plane with or without the actual line drawn.

Then I fried connections via radial lines, which just looks ugly.

Lastly, I tried surfaces connectiong radially to the z-axis.

Let me know if anything at least comes remotely to what you were looking for.

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm,a3paper,landscape]{geometry}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[x={(0.707cm,0.707cm)},z={(0cm,1cm)},y={(-0.866cm,0.5cm)}]
\draw[->] (-2,0,0) -- (2,0,0) node[right] {x};
\draw[->] (0,-2,0) -- (0,2,0) node[left] {y};
\draw[->] (0,0,-2) -- (0,0,12) node[above] {z};
\draw (1,0,0)
\foreach \z in {0,0.1,...,10}
{ -- ({cos(\z*100)},{sin(\z*100)},{\z})
};
\node[rotate=90,right=1cm] at (0,0,12) {normal rotation};
\end{tikzpicture}
\begin{tikzpicture}[x={(0.707cm,0.707cm)},z={(0cm,1cm)},y={(-0.866cm,0.5cm)}]
\draw[->] (-2,0,0) -- (2,0,0) node[right] {x};
\draw[->] (0,-2,0) -- (0,2,0) node[left] {y};
\draw[->] (0,0,-2) -- (0,0,12) node[above] {z};
\draw (1,0,0)
\foreach \z in {0,0.1,...,10}
{ -- ({cos(\z*200)},{sin(\z*100)},{\z})
};
\node[rotate=90,right=1cm] at (0,0,12) {WTF?};
\end{tikzpicture}
\begin{tikzpicture}[x={(0.707cm,0.707cm)},z={(0cm,1cm)},y={(-0.866cm,0.5cm)}]
\draw[->] (-2,0,0) -- (2,0,0) node[right] {x};
\draw[->] (0,-2,0) -- (0,2,0) node[left] {y};
\draw[->] (0,0,-2) -- (0,0,12) node[above] {z};
\draw (1,0,0)
\foreach \z in {0,0.1,...,10}
{ -- ({cos(\z*189)},{sin(\z*91)},{\z})
};
\foreach \z in {0,0.1,...,9.9}
{\fill[gray,opacity=0.2] ({cos(\z*189)},{sin(\z*91)},0) -- ({cos(\z*189)},{sin(\z*91)},{\z}) -- ({cos((\z+0.1)*189)},{sin((\z+0.1)*91)},{\z+0.1}) -- ({cos((\z+0.1)*189)},{sin((\z+0.1)*91)},0) -- cycle;
}
\node[rotate=90,right=1cm] at (0,0,12) {to floor, gray};
\end{tikzpicture}
\begin{tikzpicture}[x={(0.707cm,0.707cm)},z={(0cm,1cm)},y={(-0.866cm,0.5cm)}]
\draw[->] (-2,0,0) -- (2,0,0) node[right] {x};
\draw[->] (0,-2,0) -- (0,2,0) node[left] {y};
\draw[->] (0,0,-2) -- (0,0,12) node[above] {z};
\foreach \z in {0,0.1,...,9.9}
{   \pgfmathtruncatemacro{\mycolorpercentage}{\z/0.099}
    \fill[red!\mycolorpercentage!blue,opacity=0.1] ({cos(\z*210)},{sin(\z*42)},0) -- ({cos(\z*210)},{sin(\z*42)},{\z}) -- ({cos((\z+0.1)*210)},{sin((\z+0.1)*42)},{\z+0.1}) -- ({cos((\z+0.1)*210)},{sin((\z+0.1)*42)},0) -- cycle;
}
\node[rotate=90,right=1cm] at (0,0,12) {to floor, color gradient};
\end{tikzpicture}
\begin{tikzpicture}[x={(0.707cm,0.707cm)},z={(0cm,1cm)},y={(-0.866cm,0.5cm)}]
\draw[->] (-2,0,0) -- (2,0,0) node[right] {x};
\draw[->] (0,-2,0) -- (0,2,0) node[left] {y};
\draw[->] (0,0,-2) -- (0,0,12) node[above] {z};
\draw (1,0,0)
\foreach \z in {0,0.1,...,10}
{ -- ({cos(\z*207)},{sin(\z*101)},{\z})
};
\foreach \z in {0,0.1,...,10}
{ \draw[opacity=0.5,gray] ({cos(\z*207)},{sin(\z*101)},{\z}) -- (0,0,\z);
}
\node[rotate=90,right=1cm] at (0,0,12) {radial lines};
\end{tikzpicture}
\begin{tikzpicture}[x={(0.707cm,0.707cm)},z={(0cm,1cm)},y={(-0.866cm,0.5cm)}]
\draw[->] (-2,0,0) -- (2,0,0) node[right] {x};
\draw[->] (0,-2,0) -- (0,2,0) node[left] {y};
\draw[->] (0,0,-2) -- (0,0,12) node[above] {z};
\draw (1,0,0)
\foreach \z in {0,0.1,...,10}
{ -- ({cos(\z*237)},{sin(\z*111)},{\z})
};
\foreach \z in {0,0.1,...,9.9}
{ \fill[opacity=0.5,gray] (0,0,\z) -- ({cos(\z*237)},{sin(\z*111)},{\z}) -- ({cos((\z+0.1)*237)},{sin((\z+0.1)*111)},{(\z+0.1)}) -- (0,0,{(\z+0.1)}) -- cycle;
}
\node[rotate=90,right=1cm] at (0,0,12) {radial surfaces, gray};
\end{tikzpicture}
\begin{tikzpicture}[x={(0.707cm,0.707cm)},z={(0cm,1cm)},y={(-0.866cm,0.5cm)}]
\draw[->] (-2,0,0) -- (2,0,0) node[right] {x};
\draw[->] (0,-2,0) -- (0,2,0) node[left] {y};
\draw[->] (0,0,-2) -- (0,0,12) node[above] {z};
\draw (1,0,0)
\foreach \z in {0,0.1,...,10}
{ -- ({cos(\z*37)},{sin(\z*219)},{\z})
};
\foreach \z in {0,0.1,...,9.9}
{ \pgfmathtruncatemacro{\mycolorpercentage}{\z/0.099}
    \fill[opacity=0.3,orange!\mycolorpercentage!cyan] (0,0,\z) -- ({cos(\z*37)},{sin(\z*219)},{\z}) -- ({cos((\z+0.1)*37)},{sin((\z+0.1)*219)},{(\z+0.1)}) -- (0,0,{(\z+0.1)}) -- cycle;
}
\node[rotate=90,right=1cm] at (0,0,12) {radial, color gradient};
\end{tikzpicture}

\end{document}

enter image description here

  • Ah these are just beautiful. Great work. A function suggestion: \begin{tikzpicture}\begin{axis}[view={60}{30}]\addplot3[samples=400,samples y =0] ({cos(x*200)},{sin(x*400)},x);\end{axis}\end{tikzpicture} ;-) – percusse Jun 27 '12 at 21:49
  • 3
    @percusse: Yes, I know, lots of room for improvement... I just had to at least try before going to bed, otherwise I would have found no sleep thinking about it :D – Tom Bombadil Jun 27 '12 at 22:00
17

You can use pgfplots for this too.

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[view={-30}{30},no markers,zmax=30,
            z post scale=2,
            x post scale=0.5,
            enlargelimits=false,
            ymax=5,ymin=-5,
            xmax=5,xmin=-5]
\addplot3+[domain=-0:30,samples=200,samples y=0,ultra thick](x-5,{5*sin(deg(1.2*x))},3*x);
\addplot3+[domain=-0:30,samples=200,samples y=0](5,{5*sin(deg(1.2*x))},3*x);
\addplot3+[domain=-0:30,samples=200,samples y=0](x-5,5,3*x);
\end{axis}
\end{tikzpicture}
\end{document}

enter image description here

  • Thanks for the suggestions. However, my sketch turned out to become too messy with the rotated sine curve in it, so I did something simpler instead. Thanks again for the ideas. – user15272 Jun 29 '12 at 7:28

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