[Tex/LaTex] How to draw A ⊕ B ⊕ C as a Venn diagram

Question

This question led to a new package:

pst-venn

You see my code and please answer my two questions:

\documentclass{article}
\usepackage{amsmath,amssymb,mathptmx}
\usepackage{pstricks}
\usepackage{pst-node}
\usepackage{auto-pst-pdf}
\begin{document}
\begin{pspicture}[showgrid](-3,-3)(8,8)%[linestyle=none]
  \psclip{% 
        \pscircle(0,0){3}
        \pscircle(4,0){3} }
        \pscircle[fillcolor=blue,fillstyle=solid](2,3){3}        
  \endpsclip
 \pscircle(0,0){3}
 \pscircle(4,0){3}
 \pscircle(2,3){3}
\end{pspicture}    
\end{document}

The output picture:

Picture 1:

Its code (use TikZ):

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
  \fill[blue,even odd rule] (0,0) circle (3) (4,0) circle (3) (2,3) circle (3); 
\end{tikzpicture}

My questions:

• How to make my picture like Picture 1? Truly I don't know how to fill color to it.

• (After completing the previous question) Do you see the TikZ code of Picture 1? Look at the important option even odd rule. Do PStricks have the equivalent command, macro,.. as TikZ?

Notice: I prefer PStricks to TikZ but sometimes I recognize the TikZ code is better.

Sorry if I make you being uncomfortable.

Answer 1

A PSTricks solution just for fun!

Answer 1

\documentclass[pstricks]{standalone}
\begin{document}
\begin{pspicture}(-5,-5)(5,5)
\pscustom[fillstyle=eofill,fillcolor=blue]
{ 
  \pscircle(1.5;90){3}
  \pscircle(1.5;-30){3} 
  \pscircle(1.5;210){3} 
} 
\end{pspicture} 
\end{document}

The stroke color is left black just for a trivial reason.

Cartesian coordinates are used in response to the request.

\documentclass[pstricks]{standalone}
\begin{document}
\begin{pspicture}(-5,-5)(5,5)
\pscustom[fillstyle=eofill,fillcolor=blue]
{ 
  \pscircle(0,1.5){3}
  \pscircle(1.29,-0.75){3} 
  \pscircle(-1.29,-0.75){3} 
} 
\end{pspicture} 
\end{document}

Answer 2

Non-zero winding rule:

\documentclass[pstricks,border=12pt]{standalone}
\begin{document}
\begin{pspicture}[showgrid=t](-3,-3)(3,3)
\pscustom[fillstyle=solid,fillcolor=red]
{
    \pscircle{1}
    \pscircle{2}
}
\end{pspicture} 
\end{document}

Non-zero winding rule:

\documentclass[pstricks,border=12pt]{standalone}
\begin{document}
\begin{pspicture}[showgrid=t](-3,-3)(3,3)
\pscustom[fillstyle=solid,fillcolor=red]
{
    \psarcn(0,0){1}{360}{0}
    \pscircle{2}
}
\end{pspicture} 
\end{document}

Even-odd rule:

\documentclass[pstricks,border=12pt]{standalone}
\begin{document}
\begin{pspicture}[showgrid=t](-3,-3)(3,3)
\pscustom[fillstyle=eofill,fillcolor=red]
{
    \pscircle{1}
    \pscircle{2}
}
\end{pspicture} 
\end{document}