4 set venn diagram in TikZ

Question

Is it possible to make a 4-set venn diagram using the tikz packages, like the following one? I know it must be, but the only information I can find on the subject uses R as the language.

So, an update. I am now wondering how to best fill just the isolated fields, that is, the part only in A, the part only in B, etc. For now, I have just the part in D filled. Any suggestions? Code below:

\documentclass[12pt]{article}

\usepackage{tikz} \usetikzlibrary{positioning,shapes.geometric}

% For drawing
\def\firstellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
\def\secondellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm,
rotate=50]} \def\thirdellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm,
rotate=-50]} \def\fourthellip{(-0.3, 1cm) ellipse [x radius=3cm, y
radius=1.5cm, rotate=-50]} \def\bounding{(-5,-3) rectangle (5,4)}

\begin{document}

\begin{tikzpicture} \filldraw[fill=black, opacity=0.2] \bounding;

    \scope \fill[white] \fourthellip; \endscope \filldraw[fill=red,
    opacity=0.2] \fourthellip;

    %single colors
    \scope \fill[white] \secondellip; \fill[white] \thirdellip; \fill[white]
    \firstellip; \endscope

    \draw \firstellip node [label={[xshift=2.0cm, yshift=-0.9cm]$A$}] {};
    \draw \secondellip node [label={[xshift=2.2cm, yshift=2.1cm]$B$}] {};
    \draw \thirdellip node [label={[xshift=-2.0cm, yshift=-0.9cm]$C$}] {};
    \draw \fourthellip node [label={[xshift=-2.2cm, yshift=2.1cm]$D$}] {};
    \draw \bounding node [label=above left:$U$] {};

\end{tikzpicture}  \end{document}

And displays as follows, I'm trying to get red in the four "corners". Thanks so much:

Answer 1

There are some Venn diagrams with multiple elements coloured in this example: http://www.texample.net/tikz/examples/venn-diagram/

I've taken the principles used there and created a version with all four "corners" filled, as requested (I used yellow to distinguish from the original code which had one corner coloured red).

\documentclass[12pt]{article}

\usepackage{tikz} \usetikzlibrary{positioning,shapes.geometric}

% For drawing
\def\firstellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
\def\secondellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm,
rotate=50]} \def\thirdellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm,
rotate=-50]} \def\fourthellip{(-0.3, 1cm) ellipse [x radius=3cm, y
radius=1.5cm, rotate=-50]} \def\bounding{(-5,-3) rectangle (5,4)}

\begin{document}

\begin{tikzpicture} \filldraw[fill=black, opacity=0.2] \bounding;

    \scope \fill[white] \fourthellip; \endscope \filldraw[fill=red,
    opacity=0.2] \fourthellip;

    %single colors
    \scope \fill[white] \secondellip; \fill[white] \thirdellip; \fill[white]
    \firstellip; \endscope

    \draw \firstellip node [label={[xshift=2.0cm, yshift=-0.9cm]$A$}] {};
    \draw \secondellip node [label={[xshift=2.2cm, yshift=2.1cm]$B$}] {};
    \draw \thirdellip node [label={[xshift=-2.0cm, yshift=-0.9cm]$C$}] {};
    \draw \fourthellip node [label={[xshift=-2.2cm, yshift=2.1cm]$D$}] {};
    \draw \bounding node [label=above left:$U$] {};

    \begin{scope}
        \begin{scope}[even odd rule]% first ellipse corner
            \clip \secondellip (-5,-5) rectangle (5,5);
            \clip \thirdellip (-5,-5) rectangle (5,5);
            \clip \fourthellip (-5,-5) rectangle (5,5);
        \fill[yellow] \firstellip;
        \end{scope}
    \end{scope}
    
    \begin{scope}
        \begin{scope}[even odd rule]% second ellipse corner
            \clip \firstellip (-5,-5) rectangle (5,5);
            \clip \thirdellip (-5,-5) rectangle (5,5);
            \clip \fourthellip (-5,-5) rectangle (5,5);
        \fill[yellow] \secondellip;
        \end{scope}
    \end{scope}
    
    \begin{scope}
        \begin{scope}[even odd rule]% third ellipse corner
            \clip \secondellip (-5,-5) rectangle (5,5);
            \clip \firstellip (-5,-5) rectangle (5,5);
            \clip \fourthellip (-5,-5) rectangle (5,5);
        \fill[yellow] \thirdellip;
        \end{scope}
    \end{scope}
    

\end{tikzpicture}  \end{document}

The trick is to add a large rectangle that encompasses everything and then use the even-odd filling rule - see the texample page for more details.

(Btw - I used Overleaf (formerly WriteLaTeX) to test the code - the document can be found here: https://www.overleaf.com/latex/examples/example-venn-diagram-with-isolated-areas-filled/xjptmqsjfdlc )

Answer 2

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning,shapes.geometric}
\begin{document}
\tikzset{
  set/.style ={ 
    ellipse, 
    minimum width=3.5cm, 
    minimum height=2cm,
    draw,
}}
\begin{tikzpicture}
\foreach \x/\y/\a in {.7/0/60,.3/1/60,-.7/0/-60,-.3/1/-60} 
  \node[set, rotate=\a] at (\x,\y) {};
\end{tikzpicture}
\end{document}