Venn Diagram

Introduction

There are different types of diagrams that can be made using LaTeX, for example there is the Venn's diagram, a descriptive diagram and much more. Some diagrams are not complicated to make, but they may also take a lot of time to be made, and there are others that are much more complicated like this one:

CODE

\documentclass[border=10pt]{standalone}
              \usepackage{tikz}
              \usetikzlibrary{calc,positioning,shadows.blur,decorations.pathreplacing}
              \usepackage{etoolbox}

              \tikzset{%
                      brace/.style = { decorate, decoration={brace, amplitude=5pt} },
                     mbrace/.style = { decorate, decoration={brace, amplitude=5pt, mirror} },
                      label/.style = { black, midway, scale=0.5, align=center },
                   toplabel/.style = { label, above=.5em, anchor=south },
                  leftlabel/.style = { label,rotate=-90,left=.5em,anchor=north },
                bottomlabel/.style = { label, below=.5em, anchor=north },
                      force/.style = { rotate=-90,scale=0.4 },
                      round/.style = { rounded corners=2mm },
                     legend/.style = { right,scale=0.4 },
                      nosep/.style = { inner sep=0pt },
                 generation/.style = { anchor=base }
              }

              \newcommand\particle[7][white]{%
                \begin{tikzpicture}[x=1cm, y=1cm]
                  \path[fill=#1,blur shadow={shadow blur steps=5}] (0.1,0) -- (0.9,0)
                      arc (90:0:1mm) -- (1.0,-0.9) arc (0:-90:1mm) -- (0.1,-1.0)
                      arc (-90:-180:1mm) -- (0,-0.1) arc(180:90:1mm) -- cycle;
                  \ifstrempty{#7}{}{\path[fill=purple!50!white]
                      (0.6,0) --(0.7,0) -- (1.0,-0.3) -- (1.0,-0.4);}
                  \ifstrempty{#6}{}{\path[fill=green!50!black!50] (0.7,0) -- (0.9,0)
                      arc (90:0:1mm) -- (1.0,-0.3);}
                  \ifstrempty{#5}{}{\path[fill=orange!50!white] (1.0,-0.7) -- (1.0,-0.9)
                      arc (0:-90:1mm) -- (0.7,-1.0);}
                  \draw[\ifstrempty{#2}{dashed}{black}] (0.1,0) -- (0.9,0)
                      arc (90:0:1mm) -- (1.0,-0.9) arc (0:-90:1mm) -- (0.1,-1.0)
                      arc (-90:-180:1mm) -- (0,-0.1) arc(180:90:1mm) -- cycle;
                  \ifstrempty{#7}{}{\node at(0.825,-0.175) [rotate=-45,scale=0.2] {#7};}
                  \ifstrempty{#6}{}{\node at(0.9,-0.1)  [nosep,scale=0.17] {#6};}
                  \ifstrempty{#5}{}{\node at(0.9,-0.9)  [nosep,scale=0.2] {#5};}
                  \ifstrempty{#4}{}{\node at(0.1,-0.1)  [nosep,anchor=west,scale=0.25]{#4};}
                  \ifstrempty{#3}{}{\node at(0.1,-0.85) [nosep,anchor=west,scale=0.3] {#3};}
                  \ifstrempty{#2}{}{\node at(0.1,-0.5)  [nosep,anchor=west,scale=1.5] {#2};}
                \end{tikzpicture}
              }

              \begin{document}
              \begin{tikzpicture}[x=1.2cm, y=1.2cm]
                \draw[round] (-0.5,0.5) rectangle (4.4,-1.5);
                \draw[round] (-0.6,0.6) rectangle (5.0,-2.5);
                \draw[round] (-0.7,0.7) rectangle (5.6,-3.5);

                \node at(0, 0)   {\particle[gray!20!white]
                                 {$u$}        {up}       {$2.3$ MeV}{1/2}{$2/3$}{R/G/B}};
                \node at(0,-1)   {\particle[gray!20!white]
                                 {$d$}        {down}    {$4.8$ MeV}{1/2}{$-1/3$}{R/G/B}};
                \node at(0,-2)   {\particle[gray!20!white]
                                 {$e$}        {electron}       {$511$ keV}{1/2}{$-1$}{}};
                \node at(0,-3)   {\particle[gray!20!white]
                                 {$\nu_e$}    {$e$ neutrino}         {$<2$ eV}{1/2}{}{}};
                \node at(1, 0)   {\particle
                                 {$c$}        {charm}   {$1.28$ GeV}{1/2}{$2/3$}{R/G/B}};
                \node at(1,-1)   {\particle
                                 {$s$}        {strange}  {$95$ MeV}{1/2}{$-1/3$}{R/G/B}};
                \node at(1,-2)   {\particle
                                 {$\mu$}      {muon}         {$105.7$ MeV}{1/2}{$-1$}{}};
                \node at(1,-3)   {\particle
                                 {$\nu_\mu$}  {$\mu$ neutrino}    {$<190$ keV}{1/2}{}{}};
                \node at(2, 0)   {\particle
                                 {$t$}        {top}    {$173.2$ GeV}{1/2}{$2/3$}{R/G/B}};
                \node at(2,-1)   {\particle
                                 {$b$}        {bottom}  {$4.7$ GeV}{1/2}{$-1/3$}{R/G/B}};
                \node at(2,-2)   {\particle
                                 {$\tau$}     {tau}          {$1.777$ GeV}{1/2}{$-1$}{}};
                \node at(2,-3)   {\particle
                                 {$\nu_\tau$} {$\tau$ neutrino}  {$<18.2$ MeV}{1/2}{}{}};
                \node at(3,-3)   {\particle[orange!20!white]
                                 {$W^{\hspace{-.3ex}\scalebox{.5}{$\pm$}}$}
                                              {}              {$80.4$ GeV}{1}{$\pm1$}{}};
                \node at(4,-3)   {\particle[orange!20!white]
                                 {$Z$}        {}                    {$91.2$ GeV}{1}{}{}};
                \node at(3.5,-2) {\particle[green!50!black!20]
                                 {$\gamma$}   {photon}                        {}{1}{}{}};
                \node at(3.5,-1) {\particle[purple!20!white]
                                 {$g$}        {gluon}                    {}{1}{}{color}};
                \node at(5,0)    {\particle[gray!50!white]
                                 {$H$}        {Higgs}              {$125.1$ GeV}{0}{}{}};
                \node at(6.1,-3) {\particle
                                 {}           {graviton}                       {}{}{}{}};

                \node at(4.25,-0.5) [force]      {strong nuclear force (color)};
                \node at(4.85,-1.5) [force]    {electromagnetic force (charge)};
                \node at(5.45,-2.4) [force] {weak nuclear force (weak isospin)};
                \node at(6.75,-2.5) [force]        {gravitational force (mass)};

                \draw [<-] (2.5,0.3)   -- (2.7,0.3)          node [legend] {charge};
                \draw [<-] (2.5,0.15)  -- (2.7,0.15)         node [legend] {colors};
                \draw [<-] (2.05,0.25) -- (2.3,0) -- (2.7,0) node [legend]   {mass};
                \draw [<-] (2.5,-0.3)  -- (2.7,-0.3)         node [legend]   {spin};

                \draw [mbrace] (-0.8,0.5)  -- (-0.8,-1.5)
                               node[leftlabel] {6 quarks\\(+6 anti-quarks)};
                \draw [mbrace] (-0.8,-1.5) -- (-0.8,-3.5)
                               node[leftlabel] {6 leptons\\(+6 anti-leptons)};
                \draw [mbrace] (-0.5,-3.6) -- (2.5,-3.6)
                               node[bottomlabel]
                               {12 fermions\\(+12 anti-fermions)\\increasing mass $\to$};
                \draw [mbrace] (2.5,-3.6) -- (5.5,-3.6)
                               node[bottomlabel] {5 bosons\\(+1 opposite charge $W$)};

                \draw [brace] (-0.5,.8) -- (0.5,.8) node[toplabel]         {standard matter};
                \draw [brace] (0.5,.8)  -- (2.5,.8) node[toplabel]         {unstable matter};
                \draw [brace] (2.5,.8)  -- (4.5,.8) node[toplabel]          {force carriers};
                \draw [brace] (4.5,.8)  -- (5.5,.8) node[toplabel]       {Goldstone\\bosons};
                \draw [brace] (5.5,.8)  -- (7,.8)   node[toplabel] {outside\\standard model};

                \node at (0,1.2)   [generation] {1\tiny st};
                \node at (1,1.2)   [generation] {2\tiny nd};
                \node at (2,1.2)   [generation] {3\tiny rd};
                \node at (2.8,1.2) [generation] {\tiny generation};
              \end{tikzpicture}
              \end{document}

This is obviously only an example of what can be done with LaTeX and the Tikz package, we are not going to learn how to do complicated stuff like the previous one.

I. Venn's Diagram

In this subsection we are only going to present you how a Venn's diagram is done in LaTeX.
The Venn's diagram is one of the most known diagrams used in Mathematic, Physics and also Chemistry.
A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set. The points inside a curve labelled S represent elements of the set S, while points outside the boundary represent elements not in the set S. With this type of diagram it is easy to see if 2 sets have elements in common. For example, having two sets, S and T, it will be very easy to find S ∩ T, it is enough to check where the 2 sets overlap.
This is an example of a Venn's diagram drawn with Latex:

CODE

\documentclass{letter}
  \usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \begin{scope}[blend group=soft light]
    \fill[red!30!white]   ( 90:1.2) circle (2);
    \fill[green!30!white] (210:1.2) circle (2);
    \fill[blue!30!white]  (330:1.2) circle (2);
 \end{scope}
  \node at ( 90:2)    {Typography};
  \node at (210:2)    {Design};
  \node at (330:2)    {Coding};
  \node [font=\Large] {\LaTeX};
\end{tikzpicture}
\end{document}

In this example we see that the blue area correspond to the area which c has in common with a and b, in math we can write: c ∩ (a ∪ b).
This is how the content is created:
At the beginning we use a scope environment to apply a style to a part of the drawing. Here, we apply color blending:

CODE

\begin{scope}[blend group=soft light]

We draw the diagram parts, which in our case are simply filled circles:

CODE

\fill[red!30!white]   ( 90:1.2) circle (2);

    \fill[green!30!white] (210:1.2) circle (2);

    \fill[blue!30!white]  (330:1.2) circle (2);

Then we end the scope environment. At the end of the environment, the blending effect will end, because environments keep the settings local.
Afterwards we add nodes with text for the descriptions:

CODE

\node at ( 90:2)    {Typography};

    \node at (210:2)    {Design};

    \node at (330:2)    {Coding};

    \node [font=\Large] {\LaTeX};