Here is the TikZ source code for the following picture. This project was developed using the TikZ terminal for gnuplot. The gnuplot source code is listed in the next section

TikZ Source Code

\documentclass[10pt]{article}
\usepackage[T1]{fontenc}
\usepackage{textcomp}

\usepackage[utf8x]{inputenc}

\usepackage{gnuplot-lua-tikz}
\pagestyle{empty}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{2mm}


\begin{document}

\begin{tikzpicture}[gnuplot]
%% generated with GNUPLOT 4.2p5  (Lua version removed!; terminal rev. 81, script rev. 88)
%% 06/10/09 19:43:58
\gpsetlinewidth{1.00}
\color{gp_lt_color0}
\gpsetlinetype{gp_lt_plot0}
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\draw[gp path] (3.608,4.453)--(3.775,4.437);
\draw[gp path] (3.569,4.364)--(3.750,4.363);
\draw[gp path] (3.500,4.584)--(3.591,4.655);
\draw[gp path] (3.500,4.584)--(3.349,4.656);
\draw[gp path] (3.252,4.563)--(3.349,4.656);
\draw[gp path] (3.424,4.495)--(3.252,4.563);
\draw[gp path] (3.369,4.393)--(3.340,4.289);
\draw[gp path] (3.548,4.274)--(3.340,4.289);
\draw[gp path] (3.608,4.453)--(3.662,4.533);
\draw[gp path] (3.500,4.584)--(3.662,4.533);
\draw[gp path] (3.569,4.364)--(3.548,4.274);
\draw[gp path] (3.424,4.495)--(3.500,4.584);
\draw[gp path] (3.424,4.495)--(3.608,4.453);
\draw[gp path] (3.569,4.364)--(3.608,4.453);
\draw[gp path] (3.369,4.393)--(3.569,4.364);
\draw[gp path] (3.424,4.495)--(3.369,4.393);

\color{gp_lt_color_b}
\node[gp node left] at (5.800,3.993) {$x$};
\node[gp node left] at (5.065,5.458) {$y$};
\node[gp node right] at (4.062,6.388) {$z$};

\gpsetlinetype{gp_lt_border}

%symmetry axis
\draw[gp path, dashed] (6.266,4.632)--(5.2,4.582);
\draw[gp path, dashed] (1.695,4.419)--(2.9,4.475);



\draw[gp path] (3.058,3.600)--(3.782,4.270);
\draw[gp path, ->] (4.618,5.044)--(5.065,5.458);

\draw[gp path, <-] (4.062,6.388)--(4.062,4.564);
\draw[gp path] (4.062,4.315)--(4.062,2.670);


\draw[gp path] (3.070,4.835)--(2.324,5.065);
\draw[gp path, <-] (5.800,3.993)--(4.806,4.300);


%% coordinates of the plot area
\coordinate (gpbb south west 1) at (0.548,0.771);
\coordinate (gpbb south east 1) at (7.576,0.771);
\coordinate (gpbb north east 1) at (7.576,8.287);
\coordinate (gpbb north west 1) at (0.548,8.287);
\coordinate (gpbb north 1) at (4.062,8.287);
\coordinate (gpbb south 1) at (4.062,0.771);
\coordinate (gpbb west 1) at (0.548,4.529);
\coordinate (gpbb east 1) at (7.576,4.529);

\coordinate (center) at (4.062,4.529);

\draw[gp path] ++(center) [rotate around={-17:(center)}] ++(1.5,0) arc (0:27:1.5 and 1.05) node[anchor=north west] {$\gamma$};

\end{tikzpicture}
%% gnuplot variables
\end{document}

gnuplot Source Code

#this renders the chargecloud of a P state using the equations of Anderson, Bartchat [2001]
#this includes the height parameter for reflection symmetry conservation breakdown.

#parameter definitions:
#---------------------

#linear polarization p_l
Pl = 0.6


#alignment angle, in degrees
gamma = 35

#height parameter, ranges from 0 to 1
h = .3



#program start:
#-------------

#set the mode to parametric so we can write x,y,z as a function of u,v
set parametric
#make the 3d object opaque, and render the inner surface with a different color
set hidden3d
#remove the legend at the top-right corner
set nokey

#for rendering polar coordinates, u is the same as \phi, while v is measured from the x-y plane towards z axis
#so 
#\phi = u
#\theta = 90 - v
set angle degrees
set urange [0:360]
set vrange [-90:90]
set trange [-1:1]

#define the plot size explicitly
set xrange [-.7:.7]
set yrange [-.7:.7]
set zrange [-.7:.7]

#this defines the resolution of the plot.  larger numbers means a more fine plot
set isosample 36,28

#remove the 3d border and tics
unset border
unset xtics
unset ytics
unset ztics

#lock the xy plane at z=0
set xyplane at 0

#rotate the view

#isometric front view
#set view 60, 30

#viewing from the positive z axis
set view 90, 0

#place axes for x,y,z that pass through the origin, with linestyle -1 = border line
set xzeroaxis linetype -1
set yzeroaxis linetype -1
set zzeroaxis linetype -1

#place the tics on the axis, and remove the labels except at the ends
#set xtics axis .25
#set ytics axis .25
#set ztics axis .25

#place labels on the axes
set xlabel "$x$"
set ylabel "$y$"
set zlabel "$z$"

#set the graph size so it renders a nice cube for axes
set size 0.65,1.0

#this defines the spherical coordinates needed to plot this parametrically
fx(u,v)=cos(u)*cos(v)
fy(u,v)=sin(u)*cos(v)
fz(v)=sin(v)

#this defines the normalization constant for the m=\pm 1 states
n1=.25

#u = phi
#v = pi - theta

#combination of all angular dependence stuff
g(u,v)=n1*( (1 - h) * ( 1 + Pl * cos( 2 *( u - gamma) ) ) * cos(v) * cos(v) + h * sin(v) * sin(v) )

#combination for symmetry cross section in atomic plane
D(t) = n1*( (1 - h) * ( 1 + Pl ) * cos(t) * cos(t) + h * sin(t) * sin(t) )

#perform the plot itself
#splot g(u,v)*fx(u,v),g(u,v)*fy(u,v),g(u,v)*fz(v)

#this draws the axis for gamma
#splot[t = -1:1] t*cos(gamma), t*sin(gamma), 0


#this draws a cross section of the shape
splot[t = 0:360] D(t)*cos(t), 0 , D(t)*sin(t)