TikZ-PGF – Drawing a Venn Diagram

tikz-pgfvenn-diagrams

Below is a Venn diagram I created in TikZ.
enter image description here

Here is the code. I want to now add a set E such that
D is a proper subset of E and E is a proper subset of B. It is apparent that the set E cannot be drawn as a circle. At best, it can the boundary of E can be the arc on the right side of D, coupled with a different arc on the left side between the boundaries of B and D. And I want to have a different color for E, say yellow. What is the best way to go about?

\documentclass{article}

\usepackage{tikz}
\begin{document}
\pagestyle{empty}
\begin{tikzpicture}
    \begin{scope}[shift={(3cm,-5cm)}, fill opacity=0.5]
        \draw[fill=red, draw = black] (0,0) circle (5);
        \draw[fill=green, draw = black] (-1.5,0) circle (3);
    \draw[fill=blue, draw = black] (1.5,0) circle (3);
    \node at (0,4) (A) {\large\textbf{A}};
    \node at (-2,1) (B) {\large\textbf{B}};
    \node at (2,1) (C) {\large\textbf{C}};
    \node at (0,0) (D) {\large\textbf{D}};
    \end{scope}

\end{tikzpicture}
\end{document}

Best Answer

Here's one possibility using the intersections library to find the coordinates of the intersection points between the two inner circles and then using the .. controls <point> and <point> .. syntax to draw the curve; some additional work with transparency groups was also done to obtain the proper coloring:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections}

\begin{document}
\pagestyle{empty}
\begin{tikzpicture}

\begin{scope}[shift={(3cm,-5cm)}, fill opacity=0.5,
  mytext/.style={text opacity=1,font=\large\bfseries}]

\draw[fill=red, draw = black] (0,0) circle (5);
\draw[fill=yellow, draw = black,name path=circle 1] (-1.5,0) circle (3);
\draw[fill=blue, draw = black,name path=circle 2] (1.5,0) circle (3);

\pgftransparencygroup
\clip (-1.5,0) circle (3);
\fill[green] (1.5,0) circle (3);
\filldraw[draw,fill=green,name intersections={of=circle 1 and circle 2}] (intersection-1) .. controls +(-4,1) and +(-4,-1) ..(intersection-2);
\endpgftransparencygroup

\node[mytext] at (0,4) (A) {A};
\node[mytext] at (-3.8,0) (B) {B};
\node[mytext] at (3.8,0) (C) {C};
\node[mytext] at (0,0) (D) {D};
\node[mytext] at (-2,1) (E) {E};
\end{scope}
\end{tikzpicture}

\end{document}

enter image description here

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[Tex/LaTex] Numerical conditional within tikz keys

I am definitely unfamiliar with both beamer and tikz (do not quite get what the \only are supposed to do) but perhaps this could go in the direction you want:

\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{chains}
\newcounter{count}

% helper macro:
\long\def\GobToSemiColon #1;{}

\newcommand\myPicture{
\begin{tikzpicture}
  \begin{scope}[start chain = going below]
  \ifnum\value{count}<1 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>3 \expandafter\GobToSemiColon\fi
  \node[draw, rectangle, on chain] {display only when counter is between
    1 and 3};

  \ifnum\value{count}>-1 \expandafter\GobToSemiColon\fi
  \node[draw, rectangle, on chain] {display only when counter is
    negative}; 

  \ifnum\value{count}<100 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>200 \expandafter\GobToSemiColon\fi  
  \node[draw, rectangle, on chain] {display only if counter is between
    100 and 200};

  \ifnum\value{count}<3 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>20 \expandafter\GobToSemiColon\fi
  \node[draw, circle, on chain] {only when counter is in the range 3 to 20};
  \end{scope}
\end{tikzpicture}
}

\begin{document}
\begin{frame}
\only{\setcounter{count}{-3}\myPicture}
\only{\setcounter{count}{105}\myPicture}
\only{\setcounter{count}{39}\myPicture}
\only{\setcounter{count}{2}\myPicture}
\only{\setcounter{count}{5}\myPicture}
\end{frame}
\end{document}

beamer

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

A solution which allows to draw intersection segments of any two intersections is available as tikz library fillbetween.

This library works as general purpose tikz library, but it is shipped with pgfplots and you need to load pgfplots in order to make it work:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];

\end{tikzpicture}

\end{document}

enter image description here

The key intersection segments is described in all detail in the pgfplots reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path temp1 which is the first intersection segment of red and blue, more precisely, it is the first intersection segment in the Left argument in red and blue : red. This path is drawn as thin black path. Substitute its \draw statement by \path to make it invisible.
Compute the desired intersection segment by intersecting temp1 and green and use the correct intersection segment. By trial and error I figured that it is the third segment of path temp1 which is written as L3 (L = left argument in temp1 and green and 3 means third segment of that path).

The argument involves some trial and error because fillbetween is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an intersection segment should be the continuation of another path, use -- as before the first argument in sequence. This allows to fill paths segments:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]  
    [intersection segments={of=temp1 and green, sequence={--R2}}]
;

\end{tikzpicture}

\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] Numerical conditional within tikz keys

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

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