# Multiple 2D Gaussian ellipses in 3D plot

I'd like to plot different bivariate Gaussian distributions as shaded 2D ellipses at different points in 3D space. The 2D ellipses I would plot like Jake suggests in Gaussian ellipsoids using tikz, but technically that is already a 3D plot. Is there a possibility to extend this method?

I came up with the following example (left: example how I like the ellipses to be orientated, taken from https://arxiv.org/abs/1611.03986, right: my ansatz):

Two main points are that

• the colormap is not actually transparent and one cannot see the axis of the outer coordinate system any more,
• and that I would like to have the ellipses at a fixed point y in the xz-plane (this means that the bottom line of the black rectangles should be parallel to the x-axis and compressed accordingly).
\documentclass{standalone}
\usepackage{tikz,pgfplots}
\usepgfplotslibrary{patchplots}
\pgfplotsset{%
colormap={whitered}{color(0cm)=(transparent); color(1.cm)=(red)}%
}
\begin{document}
\begin{tikzpicture}[baseline,
declare function={bivar(\ma,\sa,\mb,\sb)=
1/(2*pi*\sa*\sb) * exp(-((x-\ma)^2/\sa^2 + (y-\mb)^2/\sb^2))/2;}]
% Outer coordinate system
\begin{axis}[
unit vector ratio*=1 1 1,
axis lines = middle,
view={120}{30},
domain = -10:10,
zmin = -5, zmax = 5,
xlabel = $x$, ylabel = $y$, zlabel = $z$,
x label style={at={(ticklabel* cs:1.)},anchor=north east},
y label style={at={(ticklabel* cs:1.)},anchor=north west},
z label style={at={(ticklabel* cs:1.)},anchor=south},
]
\coordinate (origin1) at (axis cs:0,-10,0);
\coordinate (origin2) at (axis cs:0,10,0);
\addplot3[no markers,opacity=0]{0}; % <- without this pseudo plot, the outer coordinate system does not work
\end{axis}
% Bivariate distribution 1
\begin{axis}[
at={(origin1)}, anchor={center},
width=3cm, height=3cm,
scale only axis,
axis equal image,
hide axis,
colormap name=whitered,
view={0}{90},
enlargelimits=false,
domain=-1.5:1.5, y domain=-1.5:1.5,
]
\end{axis}
% Bivariate distribution 2
\begin{axis}[
at={(origin2)}, anchor={center},
width=3cm, height=3cm,
scale only axis,
axis equal image,
hide axis,
colormap name=whitered,
view={0}{90},
enlargelimits=false,
domain=-1.5:1.5, y domain=-1.5:1.5,
]