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How would we typeset a “mexican hat” like the following

mexican hat

in TikZ?

Martin Scharrer
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Thanos D. Papaïoannou
  • 613
  • 3
  • 13

2 Answers2

37

I used arcs and a sin, cos combination to draw the hat (feel free to improve it):

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[ultra thick]
  \draw (2,-1.5) cos (3,0) sin (4,1.5) cos (5,0) sin (6,-1.5);
  \draw (2.4,-0.5) arc (114:428:4cm and 1cm);
  \draw (.55,-2.5) arc (210:330:4cm and 1cm);
  \draw (0.02,-1.45) arc (180:245:1.25cm);
  \draw (7.3,-2.57) arc (295:360:1.25cm);
\end{tikzpicture}

\end{document}

mexican hat

pmav99
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Gonzalo Medina
  • 505,128
  • By the way, I'd like to draw your attention to a question about TikZ on meta: http://meta.tex.stackexchange.com/q/1220/86 – Andrew Stacey Apr 03 '11 at 18:57
  • Thank you, Gonzalo, only your solution makes the hat slightly too pointy for my purposes. – Thanos D. Papaïoannou Apr 03 '11 at 23:44
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    @Thanos D. Papaïoannou: you can change the top of the hat modifying the sin cos combination; you could use, for example, \draw (2,-1.5) cos (2.8,-0.5) sin (4,0.9) cos (5.2,-0.5) sin (6,-1.5); instead of the corresponding line of my code. – Gonzalo Medina Apr 04 '11 at 01:04
2

Well the top of the hat looks like a statistical normal distribution. So I would plot that function. Furthermore you could use an arc for the upper part of the hat. And at last you could use a curve for the lower part of the hat. I have tried producing the hat with the following code:

\begin{tikzpicture}[scale=3]
\draw[very thick,domain=-1.5:1.5,xscale=0.5,smooth,variable=\x] plot ({\x},{(1.3*2.718281828^(-0.5*\x*\x))});
\draw[very thick] (0,-0 cm) arc (-90:70:1.5 cm and 0.4 cm);
\draw[very thick] (0,-0 cm) arc (270:110:1.5 cm and 0.4 cm);
\begin{scope}[yshift=0.4 cm]
\draw[very thick] (-10 : -1.5 cm and 0.4 cm) .. controls (-1.25,-0.8) and (1.25,-0.8) .. (-170 : -1.5 cm and 0.4 cm);
\end{scope}
\end{tikzpicture}

I agree it's not perfect, but feel free to improve. :D

willeM_ Van Onsem
  • 4,123
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    But in your code the function used for the upper part of the hat goes upwards, so you really don't get a hat. – Gonzalo Medina Apr 03 '11 at 01:21
  • I'v compiled it with my Linux machine, it displayed a hat. I work from the bottom of the ellipse and arc it to the hat. However I dont see why you would draw this with TikZ. You can use an online vectorizer, to make it vectorized and import it in your pdf using includegraphics. – willeM_ Van Onsem Apr 03 '11 at 02:12
  • Thank you, CommuSoft, this is very close to what I needed! – Thanos D. Papaïoannou Apr 03 '11 at 23:44