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 ====== How to draw diagrams in LaTeX with TikZ ======

Nice looking diagrams can be drawn in LaTeX with the versatile ''TikZ'' package. This page shows some examples that are useful for our CMS group.

''TikZ'' should work out-of-the-box with ''\usepackage{tikz}'', but the syntax is not so straightforward at first. To get started, take a look at these materials:
  * [[https://www.sharelatex.com/blog/2013/08/27/tikz-series-pt1.html|Some basic shapes]].
  * [[https://www.tug.org/TUGboat/tb29-1/tb91walczak.pdf|Some more basic shapes]].
  * [[http://www.texample.net/tikz/examples/|TeXample]]: A large database of simple and advanced examples with a [[http://www.texample.net/tikz/examples/area/physics/|physics section]], including a Feynman diagram and a Standard Model diagram. This website will be superseded by [[https://tikz.net|TikZ.net]].
  * The examples below and many more are also available on [[https://github.com/IzaakWN/CodeSnippets/tree/master/LaTeX/TikZ|GitHub]] and [[https://ineuteli.web.cern.ch/ineuteli/diagrams/|this gallery page]].
  * [[http://pgf.sourceforge.net/pgf_CVS.pdf|Official TikZ & PGF manual]].
  * [[http://tug.ctan.org/info/visualtikz/VisualTikZ.pdf|Visual Tikz]]: an extensive cheat sheet with TikZ's many features and commands. 
  * For Feynman diagrams, please see [[latex:feynman|this page]].

 ===== Control regions =====

Control regions are simple enough to draw in ''TikZ'', since it is in 2D and only requires to draw arrows, rectangulars and nodes (nodes are simple points, which useful for labeling). Below are two examples. The ''tex'' file containing both can be found [[latex:example_control_region|here]].

A simple example of 2D axes and colored rectangles, with custom colors defined in the preamble:

<code latex>
  \definecolor{mylightred}{RGB}{255,200,200}
  \definecolor{mylightblue}{RGB}{172,188,63}
  \definecolor{mylightgreen}{RGB}{150,220,150}
</code>

<WRAP group><WRAP half column lo 55%>
<code latex>
\begin{tikzpicture}[scale=6]

% define to change easily 
\def\isoe{0.15}
\def\isomu{0.20}
\def\isoSB{0.50}
\def\isomax{0.60}

% axes
\draw[->,thick]
  (0,0) -- (0,\isomax)
  node[at end,left=24pt,rotate=90] {muon isolation $I_\mu$};
\draw[->,thick]
  (0,0) -- (\isomax,0)
  node[at end,below=16pt,left] {electron isolation $I_\text{e}$};

% boxes
\draw[thick,fill=mylightgreen]
  (0,0) rectangle (\isoSB,\isoSB)
  node[anchor=north east] {SB};
\draw[thick,fill=mylightred]
  (0,0) rectangle (\isoe,\isomu)
  node[anchor=north east] {SR};

% labels
\draw
  (0,\isomu) node[anchor=east]  {\scriptsize$\isomu$}
  (0,\isoSB) node[anchor=east]  {\scriptsize$\isoSB$}
  (\isoe, 0) node[anchor=north] {\scriptsize$\isoe$}
  (\isoSB,0) node[anchor=north] {\scriptsize$\isoSB$};

\end{tikzpicture}
</code>
</WRAP><WRAP half column 40%>
\\ \\ \\ \\
{{ latex:control_region_isolation.png ? 400 }}
\\ \\ \\ \\ \\
</WRAP></WRAP>

A simple example of a rectangle, dashed lines and using the ''scope'' environment to change the coordinate system locally in the code. In this example the coordinate system is shifted and scaled, but it also possible to do rotations (''rotate=60'') or scale only horizontally (vertically) with ''xscale=1.5'' (''yscale=1.5'').

<WRAP group><WRAP half column lo 55%>
<code latex>
\begin{tikzpicture}[scale=4]

% axes
\draw[thick]
  (0,0) rectangle (1,1);

% boxes
\draw[dashed,thick]
  (0.5,-0.1) -- (0.5,1);
\draw[dashed,thick]
  (-0.1,0.5) -- (1,0.5);

% labels
\draw
  (0,0.75) node[anchor=east]  {OS}
  (0,0.25) node[anchor=east]  {SS}
  (0.25,0) node[anchor=north] {SR}
  (0.75,0) node[anchor=north] {SB};
\draw
  (0.25,0.75) node {QCD}
  (0.75,0.25) node[text width=40,align=center] {QCD\\shape};

% arrows
\begin{scope}[shift={(0.51,0.52)},scale=0.3]
  \draw[->,thick]
    (0.5,-0.5) -- (-0.5,0.5)
    node[midway, above=6pt, right=1pt] {\scriptsize$F$};
\end{scope}

\end{tikzpicture}
</code>
</WRAP><WRAP half column 40%>
\\ \\ \\ \\
{{ latex: control_region_OS_SS.png ? 300 }}
\\ \\ \\ \\ \\
</WRAP></WRAP>




 ===== Sets =====

Another simple example of a rectangle with rounded corners:

<WRAP group><WRAP half column 55% lo>
<file latex sets.tex>
\documentclass{article}
\usepackage{tikz}

% split figures into pages
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}%

\begin{document}

% SET: critical region
\begin{tikzpicture}[scale=1.0]
  \draw[black,rounded corners=10,thick]
     (0,0) rectangle (4,2)
     node[above left] {data space $\Omega$};
  \draw[black,rounded corners=10,thick,shift={(0.15,0.15)}]
    (2,0) rectangle (0,1)
     node[above right] {critical region $\omega$};
\end{tikzpicture}

\end{document}
</file>
</WRAP><WRAP half column 40%>
\\ \\ \\ \\
{{ latex:sets.png ? 300 }}
\\ \\ \\ \\
</WRAP></WRAP>



 ===== Flowchart =====

Example of a flow chart by using predefined drawing styles and a predefined box with ''\def'' and arguments ([[latex:tikz:guitar_tunings|full code]]):

<WRAP group><WRAP half column 55% lo>
<code latex>
\begin{tikzpicture}[xscale=1.3,yscale=1.2,
                    fscale/.style={font=\relsize{#1}},
                    arrow/.style={->,thick,mydarkblue,shorten <=2,shorten >=4},
                    sarrow/.style={->,thick,mydarkblue,shorten <=2,shorten >=6}]
  \def\c{0.7}
  \def\m{5}
  \def\tuning(#1,#2,#3,#4,#5){
    \node[draw=mydarkblue,thick,rounded corners=\c,inner sep=\m] (#1) at (#2,#3) [fscale=1.2,anchor=south] {#4};
    \node[fill=white,inner sep=1] at (#1.north west) [fscale=-2,right=2,anchor=west,text=mydarkgreen] {#5};
  }
  
  % TUNINGS
  \tuning(E,  1, 5, EBEGBE,      open minor/cross-note E)
  \tuning(D,  0, 4, EADGBE,      standard E)
  \tuning(Dr, 2, 4, EBEG\sh\,BE, open E)
  \tuning(C,  0, 3, DADGBE,      drop D)
  \tuning(Cl,-2, 3, EAEAC\sh\,E, open A)
  \tuning(Bl,-1, 2, DGDGBD,      open G/spanish)
  \tuning(Br, 1, 2, DADFAD,      open minor/cross-note D)
  \tuning(A,  0, 1, DGCFAD,      standard D)
  \tuning(Ar, 2, 1, DADF\sh AD,  open D/vestapol)
  
  % ARROW
  \draw[sarrow,<-] (E)  -- (D);
  \draw[sarrow]    (E)  -- (Dr);
  \draw[arrow]     (D)  -- (C);
  \draw[sarrow]    (D)  -- (Cl);
  \draw[sarrow,<-] (Cl) -- (Bl) node[fscale=-2,midway,above=1,right=-2] {capo};
  \draw[sarrow]    (C)  -- (Bl);
  \draw[sarrow]    (C)  -- (Br);
  \draw[sarrow]    (Br) -- (A);
  \draw[sarrow]    (Br) -- (Ar);
  
\end{tikzpicture}
</code>
</WRAP><WRAP half column 40%>
\\ \\ \\ \\
{{ latex:tikz:guitar_tunings.png ? 1000 }}
\\ \\ \\ \\
</WRAP></WRAP>



Example of a node with arrows to text below it ([[latex:tikz:arrows_to_nodes|full code]]). Note the use of ''|-'' between coordinates to draw a line that first goes down vertically and then horizontally. Vice versa can be done with ''-|''. The ''\strut'' command is used to ensure that the text line has a fixed height.

<WRAP group><WRAP half column 55% lo>
<code latex>
\begin{tikzpicture}[yscale=0.8,anchor=west]
  
  % FIRST COLUMN
  \node[anchor=west,draw=myblue,fill=mylightblue,thick,rounded corners=4,inner sep=1.5pt] (L) at (0,4) {\;\strut$qq\nu\nu$\;};  
  \node (L1) at (0.5,3) {\strut$jj\nu\nu$};
  \node (L2) at (0.5,2) {\strut bb$\nu\nu$};
  \node (L3) at (0.5,1) {\strut tt$\nu\nu$};
  \draw[->,myblue,thick] (L.south west)++(0.18,0) |- (L1.west);
  \draw[->,myblue,thick] (L.south west)++(0.18,0) |- (L2.west);
  \draw[->,myblue,thick] (L.south west)++(0.18,0) |- (L3.west);
  
  % SECOND COLUMN
  \begin{scope}[shift={(2.5,0)}]
    \node[draw=myblue,fill=mylightblue,thick,rounded corners=4,inner sep=1.5pt] (M) at (0,4) {\;\strut$qq\ell\ell$\;};
    \node (M1) at (0.5,3) {\strut$jj\mu\mu$};
    \node (M2) at (0.5,2) {\strut bb$\tau\tau$, b$\tau\tau$};
    \node (M3) at (0.5,1) {\strut tt$\tau\tau$};
    \draw[->,myblue,thick] (M.south west)++(0.18,0) |- (M1.west);
    \draw[->,myblue,thick] (M.south west)++(0.18,0) |- (M2.west);
    \draw[->,myblue,thick] (M.south west)++(0.18,0) |- (M3.west);
  \end{scope}
  
  % THIRD COLUMN
  \begin{scope}[shift={(5.0,0)}]
    \node[draw=myblue,fill=mylightblue,thick,rounded corners=4,inner sep=1.5pt] (R) at (0,4) {\;\strut$qq\ell\nu$\;};
    \node (R1) at (0.5,3) {\strut$jj\mu\nu$};
    \draw[->,myblue,thick] (R.south west)++(0.18,0) |- (R1.west);
  \end{scope}
  
\end{tikzpicture}
</code>
</WRAP><WRAP half column 40%>
\\ \\ \\ \\
{{ latex:tikz:arrows_to_nodes.png ? 1000 }}
\\ \\ \\ \\
</WRAP></WRAP>


 ===== Atom models =====

Here are some example of making dots and circles, again with predefined colors in the preamle (see [[latex:example_atom|complete code]] for all three figures):

<code latex>
% colors
\definecolor{mylightred}{RGB}{255,210,210}
\definecolor{mydarkred}{RGB}{140,40,40}
\definecolor{mydarkblue}{RGB}{50,70,190}
</code>

<WRAP group><WRAP third column 30%>
{{ latex:atom_thomson_model.png ? 1000 }}
**Thomson model**: uniformly and positively charged sphere with negatively charged electrons.
</WRAP><WRAP third column 30%>
{{ latex:atom_rutherford_model2.png ? 1000 }}
**Simplified Rutherford model**: positively charged nucleus, uniformly and negatively charged sphere.
</WRAP><WRAP third column 27%>
{{ latex:atom_rutherford_model.png ? 1000 }}
**Rutherford model**: positively charged nucleus, with negatively charged "corpuscles" (electrons).
</WRAP></WRAP>

<code latex>
% ATOM MODEL: Simplified Rutherford model
\begin{tikzpicture}[scale=1]
  \coordinate (O)  at (0,0);
  \draw[mylightred,fill]
    (O) circle (50pt);
  \draw[mydarkred,thick]
    (O) circle (50pt) node[above right=34pt] {$-Ze$};
  \fill[radius=2.0pt,mydarkblue]
    (O) circle node[above=2pt] {$+Ze$};
\end{tikzpicture}
</code>



 ===== Vector sums & projections =====

Here is a simple example of projecting vectors, inspired by [[http://inspirehep.net/record/720080|Jang (2006) [Fig. 3.5]]]. The ''tex'' file can be found [[latex:example_projection|here]].

By using ''\coordinate'', your code become more readable, and more easy to adapt with new coordinate values.
<code latex>
\coordinate (A) at (1,2);
\coordinate (B) at (2,-3);
\draw (A) -- (B);
</code>
In addition, you can use the ''TikZ'' library ''calc'' to do arithmetics with the coordinates, e.g.
<code latex>
\coordinate (AB) at ($(A)+(B)$); % (3,-1)
</code>
And you can also acces the ''x'' and ''y'' components with ''let \p''. E.g. to define coordinate ''P'' as a projection of ''A'' onto the ''x''-axis:
<code latex>
\coordinate (A)  at (1,2);
\path let \p{A}=(A) in coordinate (P) at (\x{A},0); % (1,0), projection of A
</code>

<WRAP group><WRAP half column lo 65%>
<code latex>
\usetikzlibrary{calc} % to sum coordinates
\begin{tikzpicture}
  
  % vector labels
  \def\pT{ \vv{p}^\text{\tiny\,vis}_\text{\tiny\,T}}
  \def\pTA{\vv{p}^\text{\tiny\,vis}_\text{\tiny\,T,1}}
  \def\pTB{\vv{p}^\text{\tiny\,vis}_\text{\tiny\,T,2}}
  
  % define point
  \coordinate (O)  at (0.0, 0.0);
  \coordinate (Z)  at (3.5, 0.0);
  \coordinate (A)  at (1.0, 1.8);
  \coordinate (B)  at (1.2,-2.16);
  \coordinate (AB) at ($(A)+(B)$);
  \path let \p{AB}=(AB) in coordinate (P) at (\x{AB},0); % projection
  
  % axis
  \draw[->,thick,dashed]
    (-0.8,0) -- (Z)
    node[at end,below] {$\vv{\zeta}$};
  
  % main vectors
  \draw[->,thick,color=red]
    (O) -- (A)
    node[below=4pt,left=4pt,color=red] {$\pTA$};
  \draw[->,thick,color=red]
    (O) -- (B)
    node[above=2pt,left=2pt,color=red] {$\pTB$};
  \draw[->,color=red]
    (O) -- (AB)
    node[below=4pt,right,color=red,scale=1] {$\pT$}; %{$\sq\pTA+\,\pTB$};
  
  % helplines
  \draw[dashed,color=red]
    (A) -- (AB);
  \draw[dashed,color=red]
    (B) -- (AB);
  \draw[dashed,color=purple]
    (AB) -- (P);

  % vector sum
  \draw[->,thick,color=purple]
    (O) -- (P)
    node[right=4pt,above,color=purple] {$\vv{p}^\text{\tiny\,vis}_{\tiny\,\zeta}$};
  
\end{tikzpicture}
</code>
</WRAP><WRAP half column 30%>
\\ \\ \\
{{ latex:projection.png ? 1000 }}
\\ \\ \\ \\
</WRAP></WRAP>

with the predefined command
<code latex>
\newcommand*{\vv}[1]{\vec{\mkern0mu#1}}
</code>
in the preamble for better alignment of the vector arrow ''\vec'' over math symbols.





 ===== For-loops: Pseudorapidity 𝜂 and polar angle 𝜃 =====

Here are two example of using a for-loop with ''TikZ'''s ''\foreach''. In this case we loop over two variables. Full code can be found [[latex:exampe_eta|here]].

<WRAP group><WRAP half column lo 65%>
<code latex>

\begin{tikzpicture}[scale=3]
 
  % limits
  \def\R{1.2}
 
  % axis labels
  \node[below=5pt,left=2pt] at (0,\R) {$y$};
  \node[left=5pt,below=2pt] at (\R,0) {$z$};
 
  % lines
  \foreach \t in {90,60,45,30,10,0}{
    \draw[->,black!60!red,thick]
      (0,0) -- ({\R*cos(\t)},{\R*sin(\t)})
      node[anchor=180+\t,black] {$\theta=\t$};
  }
 
\end{tikzpicture}
</code>
</WRAP><WRAP half column 30%>
\\
{{ latex:theta.png ? 2000 }}
\\
</WRAP></WRAP>

Using a for-loop over two variables:
<WRAP group><WRAP half column lo 65%>
<code latex>
\begin{tikzpicture}[scale=3]
  
  % limits
  \def\R{1.2} % radius/length of lines
  
  % axis labels
  \node[scale=1,below left=1] at (0,\R) {$y$}; % y axis
  \node[scale=1,below left=1] at (\R,0) {$z$}; % z axis
  
  % lines
  \foreach \t/\e in {90/0,60/0.55,45/0.88,30/1.32,10/2.43,0/+\infty}{ % loop over theta/eta
    \pgfkeys{/pgf/number format/precision=2}
    \draw[->,black!60!red,thick,line cap=round] % eta lines
      (0,0) -- (\t:\R) node[anchor=180+\t,black] {$\eta=\e$}
      node[black,pos=0.7,fill=white,scale=0.8,inner sep=1.5pt] {$\theta=\t^\circ$};
  }
  
\end{tikzpicture}
</code>
</WRAP><WRAP half column 30%>
\\
{{ latex:tikz:axis2d_pseudorapidity.png ? 2000 }}
\\
</WRAP></WRAP>

Using for-loop and calculation + rounding:
<WRAP group><WRAP half column lo 65%>
<code latex>
\begin{tikzpicture}[scale=3]
  
  % limits
  \def\R{1.2} % radius/length of lines
  
  % axis labels
  \node[scale=1,below left=1] at (0,\R) {$y$}; % y axis
  \node[scale=1,below left=1] at (\R,0) {$z$}; % z axis
  
  % lines
  \pgfkeys{/pgf/number format/precision=2} % two decimals
  \foreach \t in {90,60,45,30,10,0}{ % loop over theta
    \ifnum \t = 0
      \def\e{+\infty} % infinity symbol
    \else
      \pgfmathparse{-ln(tan(\t/2))} % pseudorapidity
      %\pgfmathroundto{\pgfmathresult} % round without traling zeroes
      \pgfmathroundtozerofill{\pgfmathresult} % round with trailing zeroes
      \pgfmathsetmacro\e{\t==90?0:\pgfmathresult} % no trailing zeroes for theta = 0
    \fi
    \draw[->,black!60!red,thick,line cap=round] % eta lines
      (0,0) -- (\t:\R) node[anchor=180+\t,black] {$\eta=\e$}
      node[black,pos=0.7,fill=white,scale=0.8,inner sep=1.5pt] {$\theta=\t^\circ$};
  }
  
\end{tikzpicture}
</code>
</WRAP><WRAP half column 30%>
\\
{{ latex:tikz:axis2d_pseudorapidity.png ? 2000 }}
\\
</WRAP></WRAP>




 ===== Labeling angles =====

Here are two different ways of labeling an angle: using ''\draw pic'' or ''\pic''. Both give the same result and need the ''TikZ'' libraries '' angles'' and '' quotes''.
<WRAP group><WRAP half column 65%>
<code latex>
\usetikzlibrary{angles,quotes} % for pic (angle labels)
\begin{tikzpicture}
  
  % define point
  \coordinate (A)  at (3, 3);
  \coordinate (O)  at (0, 0);
  \coordinate (B)  at (4, 0);

  % angle  
  \draw[thick] (A) -- (O) -- (B);
  \draw pic[->,"$\alpha_1$",draw=black,angle radius=20,angle eccentricity=1.4]
    {angle = B--O--A};
  %\pic [draw,"$\alpha_1$",angle radius=20,->,angle eccentricity=1.4]
  %  {angle = B--O--A};
  
\end{tikzpicture}
</code>
</WRAP><WRAP half column 25%>
\\ \\ \\
{{ latex:angle1.png ? 1000 }}
\\ \\ \\ \\
</WRAP></WRAP>




 ===== Plotting 2D functions =====

Examples of plotting trigonometric functions with two different methods. Full code (borrowed from a friend) can be found [[latex:tikz:functions|here]].

With ''\draw plot(\x,{f(\x r)})'' (including ''\usepackage{tikz}'' for ''\dfrac''):

<WRAP group><WRAP half column lo 61%>
<code latex>
\begin{tikzpicture}[domain=-pi:pi,xscale=2/pi]
  
  % limits
  \def\xa{ -pi-0.3}
  \def\xb{3*pi+0.4}
  \def\ya{-3.4}
  \def\yb{ 3.6}
  \def\N{100} % number of points
  
  % axes & grid
  \draw[xstep=pi/2,very thin, color=gray]
    (\xa,\ya) grid (\xb,\yb);
  \draw[->]
    (\xa,0) -- (\xb,0)
    node[right] {$x$};
  \draw[->]
    (0,\ya) -- (0,\yb)
    node[left] {$y$};
  
  % ticks
  \draw[] % x
  	node[below,scale=0.9] at ( -pi,   0) {$-\pi$}
  	node[below,scale=0.9] at ( -pi/2, 0) {$-\dfrac{\pi}{2}$}
  	node[below,scale=0.9] at (  pi,   0) {$\pi$}
  	node[below,scale=0.9] at (     0, 0) {0}
  	node[below,scale=0.9] at (  pi/2, 0) {$\dfrac{\pi}{2}$}
  	node[below,scale=0.9] at (  pi,   0) {$\pi$}
  	node[below,scale=0.9] at (3*pi/2, 0) {$\dfrac{3\pi}{2}$}
  	node[below,scale=0.9] at (2*pi,   0) {$2\pi$}
  	node[below,scale=0.9] at (5*pi/2, 0) {$\dfrac{5\pi}{2}$}
  	node[below,scale=0.9] at (3*pi,   0) {$3\pi$};
  \draw[] % y
  	node[left,scale=0.9] at ( 0,  3) {$3$}
  	node[left,scale=0.9] at ( 0,  2) {$2$}
  	node[left,scale=0.9] at ( 0,  1) {$1$}
  	node[left,scale=0.9] at ( 0,  0) {$0$}
  	node[left,scale=0.9] at ( 0, -1) {$-1$}
  	node[left,scale=0.9] at ( 0, -2) {$-2$}
  	node[left,scale=0.9] at ( 0, -3) {$-3$};
  
  % function
  \def\ea{0.28}
  \def\eb{0.26}
  \draw[color=blue,samples=\N,domain=\xa:\xb] % SIN
    plot(\x,{sin(\x r)}) % r for radians
    node[above right] at (5*pi/2,1) {$\sin(x)$};
  \draw[color=red,samples=\N,domain=\xa:\xb] % COS
    plot(\x,{cos(\x r)})
    node[above left] at (2*pi,1) {$\cos(x)$};
  \draw[color=orange] % TAN
    plot[samples=\N,domain=  \xa     :   -pi/2-\eb] (\x, {tan(\x r)})
    plot[samples=\N,domain=  -pi/2+\ea:   pi/2-\eb] (\x, {tan(\x r)})
    plot[samples=\N,domain=   pi/2+\ea: 3*pi/2-\eb] (\x, {tan(\x r)})
    plot[samples=\N,domain= 3*pi/2+\ea: 5*pi/2-\eb] (\x, {tan(\x r)})
    plot[samples=\N,domain= 5*pi/2+\ea:  \xb      ] (\x, {tan(\x r)})
    node[samples=\N,right=-2pt] at (pi/2,2.5) {$\tan(x)$};
  
\end{tikzpicture}
</code>
</WRAP><WRAP half column 35%>
\\ \\ \\ \\ \\ \\ \\ \\
{{ latex:functions1.png ? 1000 }}
\\ \\ \\ \\ \\ \\ \\ \\ \\
</WRAP></WRAP>


With ''\addplot'' in the ''axis'' environment.

<WRAP group><WRAP half column lo 61%>
<code latex>
\begin{tikzpicture}[scale=1.2]
\begin{axis}[enlargelimits=false,
             axis lines=middle,
             scale=1.2,
             xtick={-3.15159, -1.57080, 0,
                     1.57080,  3.15159, 4.71239,
                     6.28318,  7.85398, 9.42478 }, 
             xticklabels={$-\pi$, $-\frac{1}{2}\pi$, 0,
                          $\frac{1}{2}\pi$, $\pi$, $\frac{3}{2}\pi$,
                          $2\pi$, $\frac{5}{2}\pi$, $3\pi$ },
             ytick={-3,-2,-1,0,1,2,3},
             grid=major, % only a grid on the defined ticks
             samples=100 % number of points
             ]
  
  % sin
  \addplot[blue,no marks,domain=-1.2*pi:3*pi]{sin(deg(x))}; % deg to convert radians
  \node[right=10pt,above] at (axis cs:5*pi/2,1){\color{blue}$\sin(x)$};
  
  % cos
  \addplot[red,no marks,domain=-1.2*pi:3*pi] {cos(deg(x))};
  \node[above left] at (axis cs:2*pi,1){\color{red}$\cos(x)$};
  
  % tan, multiple parts because of singularities
  \addplot[orange,no marks,domain=-1.2*pi:-0.583*pi, ]{tan(deg(x))};
  \addplot[orange,no marks,domain=-0.4*pi:5*pi/12,   ]{tan(deg(x))};
  \addplot[orange,no marks,domain=27*pi/45:17*pi/12, ]{tan(deg(x))};
  \addplot[orange,no marks,domain=1.6*pi:29*pi/12,   ]{tan(deg(x))};
  \addplot[orange,no marks,domain=2.6*pi:36*pi/12,   ]{tan(deg(x))};
  \node[right] at (axis cs:pi/2,2.5){\color{orange}$\tan(x)$};
  
\end{axis}
\end{tikzpicture}
</code>
</WRAP><WRAP half column 35%>
\\ \\ \\ \\ \\ \\
{{ latex:functions2.png ? 1000 }}
\\ \\ \\ \\ \\ \\ \\ 
</WRAP></WRAP>



<WRAP group><WRAP half column lo 61%>
<code latex>
\begin{tikzpicture}
\begin{axis}[enlargelimits=false,
             axis lines=middle,
             xtick={-2,-1,0,1,2},
             ytick={-1.570780, 1.570780, 3.14159},
             yticklabels={$-\frac{1}{2}\pi$,$\frac{1}{2}\pi$,$\pi$},
             grid=major,
             samples=100
             ]
  
  % arcsin
  \addplot[domain=-1:1,no marks,blue] {rad(asin(x))};
  \node at (axis cs:1.52,1.4){\color{blue}$\arcsin(x)$};
  
  % arccos
  \addplot[domain=-1:1,no marks,red] {rad(acos(x))};
  \node at (axis cs:-1.5,2.8){\color{red}$\arccos(x)$};
  
  % arctan
  \addplot[domain=-2:2,no marks,orange] {rad(atan(x))};
  \node at (axis cs:1.52,.67){\color{orange}$\arctan(x)$};
  
\end{axis}
\end{tikzpicture}
</code>
</WRAP><WRAP half column 35%>
\\ \\
{{ latex:functions3.png ? 1000 }}
\\ \\ \\
</WRAP></WRAP>



[[latex:tikz:numerical_sine|Full code]]:
<WRAP group><WRAP half column lo 61%>
<code latex>
\begin{tikzpicture}[scale=1.5,xscale=1/80]
  
  \def\N{60}
  \def\xmin{-10}  \def\xmax{320}
  \def\ymin{-1.2} \def\ymax{1.2}
  \def\tmin{-10}  \def\tmax{300}
  \def\blue{black!50!blue}, \def\red{black!50!red}
  \def\value{0.765}
  \def\Dtheta{20}
  
  % axes
  \draw[->,thick]
    (\xmin,0) -- (\xmax,0)
    node[anchor=north west] {$\theta$};
  \draw[->,thick]
    (0,\ymin) -- (0,\ymax)
    node[anchor=south east] {$y$};
  
  % plots
  \draw[thick,\blue,variable=\t,domain=\tmin:\tmax,samples=\N,smooth]
    plot (\t,{sin(2*\t)});
  \draw[thick,\red,variable=\t,domain=\tmin:\tmax,samples=\N,smooth]
    plot (\t,\value);
  
  % function labels
  \node[\blue,above right=1pt,scale=0.9] at (45,1) {$y=\sin2\theta$};
  \node[\red, below=1pt,scale=0.9] at (135,\value) {$y=\value$};
  
  % numerical solutions
  \draw[dashed,thick] (45-\Dtheta,-\value*0.05) -- (45-\Dtheta,\value*1.05);
  \draw[dashed,thick] (45+\Dtheta,-\value*0.05) -- (45+\Dtheta,\value*1.05);
  
  % ticks
  \foreach \x in {45,90,135,180,225,270}{
    \draw[thick]
      (\x,0.05) -- (\x,-0.05) node[below,scale=0.9] {\contour{white}{$\x^\circ$}};}
  \foreach \y in {1,-1}{
    \draw[thick]
      (4,\y) -- (-4,\y) node[left,scale=0.9] {$\y$};}
   
\end{tikzpicture}
</code>
</WRAP><WRAP half column 35%>
\\ \\ \\ \\ \\ \\
{{ latex:numerical_sine.png ? 1000 }}
\\ \\ \\
</WRAP></WRAP>



Here is an example from statistics, using the ''pgfplots'' library ''fillbetween'' to make a shaded area between a function and a path. The full code can be found [[latex:tikz:statistics|here]].
The ''gauss'' function is defined as

<code latex>
\pgfmathdeclarefunction{gauss}{3}{%
  \pgfmathparse{1/(#3*sqrt(2*pi))*exp(-((#1-#2)^2)/(2*#3^2))}%
}
</code>

<WRAP group><WRAP half column lo 61%>
<code latex>
% GAUSSIANs
\begin{tikzpicture}
  
  \def\q{13.8};
  \def\B{8.5};
  \def\S{18.5};
  \def\Bs{2.60};
  \def\Ss{3.40};
  \def\xmax{\S+3.2*\Ss};
  \def\ymin{{-0.15*gauss(\B,\B,\Bs)}};
  
  \begin{axis}[every axis plot post/.append style={
               mark=none,domain={-0.05*(\xmax)}:{1.08*\xmax},samples=80,smooth},
               xmin={-0.1*(\xmax)}, xmax=\xmax,
               ymin=\ymin, ymax={1.1*gauss(\B,\B,\Bs)},
               axis lines=middle,
               axis line style=thick,
               enlargelimits=upper, % extend the axes a bit to the right and top
               ticks=none,
               xlabel=$x$,
               every axis x label/.style={at={(current axis.right of origin)},anchor=north west},
              ]
    
    % plots
    \addplot[name path=B,thick,black!10!blue] {gauss(x,\B,\Bs)};
    \addplot[name path=S,thick,black!10!red ] {gauss(x,\S,\Ss)};
    \addplot[black,dashed,name path=Q,thick]
      coordinates {(\q, {0.90*gauss(\B,\B,\Bs)}) (\q, \ymin)}
      node[below=2pt,anchor=south west] {$x_\text{obs}$};
    
    % fill
    \path[name path=xaxis]
      (0,0) -- (\xmax,0);
    \addplot[white!50!blue] fill between[of=xaxis and B, soft clip={domain=\q:\xmax}];
    \addplot[white!50!red]  fill between[of=xaxis and S, soft clip={domain=0:\q}];
    
    % labels
    \node[above,      black!20!blue] at (1.12*\B,{gauss(\B,\B,\Bs)}) {$f(x|H_0)$};
    \node[above right,black!20!red ] at (1.05*\S,{gauss(\S,\S,\Ss)}) {$f(x|H_1)$};
    \node[above left, black!20!red ] at ({0.8*\q},{gauss(1.07*\q,\B,\Bs)}) {\strut$\beta$};
    \node[above right,black!20!blue] at ({1.1*\q},{gauss(1.07*\q,\B,\Bs)}) {\strut$\alpha$};
    
  \end{axis}
\end{tikzpicture}
</code>
</WRAP><WRAP half column 35%>
\\ \\ \\ \\ \\
{{ latex:statistics_confidence_level.png ? 1000 }}
\\ \\ \\
{{ latex:statistics_p_value.png ? 1000 }}
\\ \\ \\ \\ \\ \\
</WRAP></WRAP>



 ===== Plotting 2D parametrized functions: Rutherford scattering =====

Example of a hyperbolic orbit in Rutherford scattering of an 𝛼-particle off a nucleus with parametrized functions.
<code latex>
\def\a{1}
\def\b{2}
\def\N{100}
\draw[samples=\N,variable=\t,domain=-2:2]
    plot({-\a*cosh(\t)},{\b*sinh(\t)});
</code>
Full code can be found [[latex:tikz:hyperbola|here]].

<WRAP group><WRAP half column>
\\
{{ latex:tikz:hyperbola.png ? 2000 }}
</WRAP><WRAP half column>
{{ latex:tikz:hyberbolic_scattering_orbit_impact_parameter.png ? 2000 }}
</WRAP></WRAP>









 ===== Plotting 3D functions =====

Examples of plotting trigonometric functions in 3D ([[latex:tikz:electromagnetic_wave|full code]]).

<WRAP group><WRAP half column>
{{ latex:tikz:electromagnetic_wave.png ? 1000 }}
</WRAP><WRAP half column>
{{ latex:tikz:electromagnetic_wave_colored.png ? 1000 }}
</WRAP></WRAP>

<WRAP lo>
<code latex>
\begin{tikzpicture}[x=(-15:1.2), y=(90:1.0), z=(-150:1.0),
                    line cap=round, line join=round,
                    axis/.style={black, thick,->},
                    vector/.style={>=stealth,->}]
  \large
  \def\A{1.5}
  \def\nNodes{5} % use even number
  \def\nVectorsPerNode{8}
  \def\N{\nNodes*40}
  \def\xmax{\nNodes*pi/2*1.01}
  \pgfmathsetmacro\nVectors{(\nVectorsPerNode+1)*\nNodes}
  
  \def\vE{\mathbf{E}}
  \def\vB{\mathbf{B}}
  \def\vk{\mathbf{\hat{k}}}
  
  \draw[very thick,variable=\t,domain=0:\nNodes*pi/2*1.01,samples=\N]
    plot (\t,{\A*sin(\t*360/pi)},0);
  \draw[very thick,variable=\t,domain=0:\nNodes*pi/2*1.01,samples=\N]
    plot (\t,0,{\A*sin(\t*360/pi)});
  
  % main axes
  \draw[axis] (0,0,0) -- ++(\xmax*1.1,0,0) node[right] {$x$};
  \draw[axis] (0,-\A*1.4,0) -- (0,\A*1.4,0) node[right] {$y$};
  \draw[axis] (0,0,-\A*1.4) -- (0,0,\A*1.4) node[above left] {$z$};
  
  % ...
  
\end{tikzpicture}
</code>
</WRAP>



 ===== 3D axis with spherical coordinates & CMS coordinate system =====

This piece of code is based on [[https://tex.stackexchange.com/questions/116206/how-to-draw-and-annotate-a-spherical-coordinate-system|this StackExchange thread]]. It is a simple exercise in making axes and labeling angles in 3D. ''\usepackage{tikz-3dplot}'' needs to be included. The full code can be found [[https://tikz.net/axis3d/|here]].

<WRAP group><WRAP half column lo 65%>
<code latex>
\tdplotsetmaincoords{60}{110}
\begin{tikzpicture}[scale=3,tdplot_main_coords]

  % variables
  \def\rvec{.8}
  \def\thetavec{30}
  \def\phivec{60}
  
  % axes & vector
  \coordinate (O) at (0,0,0);
  \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
  \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
  \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};
  \tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec}
    \draw[-stealth,color=red] (O) -- (P) node[above right] {$P$};
  
  % arcs
  \draw[dashed, color=red] (O) -- (Pxy);
  \draw[dashed, color=red] (P) -- (Pxy);
  \tdplotdrawarc[->]{(O)}{0.2}{0}{\phivec}
    {anchor=north}{$\phi$}
  \tdplotsetthetaplanecoords{\phivec}
  \tdplotdrawarc[->,tdplot_rotated_coords]{(0,0,0)}{0.5}{0}{\thetavec}
    {anchor=south west}{$\theta$}

\end{tikzpicture}
</code>
</WRAP><WRAP half column 25%>
\\ \\ \\ \\
{{ latex:spherical_coordinates.png ? 1000 }}
\\ \\ \\ \\ \\ 
</WRAP></WRAP>


An example of rotating the 3D axes with the CMS conventional coordinate system by using the option ''rotate around x=<//angle//>'' and more ([[https://tikz.net/axis3d_cms|full code]]):

<WRAP group><WRAP third column 20%>
\\
</WRAP><WRAP third column 55%>
{{ cms_coordinate_system.png ? 1000 }}
</WRAP><WRAP third column 20%>
\\
</WRAP></WRAP>


<WRAP lo><code latex>
% CMS conventional coordinate system with LHC and other detectors
\tdplotsetmaincoords{75}{50} % to reset previous setting
\begin{tikzpicture}[scale=2.7,tdplot_main_coords,rotate around x=90]
  
  % variables
  \def\rvec{1.2}
  \def\thetavec{40}
  \def\phivec{70}
  \def\R{1.1}
  \def\w{0.3}
  
  % axes
  \coordinate (O) at (0,0,0);
  \draw[thick,->] (0,0,0) -- (1,0,0) node[below left]{$x$};
  \draw[thick,->] (0,0,0) -- (0,1,0) node[below right]{$y$};
  \draw[thick,->] (0,0,0) -- (0,0,1) node[below right]{$z$};
  \tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec}
  
  % vectors
  \draw[->,red] (O) -- (P) node[above left] {$P$};
  \draw[dashed,red] (O)  -- (Pxy);
  \draw[dashed,red] (P)  -- (Pxy);
  \draw[dashed,red] (Py) -- (Pxy);
  
  % circle - LHC
  \tdplotdrawarc[thick,rotate around x=90,black!70!blue]{(\R,0,0)}{\R}{0}{360}{}{}
  
  % compass - the line between CMS and ATLAS has a ~12° declination (http://googlecompass.com)
  \begin{scope}[shift={(1.1*\R,0,1.65*\R)},rotate around y=12]
    \draw[<->,black!50] (-\w,0,0) -- (\w,0,0);
    \draw[<->,black!50] (0,0,-\w) -- (0,0,\w);
    \node[above left,black!50,scale=0.6] at (-\w,0,0) {N};
  \end{scope}

  % nodes
  \node[left,align=center] at (0,0,1.1) {Jura};
  \node[right] at (\R,0,0) {LHC};
  \fill[radius=0.8pt,black!20!red]
    (O) circle node[left=4pt,below=2pt] {CMS};
  \draw[thick] (0.02,0,0) -- (0.5,0,0); % partially overdraw x-axis and CMS point
  \fill[radius=0.8pt,black!20!blue]
    (2*\R,0,0) circle
    node[right=4pt,below=2pt,scale=0.9] {ATLAS};
  \fill[radius=0.8pt,black!10!orange]
    ({\R*sqrt(2)/2+\R},0,{ \R*sqrt(2)/2}) circle % 45 degrees from ATLAS
    node[left=2pt,below=2pt,scale=0.8] {ALICE};
  \fill[radius=0.8pt,black!60!green]
    ({\R*sqrt(2)/2+\R},0,{-\R*sqrt(2)/2}) circle % 45 degrees from ATLAS
    node[below=2pt,right=2pt,scale=0.8] {LHCb};
  
  % arcs
  \tdplotdrawarc[->]{(O)}{0.2}{0}{\phivec}
    {above=2pt,right=-1pt,anchor=mid west}{$\phi$}
  \tdplotdrawarc[->,rotate around z=\phivec-90,rotate around y=-90]{(0,0,0)}{0.5}{0}{\thetavec}
    {anchor=mid east}{$\theta$}

\end{tikzpicture}
</code></WRAP>





 ===== Tau lepton decay signatures =====

Inspiration from [[http://cds.cern.ch/record/1514540|Takahashi & Tomoto (2012) [Fig. 3.14, p. 37]]]. [[https://tikz.net/tau_decay/|Full code]].

\\
{{ latex:tikz:tau_decay_signatures.png ? 1500 }}
\\
<WRAP group><WRAP third column 15%>
\\
</WRAP><WRAP third column 28%>
{{ latex:tikz:tau_decay_signature_DM1.png ? 1500 }}
</WRAP><WRAP third column 32%>
{{ latex:tikz:tau_decay_signature_DM10.png ? 1500 }}
</WRAP></WRAP>
\\



 ===== Physics exercise =====


<WRAP group><WRAP column 20%>
\\
</WRAP><WRAP column 20%>
\\ \\ \\ \\ \\
{{ latex:coil.png ? 1000 }}
Oscillating mass ([[latex:tikz:coil|full code]]).
</WRAP><WRAP column 10%>
\\
</WRAP><WRAP column 20%>
{{ latex:balconydrop.png ? 1000 }}
Falling object ([[latex:tikz:balconydrop|full code]]).
</WRAP><WRAP column 10%>
\\
</WRAP></WRAP>


<WRAP group><WRAP column 2%>
\\
</WRAP><WRAP column 45%>
\\ \\ \\ \\ \\
{{ latex:islandthrow.png ? 1000 }}
Thrown object ([[latex:tikz:islandthrow|full code]]).
</WRAP><WRAP column 40%>
{{ latex:islandthrow_double.png ? 1000 }}
</WRAP><WRAP column 2%>
\\
</WRAP></WRAP>


<WRAP group><WRAP column 10%>
\\
</WRAP><WRAP column 70%>
{{ latex:tikz:solenoid.png ? 2000 }}
Solenoid ([[latex:tikz:solenoid|full code]]).
</WRAP><WRAP column 10%>
\\
</WRAP></WRAP>



 ===== Higgs decay planes =====

Decay planes of Higgs decay to measure the Higgs boson's parity. The full code can be found [[https://tikz.net/decay_planes/|here]]. Adaptation of [[https://arxiv.org/abs/hep-ph/0503172|Djouadi (2008) [Fig. 2.6, 2.11]]].

<WRAP group><WRAP third column 20%>
\\
</WRAP><WRAP third column 55%>
{{ latex:higgs_decay_planes_taus.png ? 1500 }}

{{ latex:higgs_decay_planes_ttbar.png ? 1500 }}

{{ latex:higgs_decay_planes_VV.png ? 1500 }}
</WRAP><WRAP third column 20%>
\\
</WRAP></WRAP>



 ===== Impact parameters =====

Examples of defining impact parameters in proton collisions ([[https://tikz.net/impact_parameters/|full code]]).

<WRAP group><WRAP column 28%>
{{latex:tikz:impact_parameters1.png ? 0x1000 }}
</WRAP><WRAP column 26%>
{{latex:tikz:impact_parameters2.png ? 0x1000 }}
</WRAP><WRAP column 38%>
{{latex:tikz:impact_parameters3.png ? 0x1000 }}
</WRAP></WRAP>

 ===== Timelines and scales =====

Examples of a simple time or energy scale with labels and arrows ([[https://tikz.net/timeline/|full code]]).

<WRAP group><WRAP third column 15%>
\\
</WRAP><WRAP third column 65%>

Random timeline:
{{ latex:tikz:timeline_example.png ? 1500 }}
\\ \\
Logarithmic energy scale of particle physics:
{{ latex:tikz:timeline_energy_scale_particle_physics.png ? 1500 }}
\\ \\
Timeline of particle physics ([[http://www.particleadventure.org/other/history|inspiration]]):
{{ latex:tikz:timeline_particle_physics.png ? 1500 }}
</WRAP><WRAP third column 20%>
\\
</WRAP></WRAP>



 ===== Jets cones =====

Two examples of cones. Full code can be found [[https://tikz.net/jet_cone/|here]].


<WRAP group><WRAP half column lo 65%>
<code latex>
\begin{tikzpicture}

  % cone variables
  \def\x{2.0}
  \def\y{4.0}
  \def\R{\x}
  \def\yc{\y+0.02}
  \def\e{0.4}
  
  % cone shades + frame
  \shade[right color=white,left color=mylightgreen,opacity=0.3]
    (-\x,\yc) -- (-2,4) arc (180:360:{\R} and \e) -- (\x,\yc) -- (0,0) -- cycle;
  \draw[fill=green,opacity=0.2]
    (0,\yc) circle ({\R} and \e);
  \draw
    (-\x,\y) -- (0,0) -- (\x,\y);
  \draw
    (0,\yc) circle ({\R} and \e);

  % tracks
  \draw[thick]
    (0,0) arc (320:360:-3 and 6.0); %node[above] {1};
  \draw[thick]
    (0,0) arc (-70:  0:0.8 and 3.5); %node[above] {2};
  \draw[thick]
    (0,0) arc (  0: 70:0.9 and 4.5); %node[above] {3};
  \draw[thick]
    (0,0) arc (180:140:2 and 6.0); %node[above] {4};
  \draw[thick,dashed]
    (0,0) -- (1,4.6);
  
\end{tikzpicture}
</code>
</WRAP><WRAP half column 30%>
\\ \\ \\ \\ \\
{{ latex:jet_particle_spray.png ? 1000 }}
\\ \\ \\ \\ \\ \\
</WRAP></WRAP>


<WRAP group><WRAP half column lo 65%>
<code latex>
\begin{tikzpicture}
  
  % AK8 variables
  \def\x{2.4}
  \def\y{3.5}
  \def\R{\x+0.02}
  \def\yc{\y+0.08}
  \def\e{0.6}
  
  % AK8 cone
  \shade[right color=white,left color=blue,opacity=0.2]
    (-\x,\y) -- (-\x,\yc) arc (180:360:{\R} and \e) -- (\x,\y) -- (0,0) -- cycle;
  \draw[fill=blue,opacity=0.2]
    (0,\yc) circle ({\R} and \e);
  \draw
    (-\x,\y) -- (0,0) -- (\x,\y);
  \draw
    (0,\yc) circle ({\R} and \e);
  
  % AK4 variables
  \def\x{1.0}
  \def\y{4.0}
  \def\R{\x+0.005}
  \def\yc{\y+0.04}
  \def\e{0.4}
  
  % AK4 cone 1
  \begin{scope}[rotate=12]
    \shade[right color=white,left color=green,opacity=0.3]
      (-\x,\yc) -- (-\x,\yc) arc (180:360:{\R} and \e) -- (\x,\yc) -- (0,0) -- cycle;
    \draw[fill=green,opacity=0.2]
      (0,\yc) circle ({\R} and \e);
    \draw
      (-\x,\y) -- (0,0) -- (\x,\y);
    \draw
      (0,\yc) circle ({\R} and \e);
  \end{scope}

  % AK4 cone 2
  \begin{scope}[rotate=-10]
    \shade[right color=white,left color=red,opacity=0.3]
      (-\x,\yc) -- (-\x,\yc) arc (180:360:{\R} and \e) -- (\x,\yc) -- (0,0) -- cycle;
    \draw[fill=red,opacity=0.2]
      (0,\yc) circle ({\R} and \e);
    \draw
      (-\x,\y) -- (0,0) -- (\x,\y);
    \draw
      (0,\yc) circle ({\R} and \e);
  \end{scope}
  
\end{tikzpicture}
</code>
</WRAP><WRAP half column 30%>
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
{{ latex:ak8_jet_ak4_subjets.png ? 1000 }}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 
</WRAP></WRAP>





 ===== Top jets ===

The full code can be found [[https://tikz.net/jet_top/|here]].

<WRAP group><WRAP column 30%>
{{ latex:tikz:jet_top_resolved.png ? 0x1000 }}
</WRAP><WRAP column 30%>
{{latex:tikz:jet_top_merged_partial.png ? 0x1000 }}
</WRAP><WRAP column 30%>
\\ \\ \\ \\ \\
{{latex:tikz:jet_top_merged_full.png ? 0x1000 }}
</WRAP></WRAP>

<code latex>
\newcommand\jetcone[5][blue]{{
  \pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}}
  \edef\ang{#4/2}
  \edef\e{#5}
  \edef\vang{\pgfmathresult} % angle of vector OV
  \tikzmath{
    coordinate \C;
    \C = (#2)-(#3);
    \x = veclen(\Cx,\Cy)*\e*sin(\ang)^2; % x coordinate P
    \y = tan(\ang)*(veclen(\Cx,\Cy)-\x); % y coordinate P
    \a = veclen(\Cx,\Cy)*sqrt(\e)*sin(\ang); % vertical radius
    \b = veclen(\Cx,\Cy)*tan(\ang)*sqrt(1-\e*sin(\ang)^2); % horizontal radius
    \angb = acos(sqrt(\e)*sin(\ang)); % angle of P in ellipse
  }
  \coordinate (tmpL) at ($(#3)-(\vang:\x pt)+(\vang+90:\y pt)$); % tangency
  \draw[thin,#1!40!black,fill=#1!50!black!80,rotate=\vang]
    (#3) ellipse({\a pt} and {\b pt});
  \draw[thin,#1!40!black,fill=#1!80!black!40,rotate=\vang]
    (tmpL) arc(180-\angb:180+\angb:{\a pt} and {\b pt})
    -- ($(#2)+(\vang:0.018)$) -- cycle;
}}

\begin{tikzpicture}
  \def\R{2.5}
  \coordinate (O) at (0,0);
  \coordinate (BJ) at ( 65:1.1*\R); % b jet 1
  \coordinate (J1) at ( 15:1.0*\R); % q jet 1
  \coordinate (J2) at (-20:1.0*\R); % q jet 2
  \jetcone[green!80!black]{O}{BJ}{14}{0.10}
  \jetcone{O}{J1}{16}{0.08}
  \jetcone{O}{J2}{16}{0.10}
  \node[green!50!black] at (65:1.24*\R) {b};
  \node[blue!80!black,right] at (-5:1.00*\R) {$\mathrm{W} \to qq$};
\end{tikzpicture}
</code>


 ===== Jet vectors =====

One can do some projections of jet and MET vectors to construct variables like MT2 in SUSY searches. The full code can be found [[https://tikz.net/jet_vectors/|here]].

<WRAP group><WRAP half column 54%>
{{ latex:tikz:jet_vectors.png ? 0x1000 }}
</WRAP><WRAP half column 42%>
{{latex:tikz:jet_vectors_3D.png ? 0x1000 }}
</WRAP></WRAP>

<code latex>
\newcommand\jetcone[4]{
  \pgfmathanglebetweenpoints{\pgfpointanchor{#1}{center}}{\pgfpointanchor{#2}{center}}
  \edef\tmpang{\pgfmathresult}
  \coordinate (tmpC) at ($(#2)+(\tmpang-180:{abs(#4)+0.4})$); % center
  \coordinate (tmpL) at ($(tmpC)+(\tmpang+90:#3)$); % left corner
  \coordinate (tmpR) at ($(tmpC)+(\tmpang-90:#3)$); % right corner
  \draw[cone,rotate=\tmpang]
    %(tmpR) arc(90:-90:{#4} and {#3});
    (tmpC) ellipse({#4} and {#3});
  \begin{scope}
    \clip[rotate=\tmpang] (tmpR) -- (#1) -- (tmpL) arc(90:-90:{#4+0.6} and {#3});
    \draw[vector] (#1) -- (#2);
  \end{scope}
  \draw[cone,rotate=\tmpang]
    (tmpL) arc(90:270:{#4} and {#3}) -- (#1) -- cycle;
}

% MT2
\begin{tikzpicture}
  \def\R{2.8}
  \coordinate (O) at (0,0);
  \coordinate (J1) at (170:\R); % jet 1 pT
  \coordinate (J2) at (-35:\R); % jet 2 pT
  \coordinate (M1) at (130:0.9*\R); % pTmiss component 1
  \coordinate (M2) at (-10:0.8*\R); % pTmiss component 2
  \coordinate (M) at ($(M1)+(M2)$); % total missing momentum
  
  % PTMISS
  \draw[ptmiss,-,very thin] (M1) -- (M) -- (M2);
  \draw[ptmiss] (O) -- (M1) node[left=2,above=-3] {$\ptmissX{1}$};
  \draw[ptmiss] (O) -- (M2) node[right=0] {$\ptmissX{2}$};
  \draw[ptmiss] (O) -- (M) node[above right=-1] {$\ptmiss$};
  
  % JET CONES
  %\draw[vector] (O) -- (J1);
  %\draw[vector] (O) -- (J2);
  %\cone{O}{J1}{0.3}{0.15}
  \jetcone{O}{J1}{0.4}{0.08}
  \jetcone{O}{J2}{0.4}{0.10}
  \node[vector,left] at (J1) {$\vv{p}_{j_1}$};
  \node[vector,right] at (J2) {$\vv{p}_{j_2}$};
  
  % CURLY BRACE
  \draw[line width=0.5,mygreen,decorate,decoration={brace,amplitude=6}]
    ($(J1)+(195:0.35*\R)$) -- ($(M1)+(120:0.30*\R)$) node[midway,above left=2] {$\MTX{1}$};
  \draw[line width=0.5,mygreen,decorate,decoration={brace,amplitude=6}]
    ($(M2)+(10:0.48*\R)$) -- ($(J2)+(-45:0.26*\R)$) node[midway,below=4,right=4] {$\MTX{2}$};
  
\end{tikzpicture}
</code>


 ===== Tangent to a circle or ellipse =====

Some different methods of finding the tangent to a circle or ellipse in TikZ.
Using these methods a nice cone can be made.
The full code can be found [[https://tikz.net/circle_tangent/|here]].


<WRAP group><WRAP half column 45%>
{{ latex:tikz:circle_tangent.png ? 0x250 }}
</WRAP><WRAP half column 45%>
{{latex:tikz:circle_tangent_ellipse.png ? 0x200 }}
</WRAP></WRAP>

<WRAP group><WRAP half column 45%> \\ \\
{{ latex:tikz:circle_tangent_cone1.png ? 0x200 }}
</WRAP><WRAP half column 45%>
{{latex:tikz:circle_tangent_cone2.png ? 0x250 }}
</WRAP></WRAP> \\

<code latex>
% TANGENT to CIRCLE - known: r, q
\begin{tikzpicture}
  \def\r{1.5} % radius
  \def\q{4} % distance center-external point q = |OQ|
  \def\x{{\r^2/\q}} % Q x coordinate
  \def\y{{\r*sqrt(1-(\r/\q)^2}} % Q y coordinate
  \coordinate (O) at (0,0); % circle center O
  \coordinate (Q) at (\q,0); % external point Q
  \coordinate (P) at (\x,\y); % point of tangency, P
  \draw[->] (0,-1.3*\r) -- (0,1.5*\r);
  \draw[->] (-1.3*\r,0) -- (\q+0.4*\r,0);
  \draw[dashed] (\x,0) |- (0,\y);
  \draw[myblue,thick] (O) circle(\r);
  \draw[mygreen,thick] ($(Q)!-0.2!(P)$) -- ($(Q)!1.3!(P)$);
  \draw[mygreen,thick] ($(O)!-0.3!(P)$) -- ($(O)!1.4!(P)$);
  \rightAngle{Q}{P}{O}{0.40}
  \fill[myred] (O) circle(0.05) node[below right] {O};
  \fill[myred] (Q) circle(0.05) node[below left] {Q};
  \fill[myred] (P) circle(0.05) node[above=3,right=4] {P};
\end{tikzpicture}

% TANGENT to ELLIPSE - known: a, b, q
\begin{tikzpicture}
  \def\a{1.5} % horizontal radius
  \def\b{1.0} % vertical radius
  \def\q{4} % distance center-external point q = |OQ|
  \def\x{{\a^2/\q}} % x coordinate P
  \def\y{{\b*sqrt(1-(\a/\q)^2}} % y coordinate P
  \coordinate (O) at (0,0); % circle center O
  \coordinate (Q) at (\q,0); % external point Q
  \coordinate (P) at (\x,\y); % point of tangency, P
  \draw[->] (0,-\b-0.3*\a) -- (0,\b+0.4*\a);
  \draw[->] (-1.3*\a,0) -- (\q+0.4*\a,0);
  \draw[dashed] (\x,0) |- (0,\y);
  \draw[myblue,thick] (O) ellipse({\a} and {\b});
  \draw[mygreen,thick] ($(Q)!-0.2!(P)$) -- ($(Q)!1.3!(P)$);
  \draw[mygreen,thick] ($(O)!-0.3!(P)$) -- ($(O)!1.4!(P)$);
  \fill[myred] (O) circle(0.05) node[below right] {O};
  \fill[myred] (Q) circle(0.05) node[below left] {Q};
  \fill[myred] (P) circle(0.05) node[above=3,right=4] {P};
\end{tikzpicture}

</code>
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