Draw sphere pgfplots with axis at center

Question

I want to draw a plot that illustrates the ration pattern of an isotropic antenna. I thought about pgfplots to do the job. I grabbed the code from pgfplots manual and did some changes; but it doesn't satisfies me.

As I said in the title, I want the axis to be drawn in the center, but I also want to be able to see the (0,0,0) point. So to be able to look inside, the sphere surface opacity shall be lower.

Moreover, the code is not optimized, I need to specify the min and max for all axis just to see the arrow of the axis outside the surface. Is there a better way?

\documentclass{article}

\usepackage{pgfplots}

\pgfplotsset{%
    compat=1.8,
    compat/show suggested version=false,
}

\begin{document}

\begin{tikzpicture}
\begin{axis}[%
    footnotesize,
    axis equal,
    axis lines=center,
    xlabel=$x$,
    ylabel=$y$,
    zlabel=$z$,
    xmax=2,xmin=-2,
    ymax=2,ymin=-2,
    zmax=2,zmin=-2,
    xtick=\empty,
    ytick=\empty,
    ztick=\empty,
    ]
    \addplot3[%
      surf,
      z buffer=sort,
      samples=15,
      variable=\u,
      variable y=\v,
      domain=0:180,
      y domain=0:360
    ]
    ({cos(u)*sin(v)}, {sin(u)*sin(v)}, {cos(v)});
    \end{axis}
\end{tikzpicture}

\end{document}

Answer 1

Using axis equal causes to maintain the width/height and to modify axis limits and the image scaling. In order to keep the axis limits and modify just the units, we can say scale uniformly strategy=units only. I added width=10cm to enlarge the sphere compared to the axis descriptions (different fonts for the axis description might also have done the job). Adding height=10cm as well avoids confusion as to which of the parameters width or height is to be used in the final version.

Adding view/h=45 appears to be quite good as well.

Combined with opacity as suggested by Henri, we end up at

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.8}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[%
        axis equal,
        width=10cm,
        height=10cm,
        axis lines = center,
        xlabel = {$x$},
        ylabel = {$y$},
        zlabel = {$z$},
        ticks=none,
        enlargelimits=0.3,
        view/h=45,
        scale uniformly strategy=units only,
    ]
    \addplot3[%
        opacity = 0.5,
        surf,
        z buffer = sort,
        samples = 21,
        variable = \u,
        variable y = \v,
        domain = 0:180,
        y domain = 0:360,
    ]
    ({cos(u)*sin(v)}, {sin(u)*sin(v)}, {cos(v)});
    \end{axis}
\end{tikzpicture}
\end{document}

We can also change the parameterization of the sphere to screen coordinate rather than angles and get the LEFT image (the right is the same as above)

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.8}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[%
        axis equal,
        width=10cm,
        height=10cm,
        axis lines = center,
        xlabel = {$x$},
        ylabel = {$y$},
        zlabel = {$z$},
        ticks=none,
        enlargelimits=0.3,
        view/h=45,
        scale uniformly strategy=units only,
    ]
    \addplot3[
        surf,
        opacity = 0.5,
        samples=21,
        domain=-1:1,y domain=0:2*pi,
        z buffer=sort]
    ({sqrt(1-x^2) * cos(deg(y))},
     {sqrt( 1-x^2 ) * sin(deg(y))},
     x);

    \end{axis}
\end{tikzpicture}

\end{document}

I causes an even distribution along the z axis (but not along the angles).

Answer 2

Remarks

Instead of specifying the limits by hand you can use the key enlargelimits = <value>. The get the transparency use the key opacity = <value>.

If you don't care about compile performance you can use the alternative solution, which was produced as seen on http://www.texample.net/tikz/examples/spherical-polar-pots-with-3dplot/

Implementation

\documentclass[tikz]{standalone}
\usepackage{tikz-3dplot}
\usepackage{pgfplots}
\pgfplotsset{compat=1.8}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[%
        axis equal,
        axis lines = center,
        xlabel = {$x$},
        ylabel = {$y$},
        zlabel = {$z$},
        enlargelimits = 0.5,
        ticks=none,
    ]
    \addplot3[%
        opacity = 0.5,
        surf,
        z buffer = sort,
        samples = 21,
        variable = \u,
        variable y = \v,
        domain = 0:180,
        y domain = 0:360,
    ]
    ({cos(u)*sin(v)}, {sin(u)*sin(v)}, {cos(v)});
    \end{axis}
\end{tikzpicture}

% Alternative solution: http://www.texample.net/tikz/examples/spherical-polar-pots-with-3dplot/
\tdplotsetmaincoords{70}{135}
\begin{tikzpicture}[>=stealth,line join=bevel,tdplot_main_coords,fill opacity=.5]
\tdplotsphericalsurfaceplot[parametricfill]{72}{36}%
    {1}{black}{\tdplottheta}%
    {\draw[color=black,thick,->] (0,0,0) -- (2,0,0) node[anchor=north east]{$x$};}%
    {\draw[color=black,thick,->] (0,0,0) -- (0,2,0) node[anchor=north west]{$y$};}%
    {\draw[color=black,thick,->] (0,0,0) -- (0,0,2) node[anchor=south]{$z$};}%
\end{tikzpicture}
\end{document}

Output

---

With PSTricks and pst-solides3d (just for fun)

Compile with xelatex or with latex -> dvips -> ps2pdf.

\documentclass[pstricks]{standalone}
\usepackage{pst-solides3d}
\begin{document}
\begin{pspicture}(-5,-4)(5,6)
    \psSolid[
        object=sphere,
        r=1,
        linecolor=blue,
        fillcolor=blue!10,
        action=draw*,mode=4,
        ngrid=18 18
    ]
    \axesIIID(0,0,0)(2,2,2)
\end{pspicture}
\end{document}