Plot difference of sets in tikz

Question

The image below shows $A\cup C$ .

How could I plot the inverse, that is how would one fill the part of B not in A or C $B - (A\cup C)$ , and leave A and C with no fill?

In case it's helpful, here is the code for making the picture shown:

\begin{tikzpicture}
  \filldraw[fill=lightgray] (0, 0) circle (1) {};
  \filldraw[fill=lightgray] (3.2, 0) circle (1) {};
  \draw (1.6, 0) circle (1) {};
  \node at (0, 0) {A};
  \node at (1.6, 0) {B};
  \node at (3.2, 0) {C};
\end{tikzpicture}

A very detailed discussion of Venn diagrams can be found here. — kabenyuk, Apr 24 '22 at 03:57
Minor note: the proper syntax for virvles is circle[radius=1] and the empty group {} isn't needed as it doesn't do anything. — Andrew Stacey, Apr 24 '22 at 17:09
Thanks @AndrewStacey. I guess I didn't realize that since my radius was the default value. — ramzeek, Apr 24 '22 at 21:29

SebGlav · Accepted Answer · 2022-04-24T15:30:27.423

4

The inconvenient of filling A and C in white is that if you have a couloured background, it will be bad looking.

To avoid that and keep A and C transparent, you can use even odd rule and \clip:

\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
    \begin{tikzpicture}
        \def\A{(0, 0) circle (1)}
        \def\B{(1.6, 0) circle (1)}
        \def\C{(3.2, 0) circle (1)}
    \begin{scope}
        \clip \B;
        \fill[lightgray,even odd rule] \A \B \C;
    \end{scope}

    \draw \A node {A} \B node {B} \C node {C};
\end{tikzpicture}

\end{document}

edited Apr 24 '22 at 15:30

answered Apr 24 '22 at 08:06

SebGlav

19,186

1

This is what I was looking for, just didn't know it existed. – ramzeek Apr 24 '22 at 21:28
Nice! Feel free to accpet the answer that suits you the most, then. – SebGlav Apr 24 '22 at 22:26

score 1 · Answer 2 · answered Apr 24 '22 at 03:50

Solution: fill the circles with B first and at the back, and A and C on top with white fill, then draw a circle for B on top to get its edges:

\begin{tikzpicture}
  \filldraw[fill=lightgray] (0, 0) circle (1) {};
  \filldraw[fill=lightgray] (3.2, 0) circle (1) {};
  \draw (1.6, 0) circle (1) {};
  \node at (0, 0) {A};
  \node at (1.6, 0) {B};
  \node at (3.2, 0) {C};
\filldraw[fill=lightgray] (8.6, 0) circle (1) {};
  \filldraw[fill=white] (7, 0) circle (1) {};
  \filldraw[fill=white] (10.2, 0) circle (1) {};
  \draw (8.6, 0) circle (1) {};
  \node at (7, 0) {A};
  \node at (8.6, 0) {B};
  \node at (10.2, 0) {C};
\end{tikzpicture}

score 0 · Answer 3 · answered Apr 27 '22 at 02:18

Here are some code of the cheap and nice way of @Sandy G (deleted! don't know why ^^)

\documentclass[tikz,border=5mm]{standalone}
\pagecolor{yellow!50}
\begin{document}
\begin{tikzpicture}
\def\a{1.6} 
\fill[cyan!50] (\a,0) circle(1);
\draw[fill=white] (0,0) circle(1) (2*\a,0) circle(1);
\draw (\a,0) circle(1);
\path (0,0) node {$A$} (\a,0) node {$B$} (2*\a,0) node {$C$};
\end{tikzpicture}
\end{document}

and a translation to Asymptote

// http://asymptote.ualberta.ca/
unitsize(1cm);
real a=1.6;
path p=unitcircle;
fill(shift(a,0)p,magenta+white);
filldraw(p^^shift(2a,0)p,white);
draw(shift(a,0)*p);
label("$A$"); label("$B$",(a,0)); label("$C$",(2a,0));
shipout(bbox(5mm,Fill(yellow+white)));

Plot difference of sets in tikz

3 Answers3

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