Beamer and TikZ Workshop
Andrew Mertz
William Slough
Mathematics and Computer Science Department
Eastern Illinois University
July 17, 2007
TUG 2007: Practicing TEX
Afternoon overview: TikZ
I One of many drawing choices found in the TEX jungle
I PGF is the “back end” — TikZ provides a convenient interface
I TikZ shares some ideas with MetaPost and PSTricks
I Multiple input formats: plain TEX, LATEX
I Multiple output formats: PDF, PostScript, HTML/SVG
I Works well with beamer and incremental slides
I Extensive documentation (405 pages)
TUG 2007: Practicing TEX
TikZ capabilities: a laundry list
2-d points 3-d points Cartesian coordinates
Polar coordinates Relative positions Named points
Line segments Bézier curves Rectangles
Circles Ellipses Arcs
Grids Text Drawing
Clipping Filling Shading
Iteration Transformations Libraries
TUG 2007: Practicing TEX
Layout of a TikZ-based document using LATEX
\documentclass[11pt]{article}
...
\usepackage{tikz}
% Optional pgf libraries
\usepackage{pgflibraryarrows}
\usepackage{pgflibrarysnakes}
...
\begin{document}
...
\begin{tikzpicture}
...
\end{tikzpicture}
...
\end{document}
TUG 2007: Practicing TEX
Processing a TikZ-based document
sample.tex pdflatex sample.pdf
I Text and diagrams can be combined in one file
I Stand-alone graphics can be obtained with pdfcrop
TUG 2007: Practicing TEX
2-d points
P
b
a x
\path (a, b) coordinate (P);
TUG 2007: Practicing TEX
A diamond of 2-d points
\begin{tikzpicture}
\draw (1,0) -- (0,1) -- (-1,0) -- (0,-1) -- cycle;
\end{tikzpicture}
TUG 2007: Practicing TEX
A diamond of 2-d points, with arrows
\begin{tikzpicture}[>=triangle 45] I >= sets arrow type
\draw[->] ( 1, 0) -- ( 0, 1); I ->, <-, and <->, sets where
\draw[->] ( 0, 1) -- (-1, 0); arrowheads are to be placed
\draw[->] (-1, 0) -- ( 0,-1);
\draw[->] ( 0,-1) -- ( 1, 0); I Arrows will be placed only
\end{tikzpicture} on the last part of a path
TUG 2007: Practicing TEX
A diamond of 2-d points, with arrows
\begin{tikzpicture}[>=triangle 45] I >= sets arrow type
\draw[->] ( 1, 0) -- ( 0, 1); I ->, <-, and <->, sets where
\draw[->] ( 0, 1) -- (-1, 0); arrowheads are to be placed
\draw[->] (-1, 0) -- ( 0,-1);
\draw[->] ( 0,-1) -- ( 1, 0); I Arrows will be placed only
\end{tikzpicture} on the last part of a path
TUG 2007: Practicing TEX
A diamond of 2-d points, with arrows
\begin{tikzpicture}[>=triangle 45] I >= sets arrow type
\draw[->] ( 1, 0) -- ( 0, 1); I ->, <-, and <->, sets where
\draw[->] ( 0, 1) -- (-1, 0); arrowheads are to be placed
\draw[->] (-1, 0) -- ( 0,-1);
\draw[->] ( 0,-1) -- ( 1, 0); I Arrows will be placed only
\end{tikzpicture} on the last part of a path
TUG 2007: Practicing TEX
A diamond of 2-d points, with arrows
\begin{tikzpicture}[>=triangle 45] I >= sets arrow type
\draw[->] ( 1, 0) -- ( 0, 1); I ->, <-, and <->, sets where
\draw[->] ( 0, 1) -- (-1, 0); arrowheads are to be placed
\draw[->] (-1, 0) -- ( 0,-1);
\draw[->] ( 0,-1) -- ( 1, 0); I Arrows will be placed only
\end{tikzpicture} on the last part of a path
TUG 2007: Practicing TEX
A diamond of 2-d points, with grid
\draw[step=0.25cm,color=blue!30] (-1,-1) grid (1,1);
\draw (1,0) -- (0,1) -- (-1,0) -- (0,-1) -- cycle;
TUG 2007: Practicing TEX
A few path options
I Fill path
I Change pen color
I Change pen width
I Adjust transparency
TUG 2007: Practicing TEX
A few path options: details
\begin{tikzpicture}
\draw[step=0.25cm,color=blue!30]
(-1,-1) grid (1,1);
\draw[fill,color=blue!30,draw=red,
line width=2pt,opacity=0.5]
(1,0) -- (0,1) -- (-1,0) -- (0,-1) -- cycle;
\end{tikzpicture}
TUG 2007: Practicing TEX
Points specified with polar coordinates
(α : r dim)
r
α
x
dim: A dimensional unit (cm, pt, mm, in, . . . )
TUG 2007: Practicing TEX
Specifying points with named coordinates
TUG 2007: Practicing TEX
Specifying points with named coordinates: details
\begin{tikzpicture}
\path (0,0) coordinate (origin);
\path (0:1cm) coordinate (P0);
\path (1*72:1cm) coordinate (P1);
\path (2*72:1cm) coordinate (P2);
\path (3*72:1cm) coordinate (P3);
\path (4*72:1cm) coordinate (P4);
% Pentagon edges
\draw (P0) -- (P1) -- (P2) -- (P3) -- (P4) -- cycle;
% Spokes
\draw (origin) -- (P0) (origin) -- (P1)
(origin) -- (P2) (origin) -- (P3)
(origin) -- (P4);
\end{tikzpicture}
TUG 2007: Practicing TEX
Specifying points with relative coordinates
∆y
∆x
Given coordinate P and offsets ∆x and ∆y , we can establish Q:
\path (P) ++ (∆x, ∆y ) coordinate (Q);
TUG 2007: Practicing TEX
Example with relative offsets
\draw (0,0) --
++(1,0) --
++(1,1) --
++(1,-1) --
++(1,0.5);
TUG 2007: Practicing TEX
Example with relative offsets: ++ vs. +
\draw (0,0) -- ++ specifies a point and updates the
+(1,0) -- current location
+(0,-1) --
+(-1,0) -- + only specifies a point
+(0,1);
TUG 2007: Practicing TEX
Specifying points as intersections
\fill (intersection of 0,2--4,0 and 0,-3--4,5) circle (2pt);
TUG 2007: Practicing TEX
Intersections of horizontal and vertical lines
\fill[red] (1,2 |- 4,3) circle (2pt);
\fill[red] (4,3 -| 1,2) circle (2pt);
Both (p |- q) and (q -| p) specify the intersection of the
vertical line through p and the horizontal line through q.
TUG 2007: Practicing TEX
Rectangles
a c x
\draw (a, b) rectangle (c, d);
TUG 2007: Practicing TEX
Rectangles: examples
\draw (0,0) rectangle (1,1)
rectangle (3,2)
rectangle (4,3);
\draw (0,0) rectangle (1,1)
rectangle (2,0)
rectangle (3,1);
TUG 2007: Practicing TEX
Circles
r
b
a x
\draw (a, b) circle (r dim);
TUG 2007: Practicing TEX
Circles: examples
\draw (0,0) circle (1cm) circle (0.6cm) circle (0.2cm);
\draw (0,0) circle (1cm);
\draw (0.5,0) circle (0.5cm);
\draw (0,0.5) circle (0.5cm);
\draw (-0.5,0) circle (0.5cm);
\draw (0, -0.5) circle (0.5cm);
TUG 2007: Practicing TEX
Ellipses
r2
r1
b
a x
\draw (a, b) ellipse (r1 dim and r2 dim);
TUG 2007: Practicing TEX
Ellipses: examples
\draw (0,0) ellipse (2cm and 1cm);
\draw (0,0) ellipse (0.5cm and 1cm);
\draw (0,0) ellipse (0.5cm and 0.25cm);
\draw[fill,color=blue] (0,0) ellipse (2cm and 1cm);
\draw[fill,color=white] (0,0) ellipse (1cm and 0.5cm);
\draw[fill,color=red] (0,0) ellipse (0.5cm and 0.25cm);
TUG 2007: Practicing TEX
Circular arcs
P
β
r
\draw (P) arc (α : β : r dim);
TUG 2007: Practicing TEX
Circular arcs: examples
\draw[fill, color=red] (0:0.4cm) -- (0:1cm)
arc (0:60:1cm) -- (60:0.4cm)
arc (60:0:0.4cm) -- cycle;
\draw[fill, color=yellow]
(0,0) -- (30:1cm) arc (30:330:1cm) -- cycle;
\draw (0.25,0) arc (0:180:0.25cm)
(0.5,0) arc (0:180:0.5cm)
(0.75,0) arc (0:180:0.75cm)
(1,0) arc (0:180:1cm);
TUG 2007: Practicing TEX
Bézier curves with named coordinates
y
C D
P Q
x
\draw (P) .. controls (C) and (D) .. (Q);
TUG 2007: Practicing TEX
Bézier curves: examples
C D C
P Q P D Q
C D D C
P Q P Q
TUG 2007: Practicing TEX
Bézier curves with relative coordinates
r2
r1
α β
P Q
\draw (P) .. controls +(α : r1 dim)
and +(β : r2 dim) .. (Q);
TUG 2007: Practicing TEX
Using nodes
v2
v3
v0 v1
v4
v5
\path (0:0cm) node[draw,shape=circle] (v0) {$v_0$};
TUG 2007: Practicing TEX
Using nodes: details
\begin{tikzpicture}
\tikzstyle{every node}=[draw,shape=circle];
\path (0:0cm) node (v0) {$v_0$};
\path (0:1cm) node (v1) {$v_1$};
\path (72:1cm) node (v2) {$v_2$};
\path (2*72:1cm) node (v3) {$v_3$};
\path (3*72:1cm) node (v4) {$v_4$};
\path (4*72:1cm) node (v5) {$v_5$};
\draw (v0) -- (v1)
(v0) -- (v2)
(v0) -- (v3)
(v0) -- (v4)
(v0) -- (v5);
\end{tikzpicture}
TUG 2007: Practicing TEX
Nodes on a line or curve
1
2
\draw[blue] (0,0) -- (2,3) node[black, pos=0.5]{$\frac{1}{2}$};
1
2
\draw[blue] (0,0) .. controls (1,2) and (4,2) .. (3,0)
node[black, pos=0.5]{$\frac{1}{2}$};
TUG 2007: Practicing TEX
Using nodes to draw automata
0,1
q0 q1 0
TUG 2007: Practicing TEX
Using nodes to draw automata: details
\begin{tikzpicture}[>=triangle 45]
% Nodes
\path (0,0) node[draw,shape=circle] (q0) {$q 0$};
\path (1,0) node[draw,double,shape=circle] (q1) {$q 1$};
% Initial state
\draw[->] (-0.3,0) -- (q0);
% Edges
\draw[->, shorten >=1mm]
(q0.north) .. controls +(30:0.5cm) and +(150:0.5cm)
.. (q1.north) node[pos=0.5,above] {0,1};
\draw[->, shorten >=1mm]
(q1.south) .. controls +(210:0.5cm) and +(330:0.5cm)
.. (q0.south) node[pos=0.5,below] {1};
\draw[->, shorten >=1mm]
(q1.east) .. controls +(60:0.4cm) and +(-60:0.4cm)
.. (q1.east) node[pos=0.5,right] {0};
\end{tikzpicture}
TUG 2007: Practicing TEX
Using nodes to draw automata: details
\begin{tikzpicture}[>=triangle 45]
% Nodes
\path (0,0) node[draw,shape=circle] (q0) {$q 0$};
\path (1,0) node[draw,double,shape=circle] (q1) {$q 1$};
% Initial state
\draw[->] (-0.3,0) -- (q0);
% Edges
\draw[->, shorten >=1mm]
(q0.north) .. controls +(30:0.5cm) and +(150:0.5cm)
.. (q1.north) node[pos=0.5,above] {0,1};
\draw[->, shorten >=1mm]
(q1.south) .. controls +(210:0.5cm) and +(330:0.5cm)
.. (q0.south) node[pos=0.5,below] {1};
\draw[->, shorten >=1mm]
(q1.east) .. controls +(60:0.4cm) and +(-60:0.4cm)
.. (q1.east) node[pos=0.5,right] {0};
\end{tikzpicture}
TUG 2007: Practicing TEX
Using nodes to draw automata: details
\begin{tikzpicture}[>=triangle 45]
% Nodes
\path (0,0) node[draw,shape=circle] (q0) {$q 0$};
\path (1,0) node[draw,double,shape=circle] (q1) {$q 1$};
% Initial state
\draw[->] (-0.3,0) -- (q0);
% Edges
\draw[->, shorten >=1mm]
(q0.north) .. controls +(30:0.5cm) and +(150:0.5cm)
.. (q1.north) node[pos=0.5,above] {0,1};
\draw[->, shorten >=1mm]
(q1.south) .. controls +(210:0.5cm) and +(330:0.5cm)
.. (q0.south) node[pos=0.5,below] {1};
\draw[->, shorten >=1mm]
(q1.east) .. controls +(60:0.4cm) and +(-60:0.4cm)
.. (q1.east) node[pos=0.5,right] {0};
\end{tikzpicture}
TUG 2007: Practicing TEX
Using nodes to draw automata: details
\begin{tikzpicture}[>=triangle 45]
% Nodes
\path (0,0) node[draw,shape=circle] (q0) {$q 0$};
\path (1,0) node[draw,double,shape=circle] (q1) {$q 1$};
% Initial state
\draw[->] (-0.3,0) -- (q0);
% Edges
\draw[->, shorten >=1mm]
(q0.north) .. controls +(30:0.5cm) and +(150:0.5cm)
.. (q1.north) node[pos=0.5,above] {0,1};
\draw[->, shorten >=1mm]
(q1.south) .. controls +(210:0.5cm) and +(330:0.5cm)
.. (q0.south) node[pos=0.5,below] {1};
\draw[->, shorten >=1mm]
(q1.east) .. controls +(60:0.4cm) and +(-60:0.4cm)
.. (q1.east) node[pos=0.5,right] {0};
\end{tikzpicture}
TUG 2007: Practicing TEX
Using loops
TUG 2007: Practicing TEX
Using loops: details
\begin{tikzpicture}
\foreach \i in {1,...,4} {
\path (\i,0) coordinate (X\i);
\fill (X\i) circle (1pt);
}
\foreach \j in {1,...,3} {
\path (\j,1) coordinate (Y\j);
\fill (Y\j) circle (1pt);
}
\foreach \i in {1,...,4} {
\foreach \j in {1,...,3} {
\draw (X\i) -- (Y\j);
}
}
\end{tikzpicture}
TUG 2007: Practicing TEX
Spiral
TUG 2007: Practicing TEX
Spiral: details
% Define the orginal triangle
\path ( 0 , 0) node[shape=coordinate](lastA){}
++( 60:1cm) node[shape=coordinate](lastB){}
++(-60:1cm) node[shape=coordinate](lastC){};
% Draw the orginal triangle
\draw (lastA) -- (lastB) -- (lastC) -- cycle;
\foreach \x in {1,...,60}{ % Draw 60 "sub-triangles"
% Move A toward C, B towards A, and C towards B
\path (lastA) -- (lastC) node[shape=coordinate,pos=.166](A){};
\path (lastB) -- (lastA) node[shape=coordinate,pos=.166](B){};
\path (lastC) -- (lastB) node[shape=coordinate,pos=.166](C){};
\draw (A) -- (B) -- (C) -- cycle; % Draw sub-triangle
\path (A) node[shape=coordinate](lastA){}; % Update positions
\path (B) node[shape=coordinate](lastB){};
\path (C) node[shape=coordinate](lastC){};
}
TUG 2007: Practicing TEX
Rotation
\foreach \alpha in {0,60,...,300} {
\draw[rotate=\alpha] (0,0) -- (0.5,1) --
(0,2) -- (-0.5,1) -- cycle;
}
TUG 2007: Practicing TEX
Rotation
\foreach \alpha / \c in {0/red,120/green,240/blue} {
\fill[rotate=\alpha,color=\c]
(0,0) -- (0.5,1) -- (0,2) -- (-0.5,1) -- cycle;
}
TUG 2007: Practicing TEX
Function plots
\draw[smooth,domain=0:6.28,color=red]
plot function{sin(2*x)*exp(-x/4)};
TUG 2007: Practicing TEX
Plot Types
\draw plot coordinates {point sequence};
\draw plot file {filename};
\draw plot function {gnuplot formula};
Useful options:
I mark: places a given mark at each point of the plot.
I smooth, smooth cycle: points are connected by a (closed)
smooth curve.
I xcomb, ycomb: makes a horizontal or vertical bar diagram.
I line width: sets the size of line to use.
TUG 2007: Practicing TEX
Rising Together
Change in Family Income, 1947–1979
120%
116% 114%
111%
100%
100% 99%
80% 86%
60%
40%
20%
0%
Bottom 20% Second 20% Middle 20% Fourth 20% Top 20% Top 5%
Original graph from www.faireconomy.org/research/income_charts.html
TUG 2007: Practicing TEX
Plot: details
\begin{tikzpicture}[x=1.8cm,y=1pt]
% Bars
\draw[ycomb, color=blue!50, line width=1.4cm]
plot coordinates {(0,116) (1,100) (2,111)
(3, 114) (4,99) (5,86)};
% Axes
\draw (-0.5,0) -- (-0.5,125);
\draw (-0.5,0) -- (5.5,0);
...
\end{tikzpicture}
TUG 2007: Practicing TEX
Clipping
\clip (-0.5,0.2) circle (1cm);
\clip (0.5,-0.2) circle (1cm);
\fill[color=blue!50] (-2,1.5) rectangle (2,-1.5);
TUG 2007: Practicing TEX
Yin-Yang
TUG 2007: Practicing TEX
Yin-Yang: details
\draw (0,0) circle (1cm);
\begin{scope}
\clip (0,0) circle (1cm);
\fill[black] (0cm,1cm) rectangle (-1cm,-1cm);
\end{scope}
\fill[black] (90:0.5cm) circle (0.5cm);
\fill[white] (270:0.5cm) circle (0.5cm);
\fill[white] (90:0.5cm) circle (0.1cm);
\fill[black] (270:0.5cm) circle (0.1cm);
TUG 2007: Practicing TEX
Yin-Yang: details
\draw (0,0) circle (1cm);
\begin{scope}
\clip (0,0) circle (1cm);
\fill[black] (0cm,1cm) rectangle (-1cm,-1cm);
\end{scope}
\fill[black] (90:0.5cm) circle (0.5cm);
\fill[white] (270:0.5cm) circle (0.5cm);
\fill[white] (90:0.5cm) circle (0.1cm);
\fill[black] (270:0.5cm) circle (0.1cm);
TUG 2007: Practicing TEX
Yin-Yang: details
\draw (0,0) circle (1cm);
\begin{scope}
\clip (0,0) circle (1cm);
\fill[black] (0cm,1cm) rectangle (-1cm,-1cm);
\end{scope}
\fill[black] (90:0.5cm) circle (0.5cm);
\fill[white] (270:0.5cm) circle (0.5cm);
\fill[white] (90:0.5cm) circle (0.1cm);
\fill[black] (270:0.5cm) circle (0.1cm);
TUG 2007: Practicing TEX
Yin-Yang: details
\draw (0,0) circle (1cm);
\begin{scope}
\clip (0,0) circle (1cm);
\fill[black] (0cm,1cm) rectangle (-1cm,-1cm);
\end{scope}
\fill[black] (90:0.5cm) circle (0.5cm);
\fill[white] (270:0.5cm) circle (0.5cm);
\fill[white] (90:0.5cm) circle (0.1cm);
\fill[black] (270:0.5cm) circle (0.1cm);
TUG 2007: Practicing TEX
Yin-Yang: details
\draw (0,0) circle (1cm);
\begin{scope}
\clip (0,0) circle (1cm);
\fill[black] (0cm,1cm) rectangle (-1cm,-1cm);
\end{scope}
\fill[black] (90:0.5cm) circle (0.5cm);
\fill[white] (270:0.5cm) circle (0.5cm);
\fill[white] (90:0.5cm) circle (0.1cm);
\fill[black] (270:0.5cm) circle (0.1cm);
TUG 2007: Practicing TEX
Yin-Yang: details
\draw (0,0) circle (1cm);
\begin{scope}
\clip (0,0) circle (1cm);
\fill[black] (0cm,1cm) rectangle (-1cm,-1cm);
\end{scope}
\fill[black] (90:0.5cm) circle (0.5cm);
\fill[white] (270:0.5cm) circle (0.5cm);
\fill[white] (90:0.5cm) circle (0.1cm);
\fill[black] (270:0.5cm) circle (0.1cm);
TUG 2007: Practicing TEX
Scope
The scope environment limits which paths are subject to a
clipping region or applies options to a list of paths.
\begin{scope}
\clip (0,0) circle (1cm);
\fill[black] (0cm,1cm) rectangle (-1cm,-1cm);
\end{scope}
\begin{scope}[font=\scriptsize, anchor=base]
\path (0,-10) node {Bottom 20\%};
\path (1,-10) node {Second 20\%};
\path (2,-10) node {Middle 20\%};
\path (3,-10) node {Fourth 20\%};
\path (4,-10) node {Top 20\%};
\path (5,-10) node {Top 5\%};
\end{scope}
TUG 2007: Practicing TEX
Summary
I TikZ is a language for specifying graphics
I Specifying graphics with a language provides exactness
I Familiar graphics-related concepts: points, lines, etc.
I Meshes well with pdfLATEX and beamer
I Reasonably comfortable learning curve
TUG 2007: Practicing TEX
Acknowledgments
Thanks to Till Tantau for developing TikZ!
TUG 2007: Practicing TEX
Questions?
\begin{tikzpicture}
\fill[color=blue!10] (-5,-2.5) rectangle (5,2.5);
\path (0,0) node {{\Huge \color{blue} Questions?}};
\end{tikzpicture}
TUG 2007: Practicing TEX
References
I Beamer: latex-beamer.sourceforge.net
I PGF/TikZ: www.sourceforge.net/projects/pgf/
I Animate package: www.ctan.org/tex-archive/macros/
latex/contrib/animate/
I pdfcrop: www.ctan.org/tex-archive/support/pdfcrop/
TUG 2007: Practicing TEX
