# Filling intersecting ellipse with tikz

I have a little diagram where I want to fill the ellipses.

\documentclass[border=3pt]{standalone}
\usepackage{tikz}

\begin{document}
\def\firstellipse{(0,0) ellipse (1 and .5)}
\def\secondellipse{(.7,.3) ellipse (2 and 1)}
\def\thirdellipse{(1,.6) ellipse (2.5 and 1.5)}
\def\fourthellipse{(1.3,.9) ellipse (3 and 2)}
\def\fifthellipse{(1.6,1.2) ellipse (3.5 and 2.5)}
\begin{tikzpicture}
\draw\firstellipse;
\draw\secondellipse;
\draw\thirdellipse;
\draw\fourthellipse;
\draw\fifthellipse;
\node at (0,0) {Körper};
\node at (.7,.75) {Euklidische Ringe};
\node at (1.2,1.6) {Hauptidealringe};
\node at (1.5, 2.37) {Faktorielle Ringe};
\node at (1.9, 3.2) {Integritätsringe};
\end{tikzpicture}
\end{document}


The color should be different for each ellipse, I haven't worked it out entirely yet but probably something like:

• first ellipse red!15

• second ellipse green!15

• third ellipse blue!15

• fourth ellipse cyan!15

• fifth ellipse magenta!15

However, I cannot use fill comands since only the non-intersecting parts should be filled with this color. I have used MS paint to show what I mean:

• Change the order of the nodes and colors will be overprinted Aug 27, 2017 at 9:40
• Welcome to TeX.SX! Aug 27, 2017 at 9:57

Just draw the ellipses in opposite order, starting with the largest:

\documentclass[border=3pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
\def\firstellipse{(0,0) ellipse (1 and .5)}
\def\secondellipse{(.7,.3) ellipse (2 and 1)}
\def\thirdellipse{(1,.6) ellipse (2.5 and 1.5)}
\def\fourthellipse{(1.3,.9) ellipse (3 and 2)}
\def\fifthellipse{(1.6,1.2) ellipse (3.5 and 2.5)}
\filldraw[fill=magenta!15]\fifthellipse;
\filldraw[fill=cyan!15]\fourthellipse;
\filldraw[fill=blue!15]\thirdellipse;
\filldraw[fill=green!15]\secondellipse;
\filldraw[fill=red!15]\firstellipse;
\node at (0,0) {Körper};
\node at (.7,.75) {Euklidische Ringe};
\node at (1.2,1.6) {Hauptidealringe};
\node at (1.5, 2.37) {Faktorielle Ringe};
\node at (1.9, 3.2) {Integritätsringe};
\end{tikzpicture}
\end{document}