# TikZ for High-Quality LaTeX Pictures

TikZ is a package for LaTeX for drawing pictures. It is a frontend to the Portable Graphics Format (PGF) package and is inspired from metafont, pstricks, and the standard LaTeX picture environment. In TikZ, the user programs the picture with commands that draw element by element.

The advantage of TikZ over imported graphics is that it uses fonts and line widths consistent with the rest of the LaTeX document. In contrast, imported graphics usually embed their fonts and rescaling the graphic also rescales line widths. Also, TikZ pictures are easier to adjust since the commands are part of the document.

TikZ is still developing. This tutorial addresses TikZ/PGF version 2.00 (released Feb. 2008). Some commands may be unsupported in earlier versions.

## Installation

Some TeX installations include the TikZ/PGF package by default. To install TikZ/PGF on Linux, install the pgf package through the OS package manager, or on Windows with MikTeX, use the update wizard to install the pgf package.

Otherwise, download the latest version from sourceforge.net/projects/pgf, and follow the installation instructions in pgfmanual.pdf.

## An Example

Here is an example LaTeX document with a TikZ picture.

`\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}`

## TikZ Basics

A picture is contained in a `tikzpicture`

environment. The various parts of the picture are specified with `\draw`

commands. A `\draw`

command consists of options (color, line width, ...) and a path, terminated by a semicolon:

`\draw [options] path ;`

All TikZ commands should end with a semicolon (`;`

). Beware that forgetting one can produce confusing error messages.

### Paths

A path specifies a line, curve, or collection of lines and curves to be drawn. Here are some examples of different paths:

A line:

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

A sequence of connected lines:

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

A rectangle (specified by two corners):

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

A circle:

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

The units for these are coordinates are nominally cm, though they might not correspond to physical centimeters if the figure is scaled. You can also specify multiple primitives as a single path (not necessarily connected), for example the following draws two circles and a rectangle

`\draw [blue,semithick] `

` (-1,0) circle (0.5)`

` (1,0) circle (0.5)`

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

Such a path is useful when we want to apply the same drawing options to multiple primitives.

### Text in Drawings

LaTeX code can be added to a picture using a node. Nodes can hold text, math, includegraphics, and most other kinds of LaTeX code. For example, the following draws a node at coordinates (2,3):

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

Nodes also can be specified on the vertices of a path.

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

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

Using nodes this way is useful to annotate parts of a diagram and to label axes, as we did with the x and y axes in the first example.

### Options

Options specify how to draw a path or node. TikZ is very flexible in this aspect and supports a great variety of effects. Useful drawing options include

Add an arrowhead to make an arrow:

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

Specifying line width:

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

Drawing in color:

`[blue] % Draw with the color blue`

Specifying a mixed color:

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

Draw translucent objects:

`[opacity=0.4] % Draw with 40% opacity`

Options are also used for geometric transformations:

Translation:

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

Scaling:

`[scale=1.2] % Scale coordinates by 1.2`

Coordinate scaling, reflection:

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

Rotation:

`[rotate=35] % Rotate 35 degrees`

## More Examples

The following examples demonstrate TikZ for some more elaborate figures. Full explanation of these examples is beyond the scope of this tutorial, but studying the example codes may produce helpful keywords for finding further information.

### A wavy curve

This example demonstrates the in and out options and accomplishing repeated elements with a `\foreach`

loop.

`\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}`

### Figure illustrating cubic interpolation

This picture shows how to write a multiline node with the text width option and more examples of `\foreach`

. Also, some math is used in computing the control points such that the curves interpolate the data. It uses a custom color gold; add `\definecolor{gold}{rgb}{0.85,0.65,0}`

to the preamble to reproduce.

`% 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}`

### Braces

This picture shows how to draw curly braces with the path decoration library. To include this library, add `\usetikzlibrary{decorations.pathreplacing}`

to the preamble just after `\usepackage{tikz}`

. The picture also demonstrates naming nodes with the `\node`

command.

`\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}`

## Further Information

More TikZ and PGF examples are available at www.texample.net/tikz/examples. Also see the manual pgfmanual.pdf for both tutorial and detailed reference information (find it in texmf/doc/generic/pgf/pgfmanual.pdf or search online).