TikZ for High-Quality LaTeX Pictures

\documentclass[12pt]{article}

\usepackage{tikz}

\begin{document}

This picture was drawn with TikZ:

\begin{tikzpicture}[scale=1.5]

% Draw thin grid lines with color 40% gray + 60% white

\draw [step=0.5,thin,gray!40] (-1.4,-1.4) grid (1.4,1.4);

% Draw x and y axis lines

\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};

\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};

% Draw a blue circle at the origin of radius 1

\draw [semithick,blue] (0,0) circle (1);

% Draw a triangle with vertices (0,0), (1,0), (1,0.7)

\draw [semithick,blue] (0,0) -- (1,0) -- (1,0.7) -- cycle;

\end{tikzpicture}

\end{document}

\draw [options]  path ;

\draw [options] (-5,0) -- (5,2);

\draw [options] (-1,0) -- (1,0) -- (0,1) -- (0,-1);

\draw [options] (-2,-1) rectangle (2,1);

\draw [options] (4,0) circle (0.5);

\draw [blue,semithick] 

    (-1,0) circle (0.5)

    (1,0) circle (0.5)

    (0,-0.25) rectangle (2,0.25);

\draw (2,3) node [node options] {LaTeX code};

\draw (-1,0) node [below] {Point $A$} -- 

      (1,1) node [below] {Point $B$};

[->] % Similarly, [<-] (reverse direction) or [<->] (double-headed)

[semithick] % Other widths: very thin, thin, thick, very thick

[blue] % Draw with the color blue

[blue!30!black] % Draw with 30% blue + 70% black

[opacity=0.4] % Draw with 40% opacity

[xshift=1cm,yshift=-0.5cm] % Shift 1 right and 0.5 down

[scale=1.2] % Scale coordinates by 1.2

[xscale=2.5,yscale=-1] % Scale x by 2.5 and flip upside down

[rotate=35] % Rotate 35 degrees

\begin{tikzpicture}[scale=0.8]

% Draw equation as part of the TikZ picture

\draw (-4,0) node {$P(x_n) = 0, \; n = 0,\ldots, N,$};

\draw (2,0.65) node {$P(x)$};

\draw [->,gray] (0,0) -- (6.25,0) node [below] {\small $x$};

% Draw a wavy curve through the (x_n)

\draw [semithick]  

   (0,0.4) to [out=-40,in=140] (0.5,0) 

   to [out=-40,in=240] (1.5,0) 

   to [out=60,in=160] (2.8,0) 

   to [out=-20,in=200] (4.5,0) 

   to [out=20,in=200] (6,0.5);

% Label the (x_n) with a loop

\foreach \n/\x in {0/0.5, 1/1.5, 2/2.8, 3/4.5}

{

   \fill (\x,0) circle (1.6pt) node [below=5pt] {$x_{\n}$};

}

\end{tikzpicture}

% Define the y values of the data

\newcommand{\ya}{0.5}

\newcommand{\yb}{0.1}

\newcommand{\yc}{0.1}

\newcommand{\yd}{2}

\newcommand{\ye}{2.1}

\newcommand{\yf}{1.9}

\newcommand{\yg}{1.7}

\begin{tikzpicture}[scale=1.2]

% Draw a gray box with 'Cubic ENO: Interpolate q_i with ...'

\draw (-1,2.25) 

   node [fill={gray!10},rounded corners,left,text width=32mm] 

   {\footnotesize Cubic ENO: \\

   Interpolate $q_i$ with \textcolor{red}{$\mathcal{S}^a_i$}, 

   \textcolor{gold}{$\mathcal{S}^b_i$}, 

   or \textcolor{blue}{$\mathcal{S}^c_i$}};

% Fill/draw the interval q_i

\fill [gray!15] (0,-0.15) rectangle (1,2.6);

\draw [gray,thin] (0,-0.15) -- (0,2.6) (1,-0.15) -- (1,2.6);

\draw [gray] (0.5,2.6) node [above] {$q_i$};

% Draw x labels

\draw [yshift=-0.15cm,below]

   \foreach \i in {-3,-2,-1,+2,+3}

   {

      (\i,0) node [gray] {$x_{i\i}$}

   }

   (0,0) node [black] {$x_i$}

   (1,0) node [black] {$x_{i+1}$};

% Draw Bezier curves, illustrating the three possible interpolations.

% The control points are computed such that the curves interpolate.

\draw [red,thick] (-2,\yb) .. controls 

   (-1,-5*\yb/6+3*\yc-9*\yd/6+2*\ye/6) and 

   (0,2*\yb/6-9*\yc/6+3*\yd-5*\ye/6) .. (1,\ye)

   (-1.5,0.25) node {$\mathcal{S}^a_i$};

\draw [gold,thick] (-1,\yc) .. controls 

   (0,-5*\yc/6+3*\yd-9*\ye/6+2*\yf/6) and 

   (1,2*\yc/6-9*\yd/6+3*\ye-5*\yf/6) .. (2,\yf)

   (-0.5,2) node {$\mathcal{S}^b_i$};

\draw [blue,thick] (0,\yd) .. controls 

   (1,-5*\yd/6+3*\ye-9*\yf/6+2*\yg/6) and 

   (2,2*\yd/6-9*\ye/6+3*\yf-5*\yg/6) .. (3,\yg)

   (2.5,2.25) node {$\mathcal{S}^c_i$};

% Draw datapoint markers

\foreach \p in {(-3,\ya), (-2,\yb), (-1,\yc), 

   (0,\yd), (1,\ye), (2,\yf), (3,\yg)}

{

    \fill \p circle (1pt);    

}

\end{tikzpicture}

\begin{tikzpicture}[scale=0.6]

% Draw three filled circles for points a,x,b, and define 

% them as TikZ nodes

\node (a) at (0,1) [fill,circle,inner sep=1.2pt] {};

\node (x) at (1.8,0.5) [draw,circle,inner sep=1.2pt] {};

\node (b) at (4,2) [fill,circle,inner sep=1.2pt] {};

% Label the points

\draw (a) node [above] {$a$}

   (x) node [above] {$x$}

   (b) node [above] {$b$};

% Draw a curvy line through a,x,b

\draw [thick] (a) to [out=-35,in=185] (x) 

   (x) to [in=248,out=5] (b);

% Draw curly braces using path decoration

\draw [gray,decorate,decoration={brace,amplitude=5pt},

   xshift=-4pt,yshift=-9pt] (1.8,0.5)  -- (0,1) 

   node [black,midway,below=4pt,xshift=-2pt] {\footnotesize $C_1$};

\draw [gray,decorate,decoration={brace,amplitude=5pt},

   xshift=8pt,yshift=-11pt] (4,2) -- (1.8,0.5)

   node [black,midway,below=2pt,xshift=8pt] {\footnotesize $C_2$};

\end{tikzpicture}