7

My knowledge of tikz is very limited. How can I move the middle circle (M_3) up, so that it looks like a typical Venn diagram?

My progress so far:

enter image description here

My code so far:

\documentclass{article}

\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
    \def\firstcircle{(0,0) circle (1.5cm)}
    \def\secondcircle{(0:2cm) circle (1.5cm)}
    \def\thirdcircle{(0:1cm) circle (1.5cm)}
            
    \colorlet{circle edge}{red!50}
    \colorlet{circle area}{red!20}
            
    \tikzset{filled/.style={fill=circle area, draw=circle edge, thick},
        outline/.style={draw=circle edge, thick}}
            
    \setlength{\parskip}{5mm}

    \begin{scope}
        \clip \secondcircle;
        \fill[filled] \thirdcircle;
    \end{scope}

    \begin{scope}
        \clip \firstcircle;
        \fill[filled] \thirdcircle;
    \end{scope}

    \draw[outline] \firstcircle node {$M_1$};
    \draw[outline] \secondcircle node {$M_2$};
    \draw[outline] \thirdcircle node {$M_3$};

    \node[anchor=south] at (current bounding box.north) {$M_1 \cap M_2 \cap M_3$};
\end{tikzpicture}

\end{document}

Thank you!

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  • You could change the definition of the \thirdcircle to \def\thirdcircle{([yshift=1.5cm]0:1cm) circle (1.5cm)} – vi pa Dec 5 '20 at 12:14
  • 3
    Please always make your code snippets complete MWEs, i.e. they should start with \documentclass and end with \end{document}. – schtandard Dec 5 '20 at 13:11
  • @schtandard, now the MWE is complete. Thank you! – NilsK Dec 6 '20 at 10:44
  • @vipa The answer box is down there: ↓↓↓. Please don't answer in comments; it bypasses the site's quality-control mechanisms. – wizzwizz4 Dec 6 '20 at 12:28
  • @wizzwizz4 I'll make it. – vi pa Dec 6 '20 at 12:33
5

Use polar coordinates.

\documentclass{article}

\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
    \def\firstcircle {(210:1.1cm) circle (1.5cm)}
    \def\secondcircle{(330:1.1cm) circle (1.5cm)}
    \def\thirdcircle {( 90:1.1cm) circle (1.5cm)}
            
    \colorlet{circle edge}{red!50}
    \colorlet{circle area}{red!20}
            
    \tikzset{filled/.style={fill=circle area, draw=circle edge, thick},
        outline/.style={draw=circle edge, thick}}
            
    \setlength{\parskip}{5mm}

    \begin{scope}
        \clip \secondcircle;
        \fill[filled] \thirdcircle;
    \end{scope}

    \begin{scope}
        \clip \firstcircle;
        \fill[filled] \thirdcircle;
    \end{scope}

    \draw[outline] \firstcircle node {$M_1$};
    \draw[outline] \secondcircle node {$M_2$};
    \draw[outline] \thirdcircle node {$M_3$};

    \node[anchor=south] at (current bounding box.north) {$M_1 \cap M_2 \cap M_3$};
\end{tikzpicture}

\end{document}

MWE output

(Note that the expression above your drawing does not fit the shaded area in the drawing.)

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  • Thank you for the answer @schtandard. – NilsK Dec 6 '20 at 10:39
6

In this Asymptote solution we create a set of the key points first, then using them as the centers of the circles and corresponding begin-end points of the circular arcs, we construct an addressable list of the area boundaries, so each area can be filled differently.

The color used for the intersecting region is chosen as an average of the colors of corresponding intersecting regions.

The named points are shown for convenience.

//
// Venn-diag.asy
//
// run 
//   asy Venn-diag.asy
//
//  to get a standalone  Venn-diag.pdf
//
settings.tex="pdflatex";
size(7cm);
import fontsize;defaultpen(fontsize(8pt));
texpreamble("\usepackage{lmodern}"+"\usepackage{amsmath}"
+"\usepackage{amsfonts}"+"\usepackage{amssymb}");
pair A,B,C,D,E,F,O;
transform t=rotate(120);
O=0;   A=(0,-1/sqrt(3));
B=t*A; C=t*B;
D=A-1; E=A+1; F=2B-E;
guide[] g={arc(A,D,E)&arc(B,E,A,CW)&arc(C,A,D,CW)&cycle,};
g.cyclic=true;
g.push(t*g[-1]);
g.push(t*g[-1]);
g.push(arc(B,A,E)&arc(A,E,B)&arc(C,B,A,CW)&cycle);
g.push(t*g[-1]);
g.push(t*g[-1]);
g.push(arc(C,A,B)&arc(A,B,C)&arc(B,C,A)&cycle);
pen[] fPen={lightred,deepgreen,lightblue,};
fPen.push(0.5*(fPen[0]+fPen[1]));
fPen.push(0.5*(fPen[1]+fPen[2]));
fPen.push(0.5*(fPen[2]+fPen[0]));
fPen.push(1/3*(fPen[0]+fPen[1]+fPen[2]));
for(int i=0;i<fPen.length;++i) fill(g[i],fPen[i]);
draw(circle(A,1),red+.7*bp);      
draw(circle(B,1),deepgreen+.7*bp);
draw(circle(C,1),blue+.7*bp);     
string[] s=array("ABCDEF");
pair[] p={A,B,C,D,E,F,};
dot(p,UnFill);
for(int i=0;i<p.length;++i) label("$"+s[i]+"$",p[i],dir(p[i]));  
pair L=A-(0,1/2);
for(int i=0;i<3;++i)label("$\mathbf M_"+string(i+1)+"$",t^i*L,white); 
L=(A+B+E)/3*1.2;
label("$M_1\cap M_2$",L,white); 
label("$M_2\cap M_3$",t*L,white); 
label("$M_1\cap M_3$",t^2*L,white); 
label("$M_1\cap M_2\cap M_3$",white);

enter image description here

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2

@schtandard already answered my question. However, for those who are looking for a drawing that matches the description, I provide the adapted version of @schtandard's solution:

enter image description here

\begin{tikzpicture}
    \def\firstcircle {(210:1.1cm) circle (1.5cm)}
    \def\secondcircle{(330:1.1cm) circle (1.5cm)}
    \def\thirdcircle {( 90:1.1cm) circle (1.5cm)}
            
    \colorlet{circle edge}{red!50}
    \colorlet{circle area}{red!20}
            
    \tikzset{filled/.style={fill=circle area, draw=circle edge, thick},
        outline/.style={draw=circle edge, thick}}
            
    \setlength{\parskip}{5mm}
            
    \begin{scope}
        \clip \secondcircle;
        \clip \firstcircle;
        \fill[filled] \thirdcircle;
    \end{scope}
            
    \draw[outline] \firstcircle node {$M_1$};
    \draw[outline] \secondcircle node {$M_2$};
    \draw[outline] \thirdcircle node {$M_3$};
            
    \node[anchor=south] at (current bounding box.north) {$M_1 \cap M_2 \cap M_3$};
\end{tikzpicture}
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