TikZ and PGF

https://tikz.dev/tikz
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### Snapshot with Custom Start Time

Source: https://tikz.dev/tikz-animations

Shows how to use the 'begin snapshot' option to specify a custom start time for a timeline when taking snapshots. This allows the animation's effective start to be delayed for snapshot purposes, affecting the time calculation.

```tex
\usetikzlibrary {animations}
\tikz [make snapshot of = 1s] {
  \fill :fill = { 0s = "black", 2s = "white",
  begin snapshot = 1s                         } (0,0) rectangle ++(1,1);
  \fill :fill = { 1s = "black", 3s = "white" } (2,0) rectangle ++(1,1);
}
```

--------------------------------

### Ti_k_Z 'pre' and 'post' Length Example

Source: https://tikz.dev/tikz-decorations

Demonstrates the combined use of 'pre length' and 'post length' with the 'snake' decoration to create a line with a specific start and end buffer.

```tikz
\usetikzlibrary {decorations.pathmorphing}
\begin{tikzpicture}
  [decoration=snake,
  line around/.style={decoration={pre length=#1,post length=#1}}]
   
  \draw[->,decorate] (0,0) -- ++(3,0);
  \draw[->,decorate,line around=5pt] (0,-5mm) -- ++(3,0);
  \draw[->,decorate,line around=1cm] (0,-1cm) -- ++(3,0);
\end{tikzpicture}

```

--------------------------------

### Using Blend Group for Transparency and Blend Mode

Source: https://tikz.dev/tikz-transparency

This example shows how to use the `blend group` key to simultaneously establish a transparency group and set the blend mode to 'screen'. This is a more concise way to achieve the same effect as the previous example.

```tikz
\tikz [blend group=screen] {
  \fill[red!90!black] ( 90:.6) circle (1);
  \fill[green!80!black] (210:.6) circle (1);
  \fill[blue!90!black] (330:.6) circle (1);
}

```

--------------------------------

### Basic Transparency Example

Source: https://tikz.dev/tikz-transparency

Demonstrates a basic transparency effect using opacity on lines.

```tikz
\begin{tikzpicture}[opacity=.5]
  \draw [line width=5mm] (0,0) -- (2,2);
  \draw [line width=5mm] (2,0) -- (0,2);
\end{tikzpicture}
```

--------------------------------

### Explicit Coordinate Systems Example

Source: https://tikz.dev/tikz-coordinates

Demonstrates specifying coordinate systems explicitly using 'cs:' syntax for canvas and polar coordinates.

```tikz
\begin{tikzpicture}
  \draw[help lines] (0,0) grid (3,2);
  \draw (canvas cs:x=0cm,y=2mm)
  -- (canvas polar cs:radius=2cm,angle=30);
\end{tikzpicture}
```

--------------------------------

### Implicit Coordinate Systems Example

Source: https://tikz.dev/tikz-coordinates

Shows how to specify coordinate systems implicitly, allowing TikZ to automatically detect the system.

```tikz
\begin{tikzpicture}
  \draw[help lines] (0,0) grid (3,2);
  \draw (0cm,2mm) -- (30:2cm);
\end{tikzpicture}
```

--------------------------------

### Node Placement Styles at Specific Path Positions

Source: https://tikz.dev/tikz-shapes

Demonstrates various predefined styles for placing nodes at specific points along a path, including 'at end', 'very near end', 'near end', 'midway', 'near start', 'very near start', and 'at start'. These styles offer convenient shortcuts for common positioning needs.

```tikz
\tikz \draw (0,0) .. controls +(up:2cm) and +(left:3cm) .. (1,5)
  node[at end] {\texttt{at end}}
  node[very near end] {\texttt{very near end}}
  node[near end] {\texttt{near end}}
  node[midway] {\texttt{midway}}
  node[near start] {\texttt{near start}}
  node[very near start] {\texttt{very near start}}
  node[at start] {\texttt{at start}};
```

--------------------------------

### Equivalent Label Option Syntax

Source: https://tikz.dev/tikz-shapes

Shows the equivalent 'label' option syntax for the basic quotes example.

```tikz
\tikz \node [label={[red]my label}, draw] {my node};
```

--------------------------------

### Ti_k_Z Decoration with 'pre=moveto'

Source: https://tikz.dev/tikz-decorations

Shows how to set the 'pre' decoration to 'moveto', which can alter the path's starting behavior compared to the default 'lineto'.

```tikz
\usetikzlibrary {decorations.pathmorphing}
\tikz [decoration={zigzag,pre=moveto,pre length=1cm}]
  \draw [decorate] (0,0) -- (2,1) arc (90:0:1);

```

--------------------------------

### Applying Global Edge Styles

Source: https://tikz.dev/tikz-shapes

Demonstrates how to apply a global style to all edges using the 'every edge' option. This example shows how to make all edges dashed by default.

```tikz
\begin{tikzpicture}[every edge/.style={draw,dashed}] 
  \path (0,0) edge (3,2);
\end{tikzpicture}
```

--------------------------------

### Dynamic Chain Generation with Macros and \foreach

Source: https://tikz.dev/tikz-graphs

An advanced example using macros and \foreach to generate a chain of dynamic length, controlled by a parameter passed to \tikzgraphsset.

```tikz
\usetikzlibrary {graphs}
\def\mychain#1{
 \def\mytext{1}
 \foreach \i in {2,...,#1} {
 \xdef\mytext{\mytext -> \i}
 }
                    }
\tikzgraphsset{my chain/.style={
 /utils/exec=\mychain{#1},
 parse/.expand once=\mytext}
                    }
\tikz \graph { [my chain=4] };

```

--------------------------------

### Initial Pin Style with Custom Edge

Source: https://tikz.dev/tikz-shapes

Example of setting an initial style for a node that includes a pin with a custom edge.

```tikz
\tikz [every pin edge/.style={}, \
  initial/.style={pin={[pin distance=5mm, \
  pin edge={<-,shorten <=1pt}]left:start}}]
  \node [circle,draw,initial] {my circle};
```

--------------------------------

### Create an Unconnected Graph I_n using n shortcut

Source: https://tikz.dev/tikz-graphs

An example of using the n key as a shortcut for V={1,...,n} to create an unconnected graph.

```tex
\usetikzlibrary {graphs.standard}
 \tikz \graph [clockwise, clique] { subgraph I_n [n=4] };

```

--------------------------------

### Circular Placement with Default Phase

Source: https://tikz.dev/tikz-graphs

Demonstrates 'circular placement' with the default 'phase' angle, showing the standard starting orientation of the circular layout.

```tikz
\usetikzlibrary {graphs}
\tikz \graph [circular placement] { a, b, c, d                         };

```

--------------------------------

### Basic Coordinate Transformations Example

Source: https://tikz.dev/tikz-transformations

Demonstrates the application of xshift, yshift, and rotate transformations within a Ti_k_Z scope. Transformations are applied to subsequent drawing commands.

```tikz
\begin{tikzpicture}
  \draw[help lines] (0,0) grid (3,2);
  \draw (0,0) rectangle (1,0.5);
  \begin{scope}[xshift=1cm]
  \draw [red] (0,0) rectangle (1,0.5);
  \draw[yshift=1cm] [blue] (0,0) rectangle (1,0.5);
  \draw[rotate=30] [orange] (0,0) rectangle (1,0.5);
  \end{scope}
\end{tikzpicture}
```

--------------------------------

### Basic Arrow Tip Placement

Source: https://tikz.dev/tikz-arrows

Demonstrates the use of the `->` and `>-Stealth` specifications for drawing lines with different arrow tips at the start and end. The `arrows.meta` library is required.

```tikz
\usetikzlibrary {arrows.meta}
\begin{tikzpicture}
  \draw[->] (0,0) -- (1,0);
  \draw[>-Stealth] (0,0.3) -- (1,0.3);
\end{tikzpicture}
```

--------------------------------

### Ti_k_Z Decoration with 'pre=crosses'

Source: https://tikz.dev/tikz-decorations

Illustrates using a 'crosses' decoration as the 'pre' decoration, showcasing the flexibility in choosing different decoration types for the start of the path.

```tikz
\usetikzlibrary {decorations.pathmorphing, decorations.shapes}
\tikz [decoration={zigzag,pre=crosses,pre length=1cm}]
  \draw [decorate] (0,0) -- (2,1) arc (90:0:1);

```

--------------------------------

### TiKz Foreach Loop Example

Source: https://tikz.dev/tikz-paths

Demonstrates the use of the foreach operation to draw a series of connected line segments based on a numerical range.

```tikz
\tikz \draw (0,0) foreach \x in {1,...,3} { -- (\x,1) -- (\x,0) };
```

--------------------------------

### Smooth Entry and Exit Animation in TikZ

Source: https://tikz.dev/tikz-animations

This example combines both 'exit control' and 'entry control' to create a smooth transition into and out of the animation's keyframes.

```tikz
\tikz {
  \foreach \i in {0,0.125,...,1} \draw (-0.9,.9-\i) -- ++(1.8,0);
  \node :yshift = { begin on = click,
  0s = { exit control = {1}{0}, "0cm" },
  1s = "-5mm",
  2s = { entry control = {0}{1}, "-10mm" } }
  [fill = blue!20, draw = blue, very thick, circle] {Click me!};
                     }
```

--------------------------------

### Setup Nodes for a Bipartite Graph using I_nm

Source: https://tikz.dev/tikz-graphs

Demonstrates setting up nodes for a bipartite graph using the I_nm subgraph, connecting vertices from set V to set W.

```tex
\usetikzlibrary {graphs.standard}
 \tikz \graph {
  subgraph I_nm [n=3, m=4];

  V 1 -- { W 2, W 3 };
  V 2 -- { W 1, W 3 };
  V 3 -- { W 1, W 4 };
                    };

```

--------------------------------

### Smooth Exit Animation in TikZ

Source: https://tikz.dev/tikz-animations

This example demonstrates a smooth exit from the starting position of an animation. It uses 'exit control' to define how the animation leaves the initial state.

```tikz
\tikz {
  \foreach \i in {0,0.125,...,1} \draw (-0.9,.9-\i) -- ++(1.8,0);
  \node :yshift = { begin on = click,
  0s = { exit control = {1}{0}, "0cm" },
  1s = "-5mm",
  2s = "-10mm" }
  [fill = blue!20, draw = blue, very thick, circle] {Click me!};
                     }
```

--------------------------------

### Distance Modifier Syntax Example

Source: https://tikz.dev/tikz-coordinates

Shows the basic syntax of the distance modifier to find a point a specific distance from a starting coordinate along the line to a second coordinate.

```tikz
\usetikzlibrary {calc}
\begin{tikzpicture}
  \draw [help lines] (0,0) grid (3,2);
  \draw (1,0) -- (3,2);
  \foreach \i in {0cm,1cm,15mm}
  \node at ($(1,0)!\i!(3,2)$) {\i};
\end{tikzpicture}
```

--------------------------------

### Basic Quick Graph Syntax

Source: https://tikz.dev/tikz-graphs

Demonstrates the basic usage of the 'quick' graph syntax with node and edge definitions, including options for nodes and edges. Requires 'graphs' and 'quotes' libraries.

```tikz
\usetikzlibrary {graphs,quotes}
\tikz \graph [quick] { "a" --["foo"] "b"[x=1] };

```

--------------------------------

### Shorthand Scope Environments

Source: https://tikz.dev/tikz-scopes

Demonstrates using shorthand braces for scope environments with nested options like line thickness and color.

```LaTeX
\usetikzlibrary {scopes}
\begin{tikzpicture}
  { [ultra thick]
  { [red]
  \draw (0mm,10mm) -- (10mm,10mm);
  \draw (0mm,8mm) -- (10mm,8mm);
  }
  \draw (0mm,6mm) -- (10mm,6mm);
  }
  { [green]
  \draw (0mm,4mm) -- (10mm,4mm);
  \draw (0mm,2mm) -- (10mm,2mm);
  \draw[blue] (0mm,0mm) -- (10mm,0mm);
  }
\end{tikzpicture}
```

--------------------------------

### Basic Pic Usage with Options

Source: https://tikz.dev/tikz-pics

Demonstrates how to use a defined 'pic' with different options to alter its appearance or behavior. Options like color, draw, and shading can be applied.

```tikz
\tikz \pic {my pic}; \space
```

```tikz
\tikz \pic [red] {my pic}; \space
```

```tikz
\tikz \pic [draw] {my pic}; \space
```

```tikz
\tikz \pic [draw=red] {my pic}; \space
```

```tikz
\tikz \pic [draw, shading=ball] {my pic}; \space
```

```tikz
\tikz \pic [fill=red!50] {my pic};
```

--------------------------------

### External File Format for TikZ Plots

Source: https://tikz.dev/tikz-plots

Example of a data file format compatible with TikZ plotting. Each line contains x and y coordinates, optionally followed by a type indicator ('i', 'o', 'u'). Lines starting with '#' or '%' are ignored.

```text
#Curve 0, 20 points
#x y type
0.00000 0.00000  i
0.52632 0.50235  i
1.05263 0.86873  i
1.57895 0.99997  i
                ...
9.47368 -0.04889  i
10.00000 -0.54402  i
```

--------------------------------

### Nested Decorations on a Rectangle

Source: https://tikz.dev/tikz-decorations

Shows how to apply multiple decorations by nesting the 'decorate' command. This example applies a 'zigzag' decoration inside a 'crosses' decoration.

```tikz
\usetikzlibrary { decorations.pathmorphing, decorations.shapes, }
\tikz \fill [fill=blue!20,draw=blue,thick]
  decorate[decoration={crosses,segment length=2mm}] {
  decorate[decoration={zigzag,segment length=10mm,amplitude=2.5mm}] {
  (0,0) rectangle (3,2)
  }
  };

```

--------------------------------

### Path to Current Subpath Start

Source: https://tikz.dev/tikz-paths

Draws a path that returns to the starting point of the current subpath using 'current subpath start'. This does not close the path like '--cycle'.

```tikz
\tikz [line width=2mm]
  \draw (0,0) -- (1,0) -- (1,1)
  -- (0,1) -- (current subpath start);

```

--------------------------------

### Realistic Use of Flex=0 with Open Arrow Tip

Source: https://tikz.dev/tikz-arrows

A practical example of using 'flex=0' with an open arrow tip, ensuring the arrow points along the tangent.

```tikz
\usetikzlibrary {arrows.meta,bending}
\begin{tikzpicture}
  \wall
  \draw [red!25,line width=1mm] (-1,0) -- (1,0);
  \draw [red,line width=1mm,-{Stealth[length=1cm,flex=0]}]
  (-1,-.5) .. controls (0,-.5) and (0,0) .. (1,0);
\end{tikzpicture}
```

--------------------------------

### TikZ Example with Multiple Arrow Tips

Source: https://tikz.dev/tikz-arrows

Demonstrates the use of multiple, individually configured arrow tips on a single line, including bending and different styles. Requires the arrows.meta, bending, and positioning libraries.

```tikz
\usetikzlibrary {arrows.meta,bending,positioning}
\tikz {
  \node [circle,draw] (A) {A};
  \node [circle,draw] (B) [right=of A] {B};
  
  \draw [draw = blue, thick,
  arrows={
  Computer Modern Rightarrow [sep]
  - Latex[blue!50,length=8pt,bend,line width=0pt]
  Stealth[length=8pt,open,bend,sep]}]
  (A) edge [bend left=45] (B)
  (B) edge [in=-110, out=-70,looseness=8] (B);
 }
```

--------------------------------

### Complex Edge Labeling Example

Source: https://tikz.dev/tikz-trees

A more complex example showing how to add multiple labels to edges from parent nodes, demonstrating fine-grained control over edge appearance.

```tikz
\begin{tikzpicture}
  \node {root}
  child {node {left}
  edge from parent
  node[left] {a}
  node[right] {b}
  }
  child {node {right}
  child {node {child}
  edge from parent
  node[left] {c}
  }
  child {node {child}}
  edge from parent
  node[near end] {x}
  };
\end{tikzpicture}
```

--------------------------------

### Filling Paths with Solid Colors

Source: https://tikz.dev/tikz-actions

Demonstrates filling paths with solid colors using the `fill` command. Includes examples of simple lines, circles, and combined shapes.

```tikz
\begin{tikzpicture}
  \fill (0,0) -- (1,1) -- (2,1);
  \fill (4,0) circle (.5cm) (4.5,0) circle (.5cm);
  \fill[even odd rule] (6,0) circle (.5cm) (6.5,0) circle (.5cm);
  \fill (8,0) -- (9,1) -- (10,0) circle (.5cm);
\end{tikzpicture}
```

--------------------------------

### Using Different Arrow Tip Styles

Source: https://tikz.dev/tikz-arrows

Demonstrates the use of different arrow tip styles like Latex, Stealth, and custom combinations with '>->', '|<->>|', and '|<<.<->|'. Ensure the 'arrows.meta' library is loaded.

```tikz
\usetikzlibrary {arrows.meta}
\begin{tikzpicture}[scale=2,ultra thick]
  \begin{scope}[>=Latex]
  \draw[>->] (0pt,3ex) -- (1cm,3ex);
  \draw[|<->>|] (0pt,2ex) -- (1cm,2ex);
  \end{scope}
  \begin{scope}[>=Stealth]
  \draw[>->] (0pt,1ex) -- (1cm,1ex);
  \draw[|<<.<->|] (0pt,0ex) -- (1cm,0ex);
  \end{scope}
\end{tikzpicture}
```

--------------------------------

### Draw Two Parallel Lines

Source: https://tikz.dev/tikz-paths

Illustrates the use of move-to operations to start new, unconnected path segments. Each coordinate without a preceding '--' starts a new subpath.

```tikz
\begin{tikzpicture}
  \draw (0,0) --(2,0) (0,1) --(2,1);
\end{tikzpicture}

```

--------------------------------

### Control TiKZ Animation Start and End Times

Source: https://tikz.dev/tikz-animations

Specifies the start and end points of an animation timeline relative to the display of the graphic. The 'begin' key sets the initial offset, and 'end' truncates the timeline.

```tikz
\tikz \node [fill = green!50!black, text = white]
  :rotate = { 1s = "0", 5s = "90", begin = 2s, end = 4s }
  {Click me};

```

--------------------------------

### Trigger TiKZ Animation with Events

Source: https://tikz.dev/tikz-animations

Defines custom start times ('moment 0s') for an animation timeline based on specific events, such as a click. Multiple 'begin on' events can be specified, accumulating as possible start triggers.

```tikz
\tikz \node [fill = green, text = white] :fill =
  { 1s = "red", 2s = "blue", begin on = click }
  {Click me};

```

--------------------------------

### TikZ Knockout Group Example

Source: https://tikz.dev/tikz-transparency

Illustrates a TikZ knockout group. This example uses a white rectangle and a transparent text node within a knockout group to reveal a background shading through the text's area.

```tikz
\begin{tikzpicture}
  \shade [left color=red,right color=blue] (-2,-1) rectangle (2,1);
  \begin{scope}[transparency group=knockout]
  \fill [white] (-1.9,-.9) rectangle (1.9,.9);
  \node [opacity=0,
  font=\fontencoding{T1}\fontfamily{ptm}\fontsize{45}{45}\bfseries]
  {Ti\emph{k}Z};
  \end{scope}
\end{tikzpicture}
```

--------------------------------

### Overview of TikZ Decorations

Source: https://tikz.dev/tikz-decorations

Demonstrates various built-in TikZ decorations including zigzag, brace, triangles, coil, and expanding waves. Ensure the relevant decoration libraries are loaded.

```tikz
\usetikzlibrary { decorations.pathmorphing, decorations.pathreplacing, decorations.shapes, }
\begin{tikzpicture}[thick]
  \draw  (0,3) -- (3,3);
  \draw[decorate,decoration=zigzag] (0,2.5) -- (3,2.5);
  \draw[decorate,decoration=brace] (0,2) -- (3,2);
  \draw[decorate,decoration=triangles] (0,1.5) -- (3,1.5);
  \draw[decorate,decoration={coil,segment length=4pt}] (0,1) -- (3,1);
  \draw[decorate,decoration={coil,aspect=0}] (0,.5) -- (3,.5);
  \draw[decorate,decoration={expanding waves,angle=7}] (0,0) -- (3,0);
\end{tikzpicture}
```

--------------------------------

### Basic Snapshot Usage

Source: https://tikz.dev/tikz-animations

Illustrates the fundamental use of the \tikz [make snapshot of = ⟨time⟩] command to capture the state of animations at a specific time. This example shows two rectangles with fill colors changing over time, with snapshots taken at 1s.

```tex
\usetikzlibrary {animations}
\tikz [make snapshot of = 1s] {
  \fill :fill = { 0s = "black", 2s = "white" } (0,0) rectangle ++(1,1);
  \fill :fill = { 1s = "black", 3s = "white" } (2,0) rectangle ++(1,1);
}
```

--------------------------------

### Bézier Curves with Relative Control Points

Source: https://tikz.dev/tikz-coordinates

Relative coordinates are interpreted specially for Bézier curve control points. The first control point is relative to the curve's start, the second to the end, and the end point is relative to the start.

```tikz
\begin{tikzpicture}
  \draw (1,0) .. controls +(30:1cm) and +(60:1cm) .. (3,-1);
  \draw[gray,->] (1,0) -- +(30:1cm);
  \draw[gray,<-] (3,-1) -- +(60:1cm);
\end{tikzpicture}
```

--------------------------------

### Draw plot with marks starting at a specific phase

Source: https://tikz.dev/tikz-plots

Use `mark phase` to specify the starting point for drawing marks when `mark repeat` is also used. The first mark is drawn at the `mark phase` index, and subsequent marks follow the `mark repeat` interval.

```tikz
\tikz \draw plot[mark=x,mark repeat=3,mark phase=6,smooth] file {plots/pgfmanual-sine.table};
```

--------------------------------

### TiKZ Minimum Width and Height Example

Source: https://tikz.dev/tikz-shapes

Demonstrates setting both `minimum height` and `minimum width` for a node. This ensures the node's bounding box meets both dimensional requirements.

```tikz
\begin{tikzpicture}
  \draw (0,0) node[minimum height=2cm,minimum width=3cm,draw] {$3 \times 2$};
\end{tikzpicture}
```

--------------------------------

### Add User-Defined Path with To Operation

Source: https://tikz.dev/tikz-paths

The to operation adds a user-defined path from a start coordinate to a target coordinate. It can create straight lines or curves based on specified angles using 'in' and 'out' options. Macros \tikztostart and \tikztotarget are available for referencing start and end points.

```tikz
\begin{tikzpicture}
  \draw[help lines] (0,0) grid (3,2);
  \node (a) at (2,2) {a};
  
  \draw (0,0) to (0,2);
  \draw[red] (10pt,10pt) to (a);
  \draw[blue] (3,0) -- (3,2) -- (a) to cycle;
\end{tikzpicture}
```

--------------------------------

### Arrow with Arrowtip at Both Ends

Source: https://tikz.dev/tikz-arrows

Draws a line with an arrowtip at the start and another at the end.

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

--------------------------------

### Dash Phase

Source: https://tikz.dev/tikz-actions

Shifts the starting point of the dash pattern by a specified phase.

```APIDOC
## /tikz/dash phase=`⟨ _dash phase_ ⟩

### Description
Shifts the start of the dash pattern by the specified phase value.

### Parameters
#### Path Parameters
- **⟨ _dash phase_ ⟩** (string) - Required - The amount to shift the dash pattern start (e.g., '0pt', '10pt').
```

--------------------------------

### Create Complete Bipartite Graphs with Directed Edges

Source: https://tikz.dev/tikz-graphs

Illustrates creating complete bipartite graphs K_nm with directed edges, using different vertex sets and edge directions.

```tex
\usetikzlibrary {graphs.standard}
 \tikz \graph [simple, branch right, grow down]
                     {
  subgraph K_nm [V={1,2,3}, W={a,b,c,d}, ->];
  subgraph K_nm [V={2,3}, W={b,c}, <-];
                     };

```

--------------------------------

### Tangent Coordinate System Example

Source: https://tikz.dev/tikz-coordinates

Demonstrates the tangent coordinate system to find points tangent to a node's border. Requires the 'calc' library. Use 'solution' to specify which tangent point if multiple exist.

```tikz
\usetikzlibrary {calc}
\begin{tikzpicture}
  \draw[help lines] (0,0) grid (3,2);
  
  \coordinate (a) at (3,2);
  
  \node [circle,draw] (c) at (1,1) [minimum size=40pt] {$c$};
  
  \draw[red] (a) -- (tangent cs:node=c,point={(a)},solution=1) --
  (c.center) -- (tangent cs:node=c,point={(a)},solution=2) -- cycle;
\end{tikzpicture}
```

--------------------------------

### Positioning Decorations with Raise

Source: https://tikz.dev/tikz-decorations

Demonstrates how to use the 'raise' option to offset decorations along the path. A positive value raises the decoration, while a negative value lowers it.

```Ti_k_Z
\usetikzlibrary {decorations.shapes}
\begin{tikzpicture}
  \draw [help lines] (0,0) grid (3,2);
  
  \draw (0,0) -- (1,1) arc (90:0:2 and 1);
  \draw decorate                     [decoration=crosses]
  { (0,0) -- (1,1) arc (90:0:2 and 1) };
  \draw[red] decorate                     [decoration={crosses,raise=5pt}]
  { (0,0) -- (1,1) arc (90:0:2 and 1) };
\end{tikzpicture}
```

--------------------------------

### Multiple Arrow Tips

Source: https://tikz.dev/tikz-arrows

Demonstrates how multiple arrow tips are added to the start or end of a line.

```tikz
\tikz \draw [<<<->>>>] (0,0) -- (2,0);
```

--------------------------------

### Animation Triggered by Mouse Out Event

Source: https://tikz.dev/tikz-animations

This is a shorthand for 'event=mouseout'. The animation starts when the mouse leaves the object.

```tikz
\tikz \node :rotate = { 0s="0", 2s="90", begin on = {mouse out} }
  [fill = blue!20, draw = blue, circle, ultra thick] {Here!};
```

--------------------------------

### Loading the Ti*k*Z intersections library

Source: https://tikz.dev/tikz-coordinates

Shows how to load the 'intersections' library for calculating intersections of arbitrary paths. Use the appropriate command for LaTeX/plain TeX or ConTeXt.

```tikz
\usetikzlibrary{intersections} % LaTeX and plain TeX
```

```tikz
\usetikzlibrary[intersections] % ConTeXt
```

--------------------------------

### Transformations Mid-Path Example

Source: https://tikz.dev/tikz-transformations

Illustrates how transformations can be applied mid-path. The transformation affects only the coordinates that follow it.

```tikz
\tikz \draw (0,0) rectangle (1,0.5) [xshift=2cm] (0,0) rectangle (1,0.5);
```

--------------------------------

### Using Shorthands for Harpoon and Swap

Source: https://tikz.dev/tikz-arrows

Demonstrates the 'left' and 'right' shorthands for 'harpoon' and 'harpoon,swap' respectively.

```tikz
 \usetikzlibrary {arrows.meta}
 \tikz [ultra thick] \draw [arrows =                     {-Stealth[left]}] (0,0) -- (1,0);
 
```

```tikz
 \usetikzlibrary {arrows.meta}
 \tikz [ultra thick] \draw [arrows =                     {-Stealth[right]}] (0,0) -- (1,0);
 
```

--------------------------------

### Animation Triggered by Click Event

Source: https://tikz.dev/tikz-animations

This is a shorthand for 'event=click'. The animation starts when the user clicks on the triggering object.

```tikz
\tikz \node :rotate = { 0s="0", 2s="90", begin on = {click}}
  [fill = blue!20, draw = blue, circle, ultra thick] {Here!};
```

--------------------------------

### Drawing a Triangular Path in Ti_k_Z

Source: https://tikz.dev/tikz-design

Illustrates how to define and draw a simple triangular path using Ti_k_Z syntax, similar to MetaPost.

```tex
(5pt,0pt) -- (0pt,0pt) -- (0pt,5pt) -- cycle
```

--------------------------------

### Y-Shift Transformation Example

Source: https://tikz.dev/tikz-transformations

Shows the 'yshift' option, which adds a specified dimension to the y-coordinate of all subsequent coordinates.

```tikz
This option does not take any parameter. Its effect is to cancel all current transformations except for the shifting. This means that the origin will remain where it is, but any rotation around the origin or scaling relative to the origin or skewing will no longer have an effect.
This option is useful in situations where a complicated transformation is used to “get to a position”, but you then wish to draw something “normal” at this position.
```

--------------------------------

### Tree with Named and Positioned Children using Foreach

Source: https://tikz.dev/tikz-trees

Shows how to use 'foreach' with multiple variables to assign names and positions to children. This example is equivalent to manually specifying each child with its respective options.

```tikz
node {root} child[\pos] foreach \name/\pos in {1/left,2/right} {node[\pos] {\name}}
```

```tikz
node {root} child[left] {node[left] {1}} child[right] {node[right] {2}}
```

--------------------------------

### X-Shift Transformation Example

Source: https://tikz.dev/tikz-transformations

Illustrates the use of 'xshift' to add a specified dimension to the x-coordinate of all subsequent coordinates.

```tikz
\begin{tikzpicture}
  \draw[help lines] (0,0) grid (3,2);
  \draw (0,0) -- (1,1) -- (1,0);
  \draw[xshift=2cm,blue] (0,0) -- (1,1) -- (1,0);
  \draw[xshift=-10pt,red] (0,0) -- (1,1) -- (1,0);
\end{tikzpicture}
```

--------------------------------

### Cartesian Placement with Node Width and Depth

Source: https://tikz.dev/tikz-graphs

Demonstrates the default Cartesian placement strategy, showing the computed logical width and depth for each node. This example requires the 'graphs' TikZ library.

```tikz
\usetikzlibrary {graphs}
\tikz
  \graph [nodes={align=center, inner sep=1pt}, grow right=7mm,
  typeset={\tikzgraphnodetext\[-4pt]
  \tiny\mywidth\[-6pt]\tiny\mydepth}, 
  placement/compute position/.append code=
 \pgfkeysgetvalue{/tikz/graphs/placement/width}{\mywidth}
  \pgfkeysgetvalue{/tikz/graphs/placement/depth}{\mydepth}] 
                     {
  a,
  b,
  c -> d -> {
  e -> f -> g,
  h -> i
  } -> j,
  k -> l
                     };

```

--------------------------------

### Ti*k*Z Quote Syntax Example

Source: https://tikz.dev/tikz-animations

Demonstrates the quote syntax for specifying values in Ti*k*Z animations, including handling commas within values.

```tikz
sync = {value = red, entry}
```

--------------------------------

### Animation Triggered by Mouse Move Event

Source: https://tikz.dev/tikz-animations

This is a shorthand for 'event=mousemove'. The animation starts each time the mouse moves while over the object.

```tikz
\tikz \node :rotate = { 0s="0", 2s="90", begin on = {mouse move} }
  [fill = blue!20, draw = blue, circle, ultra thick] {Here!};
```

--------------------------------

### Looping through Snapshot Times

Source: https://tikz.dev/tikz-animations

Demonstrates how to use a \foreach loop to generate multiple snapshots of an animation at different specified times. This is useful for showing animation progression on paper.

```tex
\foreach \t in {0.5, 1, 1.5, 2}
  \tikz [make snapshot of = \t]
  \fill :fill = {0s="black", 2s="red"} (0,0) circle [radius = 5mm];
```

--------------------------------

### Animation Triggered by Mouse Over Event

Source: https://tikz.dev/tikz-animations

This is a shorthand for 'event=mouseover'. The animation starts the moment the mouse cursor moves over the object.

```tikz
\tikz \node :rotate = { 0s="0", 2s="90", begin on = {mouse over} }
  [fill = blue!20, draw = blue, circle, ultra thick] {Here!};
```

--------------------------------

### Animation Triggered by Mouse Up Event

Source: https://tikz.dev/tikz-animations

This is a shorthand for 'event=mouseup'. The animation starts when a pressed mouse button is released on the object.

```tikz
\tikz \node :rotate = { 0s="0", 2s="90", begin on = {mouse up} }
  [fill = blue!20, draw = blue, circle, ultra thick] {Here!};
```

--------------------------------

### Filling Paths with Patterns

Source: https://tikz.dev/tikz-actions

Illustrates filling paths with tiling patterns using the `pattern` option. Requires loading the `patterns` library. Shows different patterns like `dots` and `fivepointed stars`.

```tikz
\usetikzlibrary {patterns}
\begin{tikzpicture}
  \draw[pattern=dots] (0,0) circle (1cm);
  \draw[pattern=fivepointed stars] (0,0) rectangle (3,1);
\end{tikzpicture}
```

--------------------------------

### Animation Triggered by Mouse Down Event

Source: https://tikz.dev/tikz-animations

This is a shorthand for 'event=mousedown'. The animation starts when the user presses a mouse button down on the object.

```tikz
\tikz \node :rotate = { 0s="0", 2s="90", begin on = {mouse down}}
  [fill = blue!20, draw = blue, circle, ultra thick] {Here!};
```

--------------------------------

### Advanced Quick Graph Syntax with Groups

Source: https://tikz.dev/tikz-graphs

Illustrates a more complex 'quick' graph specification involving multiple edges, node options, and grouping with shared node options. Requires the 'graphs' library.

```tikz
\usetikzlibrary {graphs}
\tikz \graph [quick] {
 "a"/"$a$" -- "b"[x=1] --[red] "c"[x=2];
 { [nodes=blue] "a" -- "d"[y=1]; };
};

```

--------------------------------

### Round Cap Example

Source: https://tikz.dev/tikz-arrows

Shows the basic Round Cap, which ends a line with a half-circle or a half-ellipse if the length is modified.

```tikz
Round Cap[]
```

--------------------------------

### Basic Downward Growing Tree

Source: https://tikz.dev/tikz-trees

A simple example demonstrating a downward-growing tree structure with a root and child nodes.

```tikz
\begin{tikzpicture}
  \node {root}
  child                 {node {left}}
  child                 {node {right}
  child                 {node {child}}
  child                 {node {child}}
  };
\end{tikzpicture}
```

--------------------------------

### Animating :xshift

Source: https://tikz.dev/tikz-animations

Animate horizontal shifts using the :xshift attribute. Specify the starting and ending horizontal displacements for the animation.

```tikz
\tikz \node :xshift = { 0s="0pt", 2s="5mm", begin on=click}  
  [fill = blue!20, draw = blue, ultra thick, circle] {Click me!};  
```

--------------------------------

### Mirroring Decorations

Source: https://tikz.dev/tikz-decorations

Shows how to use the 'mirror' option to reflect decorations along the path. This is applied after 'transform' and 'raise'.

```Ti_k_Z
\usetikzlibrary {decorations.pathreplacing}
\begin{tikzpicture}
  \node (a) {A};
  \node (b) at (2,1) {B};
  \draw  (a) -- (b);
  \draw[decorate,decoration=brace] (a) -- (b);
  \draw[decorate,decoration={brace,mirror},red] (a) -- (b);
  \draw[decorate,decoration={brace,mirror,raise=5pt},blue] (a) -- (b);
\end{tikzpicture}
```

--------------------------------

### Animate Visibility

Source: https://tikz.dev/tikz-animations

Control the visibility of a node. This example sets the node to be initially invisible and remain invisible, triggered by a click.

```tikz
\tikz :visible = {begin on=click, 0s="false", 2s="false"}
  \node (node) [fill = blue!20, draw = blue, very thick, circle] {Click me!};
```

--------------------------------

### Ti_k_Z Decoration with Default 'pre' (lineto)

Source: https://tikz.dev/tikz-decorations

Demonstrates the default 'pre' decoration behavior, which is 'lineto'. This is useful for understanding how Ti_k_Z handles the start of a decoration when 'pre' is not explicitly set to 'curveto'.

```tikz
\usetikzlibrary {decorations.pathmorphing}
\tikz [decoration={zigzag,pre=lineto,pre length=1cm}]
  \draw [decorate] (0,0) -- (2,1) arc (90:0:1);

```

--------------------------------

### TiKz Projection Modifier Syntax Example

Source: https://tikz.dev/tikz-coordinates

Demonstrates the basic syntax of a TiKz projection modifier. This is a literal coordinate representation.

```tikz
(1,2)!(0,5)!(3,4)
```

--------------------------------

### Ti_k_Z Decoration with Extended 'pre length' (default 'lineto')

Source: https://tikz.dev/tikz-decorations

This example uses a 'pre length' of 3cm with the default 'pre' decoration ('lineto'), demonstrating a longer initial segment before the main decoration begins.

```tikz
\usetikzlibrary {decorations.pathmorphing}
\tikz [decoration={zigzag,pre length=3cm}]
  \draw [decorate] (0,0) -- (2,1) arc (90:0:1);

```

--------------------------------

### Animation Triggered by Another Animation's Begin Event

Source: https://tikz.dev/tikz-animations

This is a shorthand for 'event=begin'. The animation starts when another referenced animation begins.

```tikz
\tikz \node [animate = {
  myself:rotate = { 0s="0", 2s="90", begin
  on = {begin, of
  next=anim}},
  myself:xshift = { 0s="0mm", 2s="5mm", begin
  on = {click}, name=anim}
  }]
```

--------------------------------

### Loading TikZ Package in ConTeXt

Source: https://tikz.dev/tikz-scopes

ConTeXt users should use the \usemodule command to load the TikZ package.

```context
\usemodule[tikz] % ConTeXt
```

--------------------------------

### Basic TikZ Matrix Example

Source: https://tikz.dev/tikz-matrices

Demonstrates the creation of a TikZ matrix with different cell contents, including shapes and nodes. The matrix itself is styled with fill and border. The matrix is positioned and an arrow points to its west anchor.

```tikz
\begin{tikzpicture}
  \draw[help lines] (0,0) grid (4,2);
  \node [matrix,fill=red!20,draw=blue,very thick] (my matrix) at (2,1)
  {
  \draw (0,0) circle (4mm); & \node[rotate=10] {Hello}; \\
  \draw (0.2,0) circle (2mm); & \fill[red] (0,0) circle (3mm); \\
  };

  \draw [very thick,->] (0,0) |- (my matrix.west);
\end{tikzpicture}
```

--------------------------------

### Partway Modifier Syntax Example

Source: https://tikz.dev/tikz-coordinates

Demonstrates the basic syntax of the partway modifier to find a coordinate a fraction of the way between two points.

```tikz
(1,2)!.75!(3,4)
```

--------------------------------

### Create Tree-like Graph with TikZ Graphs

Source: https://tikz.dev/tikz-graphs

Demonstrates the basic syntax for creating a tree-like graph structure using the TikZ 'graphs' library. This is a foundational example for more complex graph specifications.

```tikz
\usetikzlibrary {graphs}
 \tikz \graph { a -> {b,c} };

```

--------------------------------

### TiKZ Minimum Size Example

Source: https://tikz.dev/tikz-shapes

Illustrates setting a uniform minimum size for both height and width using the `minimum size` option. This is useful for creating square nodes or ensuring a consistent base size for different shapes.

```tikz
\begin{tikzpicture}
  \draw (0,0) node[minimum size=2cm,draw] {square};
  \draw (0,-2) node[minimum size=2cm,draw,circle] {circle};
\end{tikzpicture}
```

--------------------------------

### Shift Only Transformation Example

Source: https://tikz.dev/tikz-transformations

Demonstrates the 'shift only' option, which cancels all transformations except for shifting. This is useful for drawing normally at a transformed position.

```tikz
\begin{tikzpicture}
  \draw[help lines] (0,0) grid (3,2);
  \draw  (0,0) -- (1,1) -- (1,0);
  \draw[rotate=30,xshift=2cm,blue] (0,0) -- (1,1) -- (1,0);
  \draw[rotate=30,xshift=2cm,shift only,red] (0,0) -- (1,1) -- (1,0);
\end{tikzpicture}
```
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