Learning Objectives:

Intermediate techniques of TikZ:

• Tree
• Grouping
• Plotting
• Calculate Coordinates
• For loop

Tree

General Tree

\begin{tikzpicture}
	\node(0){a}
		child{node{b}}
		child{node{c}
			child{node{d}}
			child{node{e}}
		};
\end{tikzpicture}

Game Tree

Since nodes in game trees are often defined by dots, we need to specify them.

\begin{tikzpicture}
\tikzstyle{hollow node}=[circle,draw,inner sep=1.5]
\tikzstyle{solid node}=[circle,draw,inner sep=1.5,fill=black]
\node[hollow node]{}
	child{node[solid node]{}}
	child{node[solid node]{}}
	child{node[solid node]{}}
;
\end{tikzpicture}

Grouping

We can apply decoration to multiple lines.

Scope

Using scope is to allow decorations to be applied to multiple lines.

\begin{tikzpicture}
\begin{scope} [red, thick]
	\draw (0,0)--(3,3);
	\draw (0,3)--(3,0);
\end{scope}
\end{tikzpicture}

Style

Using style is to allow decorations to be applied with flexibility:

\begin{tikzpicture}[marked/.style = {red, very thick}]
\draw[marked] (0,0)--(3,3);
\draw[marked] (0,3)--(3,0);
\end{tikzpicture}

tikzset

Using style is to allow decorations to be applied to multiple figures.

\tikzset[marked/.style = {red, very thick}]
\tikzset[trivial/.style = {blue, thin}]
\begin{tikzpicture}
\draw[marked] (0,0)--(3,3);
\draw[trivial] (0,3)--(3,0);
\end{tikzpicture}

Plotting

Mathematical Expression

\begin{tikzpicture}
\draw[blue,<->] (4,0) -| (0,4); 
\draw[red, domain=0:2] plot (\x,\x*\x);
\end{tikzpicture}

Data plot

For data plot, we need to load the package \usepackage{pgfplots}.

\usepackage{tikz}
\usepackage{pgfplots}
\begin{tikzpicture}
\begin{axis}[xlabel=x,ylabel=y]
	\addplot coordinates {(1,1) (2,0) (3,3) (4,2)};
\end{axis}

Scale

Zoom out

We can use scale=0.5 to make the zoom out.

\begin{tikzpicture}[scale=0.5]
	\draw (0,0)--(1,1);
	\draw (0,1)--(1,0);
\end{tikzpicture}

Zoom in

We can use scale=2 to make the zoom in.

\begin{tikzpicture}[scale=2]
	\draw (0,0)--(1,1);
	\draw (0,1)--(1,0);
\end{tikzpicture}

Find coordinates

Grid

One of the main difficulties in using TikZ to draw diagram is to find the appropriate coordinates. One way to see where is should put the coordinate is by using grid

\begin{tikzpicture}
\draw[step=1,gray,very thin] (0,0) grid (4,4);
\end{tikzpicture}

Relative to two points

To calculate new coordinates based on $(a,b)$ and $(c,d)$, we can use |- and -|. We have $(a,d)$ if we have (a,b|-c,d) and $(c,b)$ if we have (a,b-|c,d)

\begin{tikzpicture}
\node[circle, fill=red] at (1,1) {};
\node[circle, fill=blue] at (3,3){};
\node[circle, fill=green] at (1,1|- 3,3){};
\node[circle, fill=purple] at (1,1-| 3,3){};
\end{tikzpicture}

Average of two points

To calculate mid point of based on $(a,b)$ and $(c,d)$, we can use ($(a,b)!0.5!(c,d)$).

\begin{tikzpicture}
\node[circle, fill=red] at (1,1) {};
\node[circle, fill=blue] at (3,3){};
\node[circle, fill=green] at ($(1,1)!0.5!(3,3)$){};
\node[circle, fill=purple] at ($(1,1)!0.25!(3,3)$){};
\end{tikzpicture}

Intersection of two named paths

To calculate in intersections, we need to use \usetikzlibrary{intersections}.

\usetikzlibrary{intersections}
\begin{tikzpicture}
\draw[name path=Demand] (0,3) -- (3,0);
\draw[name path=Supply] (0,0) -- (3,3);
\path [name intersections={of=Demand and Supply,by=E}];
\fill [red] (E) circle (2pt);
\end{tikzpicture}

Multiple intersections of two named paths

\usepackage{tikz}
\usetikzlibrary{intersections}
\begin{tikzpicture}
\draw[name path=circle] (0,0) circle (2);
\draw[name path=line] (-3,-3) -- (3,3);
\fill [red, name intersections={of = circle and line}] (intersection-1) circle (4pt);
\fill [blue, name intersections={of =circle and line}] (intersection-2) circle (4pt);
\end{tikzpicture}

Example: Demand and Supply

We illustrate how to draw demand and supply curve using the techniques presented above:

\usepackage{tikz}
\usetikzlibrary{calc,intersections}
\begin{tikzpicture}[scale=0.8]
\draw [thick](0,6) node [left] {P} |- (6,0) node [below] {Q};
\draw[thick,blue!90, name path =Supply](1,1)--(5,5) node[right]{Supply};
\draw[thick,blue!90, name path=Demand](1,5)--(5,1) node[right]{Demand};
\path [name intersections={of=Demand and Supply,by=E}];
\draw[dashed] (E -| 0,0) node[left]{$P^*$}--(E)--(E |- 0,0) node[below]{$Q^*$};
\draw[black,fill] (E) circle [radius=0.15];
\end{tikzpicture}

Programming

For Loop

The syntax to write a for loop is \foreach and variable would be \x.

\draw (0,0)--(6,0);
\foreach \x in {0,...,6}{
	\draw (\x,-1)--(\x,1);
}