16

I would like to make a Mexican hat potential (like this one from Wikipedia)

enter image description here

drawing through TikZ, and I am sure the function to use is straightforward, but I have not managed to find the right solution myself... !

I am using this as a starting point, just need the right function...

\tdplotsetmaincoords{70}{135}
\tdplotsetpolarplotrange{90}{180}{0}{360}
\begin{tikzpicture}[line join=bevel,tdplot_main_coords, fill opacity=.7]
\tdplotsphericalsurfaceplot[parametricfill]{72}{36}%
{4}{black}{\tdplottheta}%
{\draw[color=black,thick,->] (0,0,0) -- (20,0,0) node[anchor=north east]{$x$};}%
{\draw[color=black,thick,->] (0,0,0) -- (0,20,0) node[anchor=north west]{$y$};}%
{\draw[color=black,thick,->] (0,0,0) -- (0,0,3) node[anchor=south]{$z$};}%
\end{tikzpicture}

Any hints will be gratefully appreciated!!

Thanks again!

I now have a little problem getting the axis right. I want them placed in the middle of the plot, but I cannot seem to get the labels correct? Also, I would like to rotate the axis so that the x,y arrows point towards us, and the z up as it is now. Any tips? This is what I have now: 

\pgfplotsset{
   standard/.style={
    axis x line=middle,
    axis y line=middle,
    axis z line=middle,
    enlarge x limits=0.15,
    enlarge y limits=0.15,
    enlarge x limits=0.15,
    every axis x label/.style={at={(current axis.right of origin)},anchor=north west},
    every axis y label/.style={at={(current axis.above origin)},anchor=north east},
    every axis z label/.style={at={(current axis.above origin)},anchor=south}
}
}

\begin{tikzpicture}
 \begin{axis}[
 standard,
        colormap={blackwhite}{gray(0cm)=(1); gray(1cm)=(0)},
        samples=30,
        domain=0:360,
        y domain=0:1.25,
        zmin=0,
        zmax=2,
        xlabel=$\mathcal{RE}\,(\phi)$,
        ylabel=$\mathcal{IM}\,(\phi)$,
        zlabel=$V$,
        yticklabels={,,},
        xticklabels={,,},
        zticklabels={,,}
    ]
     \addplot3 [surf, shader=flat, draw=black,  z buffer=sort] ({sin(x)*y}, {cos(x)*y}, {(y^2-1)^2});
      %\addplot3 [surf, shader=flat, draw=black, fill=white, z buffer=sort] (x^4-x^2, y^4-y^2, 1);
    \end{axis}
\end{tikzpicture}

It produces the following figure:

enter image description here

But as you see the axis labelling is not optimal, and the axis is rotated the wrong direction..

Thanks so much so far!

Martin Scharrer
  • 262,582
user24949
  • 161

1 Answers1

21

PGFPlots can plot 3D parametric functions. Here's the output using the function that is used for the Wikipedia image:

enter image description here

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            hide axis,
            samples=30,
            domain=0:360,
            y domain=0:1.25
        ]
        \addplot3 [surf, shader=flat, draw=black, fill=white, z buffer=sort] ({sin(x)*y}, {cos(x)*y}, {(y^2-1)^2});
        \end{axis}
    \end{tikzpicture}
\end{document}
Jake
  • 232,450