> ## Documentation Index
> Fetch the complete documentation index at: https://resources.latex-cloud-studio.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Creating Diagrams with TikZ

> Master TikZ for creating professional diagrams in LaTeX. Learn drawing commands, libraries, flowcharts, graphs, and advanced visualization techniques.

Create publication-quality diagrams directly in LaTeX using TikZ. This comprehensive guide covers basic shapes to complex technical illustrations, including flowcharts, graphs, circuits, and scientific diagrams.

<Info>
  **Prerequisites**: Basic LaTeX knowledge\
  **Time to complete**: 40-45 minutes\
  **Difficulty**: Intermediate to Advanced\
  **What you'll learn**: TikZ syntax, libraries, drawing techniques, and practical examples
</Info>

## Introduction to TikZ

### What is TikZ?

TikZ (TikZ ist kein Zeichenprogramm - TikZ is not a drawing program) is a powerful package for creating graphics programmatically in LaTeX. It provides:

<CardGroup cols={2}>
  <Card title="Precise Control" icon="ruler">
    Exact positioning and measurements
  </Card>

  <Card title="Consistency" icon="palette">
    Matching document fonts and styles
  </Card>

  <Card title="Programmable" icon="code">
    Loops, variables, and calculations
  </Card>

  <Card title="Integration" icon="puzzle-piece">
    Seamless LaTeX integration
  </Card>
</CardGroup>

### Basic Setup

<CodeGroup>
  ```latex tikz-setup.tex theme={null}
  \documentclass{article}
  \usepackage{tikz}

  % Load common libraries
  \usetikzlibrary{
      arrows.meta,      % Arrow styles
      positioning,      % Relative positioning
      shapes.geometric, % Additional shapes
      calc,            % Coordinate calculations
      patterns,        % Fill patterns
      decorations.pathmorphing, % Path decorations
      backgrounds,     % Background layers
      fit,            % Fitting nodes
      chains,         % Chain positioning
      shadows         % Drop shadows
  }

  \begin{document}

  % Inline TikZ
  \begin{tikzpicture}
      \draw (0,0) -- (2,1);
  \end{tikzpicture}

  % Centered figure
  \begin{figure}[htbp]
      \centering
      \begin{tikzpicture}
          % Drawing commands here
      \end{tikzpicture}
      \caption{TikZ diagram}
  \end{figure}

  \end{document}
  ```

  ```latex basic-shapes.tex theme={null}
  % Basic shapes and lines
  \begin{tikzpicture}
      % Grid for reference (remove in final)
      \draw[help lines, gray] (0,0) grid (6,4);
      
      % Lines
      \draw (0,0) -- (2,1);                    % Straight line
      \draw[thick] (3,0) -- (5,1);             % Thick line
      \draw[dashed] (0,2) -- (2,3);            % Dashed line
      \draw[->] (3,2) -- (5,3);                % Arrow
      \draw[<->, red] (0,3.5) -- (2,3.5);      % Double arrow
      
      % Basic shapes
      \draw (1,1) circle (0.5);                % Circle
      \draw[fill=blue!20] (4,1) circle (0.5);  % Filled circle
      \draw (0,0) rectangle (1,0.8);           % Rectangle
      \draw[rounded corners] (3,0) rectangle (4,0.8); % Rounded
      
      % Nodes (shapes with text)
      \node[circle, draw] at (1,3) {A};
      \node[rectangle, draw, fill=green!20] at (4,3) {Box};
  \end{tikzpicture}
  ```
</CodeGroup>

## Basic Drawing

### Coordinates and Paths

<CodeGroup>
  ```latex coordinates.tex theme={null}
  \begin{tikzpicture}[scale=1.5]
      % Cartesian coordinates
      \draw[->] (-0.5,0) -- (4,0) node[right] {$x$};
      \draw[->] (0,-0.5) -- (0,3) node[above] {$y$};
      
      % Points
      \fill (1,1) circle (2pt) node[below] {$(1,1)$};
      \fill (3,2) circle (2pt) node[right] {$(3,2)$};
      
      % Path with multiple segments
      \draw[thick, blue] (0,0) -- (1,1) -- (2,0.5) -- (3,2);
      
      % Curved path
      \draw[thick, red] (0,2) .. controls (1,3) and (2,1) .. (3,2.5);
      
      % Closed path
      \draw[thick, green, fill=green!20] 
          (0.5,0.5) -- (1.5,0.5) -- (1,1.5) -- cycle;
          
      % Polar coordinates
      \draw[purple] (0,0) -- (45:2) node[midway, above] {$(45:2)$};
      
      % Relative coordinates
      \draw[orange, thick] (2,1) -- ++(1,0.5) -- ++(0.5,-0.5);
  \end{tikzpicture}
  ```

  ```latex path-operations.tex theme={null}
  \begin{tikzpicture}[scale=1.2]
      % Different path operations
      
      % Straight lines with corners
      \draw[blue] (0,0) -| (2,1);  % Horizontal then vertical
      \draw[red] (3,0) |- (5,1);   % Vertical then horizontal
      
      % Bezier curves
      \draw[thick] (0,2) .. controls (1,3) .. (2,2);
      \draw[thick, green] (3,2) .. controls (3.5,3) and (4.5,3) .. (5,2);
      
      % Arcs
      \draw[thick, orange] (1,3) arc (0:90:1);
      \draw[thick, purple] (4,3) arc (180:45:1.5);
      
      % Smooth curves through points
      \draw[thick, brown] plot[smooth] coordinates {
          (0,4) (0.5,4.5) (1,4.2) (1.5,4.8) (2,4.3)
      };
      
      % Cycle back to start
      \draw[thick, cyan, fill=cyan!20] 
          (3,4) -- (4,4.5) -- (5,4) -- (4,3.5) -- cycle;
  \end{tikzpicture}
  ```
</CodeGroup>

### Nodes and Labels

<CodeGroup>
  ```latex nodes-basics.tex theme={null}
  \begin{tikzpicture}[
      every node/.style={font=\sffamily},
      main node/.style={circle, draw, minimum size=1cm}
  ]
      % Basic nodes
      \node (A) at (0,0) {Simple text};
      \node[draw] (B) at (3,0) {Boxed text};
      \node[circle, draw] (C) at (6,0) {Circle};
      
      % Styled nodes
      \node[main node, fill=blue!20] (D) at (0,2) {D};
      \node[rectangle, draw, rounded corners, fill=red!20] (E) at (3,2) {Rect};
      \node[ellipse, draw, fill=green!20] (F) at (6,2) {Ellipse};
      
      % Node connections
      \draw[->] (A) -- (B);
      \draw[->] (B) -- (C);
      \draw[<->, thick] (D) -- (E);
      \draw[->, dashed] (E) -- (F);
      
      % Labels on edges
      \draw[->] (D) -- (A) node[midway, left] {edge};
      \draw[->] (F) -- (C) node[near start, right] {label};
  \end{tikzpicture}
  ```

  ```latex node-positioning.tex theme={null}
  \begin{tikzpicture}[
      node distance=2cm,
      box/.style={rectangle, draw, minimum width=2cm, minimum height=1cm}
  ]
      % Central node
      \node[box, fill=yellow!30] (center) {Center};
      
      % Relative positioning
      \node[box, above=of center] (top) {Above};
      \node[box, below=of center] (bottom) {Below};
      \node[box, left=of center] (left) {Left};
      \node[box, right=of center] (right) {Right};
      
      % Diagonal positioning
      \node[box, above right=of center] (tr) {Top Right};
      \node[box, below left=of center] (bl) {Bottom Left};
      
      % Custom distances
      \node[box, above=3cm of center] (far) {Far Above};
      \node[box, right=1cm of center] (near) {Near Right};
      
      % Connect all to center
      \foreach \n in {top, bottom, left, right, tr, bl, far, near}
          \draw[->] (center) -- (\n);
  \end{tikzpicture}
  ```
</CodeGroup>

## Flowcharts and Diagrams

### Basic Flowcharts

<CodeGroup>
  ```latex simple-flowchart.tex theme={null}
  \begin{tikzpicture}[
      node distance=2cm,
      startstop/.style={rectangle, rounded corners, draw, fill=red!30, minimum width=3cm, minimum height=1cm},
      process/.style={rectangle, draw, fill=blue!30, minimum width=3cm, minimum height=1cm},
      decision/.style={diamond, draw, fill=green!30, minimum width=3cm, minimum height=1cm, aspect=2},
      io/.style={trapezium, trapezium left angle=70, trapezium right angle=110, draw, fill=yellow!30, minimum width=3cm, minimum height=1cm},
      arrow/.style={thick, ->, >=stealth}
  ]
      % Nodes
      \node[startstop] (start) {Start};
      \node[io, below=of start] (input) {Input data};
      \node[process, below=of input] (process1) {Process data};
      \node[decision, below=of process1] (decision) {Valid?};
      \node[process, below=of decision] (process2) {Generate output};
      \node[startstop, below=of process2] (stop) {End};
      
      % Alternative path
      \node[process, right=3cm of decision] (error) {Handle error};
      
      % Connections
      \draw[arrow] (start) -- (input);
      \draw[arrow] (input) -- (process1);
      \draw[arrow] (process1) -- (decision);
      \draw[arrow] (decision) -- node[left] {Yes} (process2);
      \draw[arrow] (decision) -- node[above] {No} (error);
      \draw[arrow] (error) |- (input);
      \draw[arrow] (process2) -- (stop);
  \end{tikzpicture}
  ```

  ```latex complex-flowchart.tex theme={null}
  \begin{tikzpicture}[
      node distance=1.5cm and 2cm,
      box/.style={rectangle, draw, fill=#1, minimum width=2.5cm, minimum height=0.8cm, font=\small},
      decision/.style={diamond, draw, fill=orange!30, aspect=1.5, font=\small},
      cloud/.style={cloud, draw, fill=gray!20, minimum width=2cm, minimum height=1cm},
      database/.style={cylinder, draw, fill=purple!30, minimum width=2cm, minimum height=1cm, shape border rotate=90},
      arr/.style={->, >=latex, thick}
  ]
      % System architecture flowchart
      \node[cloud] (user) {User};
      \node[box=blue!30, below=of user] (ui) {UI Layer};
      \node[box=green!30, below=of ui] (api) {API Gateway};
      \node[decision, below=of api] (auth) {Authenticated?};
      \node[box=yellow!30, below left=of auth] (login) {Login Service};
      \node[box=cyan!30, below right=of auth] (service) {Business Logic};
      \node[database, below=of service] (db) {Database};
      \node[box=red!30, right=of service] (cache) {Cache};
      
      % Connections with labels
      \draw[arr] (user) -- (ui);
      \draw[arr] (ui) -- (api) node[midway, right] {HTTP};
      \draw[arr] (api) -- (auth);
      \draw[arr] (auth) -- node[left] {No} (login);
      \draw[arr] (auth) -- node[right] {Yes} (service);
      \draw[arr] (login) -| (api);
      \draw[arr] (service) -- (db) node[midway, right] {Query};
      \draw[arr, <->] (service) -- (cache) node[midway, above] {Read/Write};
      \draw[arr] (db) -| (cache) node[near start, left] {Update};
  \end{tikzpicture}
  ```
</CodeGroup>

### State Diagrams

<CodeGroup>
  ```latex state-diagram.tex theme={null}
  \begin{tikzpicture}[
      >=stealth,
      node distance=3cm,
      state/.style={circle, draw, minimum size=1.5cm, font=\small},
      initial/.style={state, fill=green!30},
      final/.style={state, double, fill=red!30},
      transition/.style={->, thick}
  ]
      % States
      \node[initial] (idle) {Idle};
      \node[state, right=of idle] (loading) {Loading};
      \node[state, right=of loading] (active) {Active};
      \node[state, below=of active] (error) {Error};
      \node[final, below=of idle] (terminated) {Done};
      
      % Transitions
      \draw[transition] (idle) -- node[above] {start} (loading);
      \draw[transition] (loading) -- node[above] {success} (active);
      \draw[transition] (loading) -- node[right] {fail} (error);
      \draw[transition] (active) -- node[right] {complete} (terminated);
      \draw[transition] (error) -- node[below] {retry} (loading);
      \draw[transition] (error) -- node[left] {abort} (terminated);
      \draw[transition, bend left=30] (active) to node[above] {reset} (idle);
      
      % Self loop
      \draw[transition] (active) to[loop above] node {update} (active);
  \end{tikzpicture}
  ```

  ```latex automaton.tex theme={null}
  \begin{tikzpicture}[
      shorten >=1pt,
      node distance=2.5cm,
      on grid,
      auto,
      state/.style={circle, draw, minimum size=1.2cm},
      accepting/.style={state, double}
  ]
      % Finite automaton
      \node[state, initial] (q0) {$q_0$};
      \node[state] (q1) [right=of q0] {$q_1$};
      \node[state] (q2) [right=of q1] {$q_2$};
      \node[accepting] (q3) [right=of q2] {$q_3$};
      
      % Transitions
      \path[->]
          (q0) edge node {0} (q1)
          (q0) edge[loop above] node {1} (q0)
          (q1) edge node {1} (q2)
          (q1) edge[bend left] node {0} (q0)
          (q2) edge node {0} (q3)
          (q2) edge[bend left] node[below] {1} (q1)
          (q3) edge[loop above] node {0,1} (q3);
          
      % Label
      \node[below=2cm of q1, text width=6cm, align=center] {
          Finite automaton accepting strings with exactly three 0s
      };
  \end{tikzpicture}
  ```
</CodeGroup>

## Graphs and Trees

### Graph Structures

<CodeGroup>
  ```latex simple-graph.tex theme={null}
  \begin{tikzpicture}[
      node distance=2cm,
      vertex/.style={circle, draw, fill=blue!20, minimum size=8mm},
      edge/.style={thick}
  ]
      % Vertices
      \node[vertex] (A) {A};
      \node[vertex, right=of A] (B) {B};
      \node[vertex, below right=of A] (C) {C};
      \node[vertex, below left=of A] (D) {D};
      \node[vertex, below=of C] (E) {E};
      
      % Edges
      \draw[edge] (A) -- (B);
      \draw[edge] (A) -- (C);
      \draw[edge] (A) -- (D);
      \draw[edge] (B) -- (C);
      \draw[edge] (C) -- (D);
      \draw[edge] (C) -- (E);
      \draw[edge] (D) -- (E);
      
      % Edge labels
      \draw[edge] (B) -- node[above right] {5} (E);
  \end{tikzpicture}
  ```

  ```latex directed-graph.tex theme={null}
  \begin{tikzpicture}[
      scale=1.5,
      vertex/.style={circle, draw, fill=orange!30, minimum size=10mm, font=\footnotesize},
      edge/.style={->, >=stealth, thick},
      weight/.style={midway, font=\scriptsize, fill=white, inner sep=1pt}
  ]
      % Weighted directed graph
      \node[vertex] (1) at (0,2) {1};
      \node[vertex] (2) at (2,3) {2};
      \node[vertex] (3) at (4,2) {3};
      \node[vertex] (4) at (3,0) {4};
      \node[vertex] (5) at (1,0) {5};
      
      % Weighted edges
      \draw[edge] (1) -- node[weight] {3} (2);
      \draw[edge] (2) -- node[weight] {1} (3);
      \draw[edge] (3) -- node[weight] {4} (4);
      \draw[edge] (4) -- node[weight] {2} (5);
      \draw[edge] (5) -- node[weight] {6} (1);
      \draw[edge] (1) -- node[weight] {5} (3);
      \draw[edge] (2) -- node[weight] {2} (4);
      
      % Self loop
      \draw[edge] (3) to[loop right] node[weight] {1} (3);
  \end{tikzpicture}
  ```
</CodeGroup>

### Tree Structures

<CodeGroup>
  ```latex binary-tree.tex theme={null}
  \begin{tikzpicture}[
      level distance=1.5cm,
      level 1/.style={sibling distance=4cm},
      level 2/.style={sibling distance=2cm},
      level 3/.style={sibling distance=1cm},
      treenode/.style={circle, draw, fill=green!30, minimum size=8mm},
      edge from parent/.style={draw, ->, >=stealth}
  ]
      % Binary tree
      \node[treenode] {8}
          child {
              node[treenode] {3}
              child {
                  node[treenode] {1}
              }
              child {
                  node[treenode] {6}
                  child {
                      node[treenode] {4}
                  }
                  child {
                      node[treenode] {7}
                  }
              }
          }
          child {
              node[treenode] {10}
              child[missing] {}
              child {
                  node[treenode] {14}
                  child {
                      node[treenode] {13}
                  }
                  child[missing] {}
              }
          };
  \end{tikzpicture}
  ```

  ```latex tree-layouts.tex theme={null}
  \begin{tikzpicture}[
      grow=down,
      level 1/.style={sibling distance=5cm},
      level 2/.style={sibling distance=2.5cm},
      level 3/.style={sibling distance=1.5cm},
      edge from parent/.style={draw, thick},
      nodeStyle/.style={rectangle, draw, fill=cyan!20, minimum width=2cm, minimum height=0.8cm, font=\small},
      leafStyle/.style={nodeStyle, fill=yellow!30}
  ]
      % Organizational chart style tree
      \node[nodeStyle] {CEO}
          child {
              node[nodeStyle] {CTO}
              child {
                  node[nodeStyle] {Dev Team}
                  child { node[leafStyle] {Frontend} }
                  child { node[leafStyle] {Backend} }
              }
              child {
                  node[nodeStyle] {DevOps}
                  child { node[leafStyle] {Cloud} }
                  child { node[leafStyle] {Security} }
              }
          }
          child {
              node[nodeStyle] {CFO}
              child { node[leafStyle] {Accounting} }
              child { node[leafStyle] {Finance} }
          }
          child {
              node[nodeStyle] {CMO}
              child { node[leafStyle] {Marketing} }
              child { node[leafStyle] {Sales} }
          };
          
      % Alternative: horizontal tree
      \begin{scope}[xshift=10cm]
          \tikzset{
              grow=right,
              level 1/.style={sibling distance=2cm, level distance=2.5cm},
              level 2/.style={sibling distance=1cm, level distance=2.5cm}
          }
          \node[nodeStyle] {Root}
              child { 
                  node[nodeStyle] {A}
                  child { node[leafStyle] {A1} }
                  child { node[leafStyle] {A2} }
              }
              child {
                  node[nodeStyle] {B}
                  child { node[leafStyle] {B1} }
              };
      \end{scope}
  \end{tikzpicture}
  ```
</CodeGroup>

## Scientific Diagrams

### Mathematical Diagrams

<CodeGroup>
  ```latex function-plot.tex theme={null}
  \begin{tikzpicture}[scale=1.5]
      % Axes
      \draw[->] (-0.5,0) -- (4,0) node[right] {$x$};
      \draw[->] (0,-0.5) -- (0,3) node[above] {$y$};
      
      % Grid
      \draw[gray, very thin] (0,0) grid (3.5,2.5);
      
      % Function plots
      \draw[blue, thick, domain=0:3.5, samples=100] 
          plot (\x, {0.5*\x*\x - \x + 1});
      \draw[red, thick, domain=0:3.5, samples=100] 
          plot (\x, {sin(\x r) + 1});
      \draw[green, thick, domain=0.1:3.5, samples=100] 
          plot (\x, {ln(\x) + 1});
          
      % Labels
      \node[blue] at (3,2.2) {$f(x) = \frac{1}{2}x^2 - x + 1$};
      \node[red] at (2,0.3) {$g(x) = \sin(x) + 1$};
      \node[green] at (3.2,1.3) {$h(x) = \ln(x) + 1$};
      
      % Points of interest
      \fill[blue] (2,1) circle (2pt) node[above right] {$(2,1)$};
  \end{tikzpicture}
  ```

  ```latex geometric-diagram.tex theme={null}
  \begin{tikzpicture}[scale=2]
      % Triangle with labels
      \coordinate[label=left:$A$] (A) at (0,0);
      \coordinate[label=right:$B$] (B) at (3,0);
      \coordinate[label=above:$C$] (C) at (1.5,2);
      
      % Draw triangle
      \draw[thick] (A) -- (B) -- (C) -- cycle;
      
      % Angles
      \draw[fill=red!20] (A) -- (0.5,0) arc (0:53.13:0.5) -- cycle;
      \draw[fill=blue!20] (B) -- (2.5,0) arc (180:126.87:0.5) -- cycle;
      \draw[fill=green!20] (C) -- (1.5,1.5) arc (270:270-73.74:0.5) -- cycle;
      
      % Angle labels
      \node at (0.7,0.2) {$\alpha$};
      \node at (2.3,0.2) {$\beta$};
      \node at (1.5,1.6) {$\gamma$};
      
      % Side labels
      \node[below] at (1.5,0) {$c$};
      \node[above right] at (2.25,1) {$a$};
      \node[above left] at (0.75,1) {$b$};
      
      % Height
      \draw[dashed] (C) -- (1.5,0) node[midway, right] {$h$};
      \fill (1.5,0) circle (1pt);
  \end{tikzpicture}
  ```
</CodeGroup>

### Physics Diagrams

<CodeGroup>
  ```latex physics-diagram.tex theme={null}
  \begin{tikzpicture}[
      force/.style={->, thick, blue},
      mass/.style={rectangle, draw, fill=gray!30, minimum width=1.5cm, minimum height=1.5cm}
  ]
      % Free body diagram
      \node[mass] (m) {$m$};
      
      % Forces
      \draw[force] (m.north) -- ++(0,2) node[above] {$N$};
      \draw[force] (m.south) -- ++(0,-2) node[below] {$mg$};
      \draw[force] (m.east) -- ++(1.5,0) node[right] {$F$};
      \draw[force] (m.west) -- ++(-1,0) node[left] {$f$};
      
      % Surface
      \draw[thick] (-3,-0.75) -- (3,-0.75);
      \foreach \x in {-3,-2.5,...,3} {
          \draw (\x,-0.75) -- (\x-0.25,-1);
      }
      
      % Angle for inclined plane
      \begin{scope}[xshift=6cm]
          \draw[thick] (0,0) -- (4,0) -- (4,2) -- cycle;
          \node[mass, rotate=26.57] at (2.5,1.25) {$m$};
          \draw[force] (2.5,1.25) -- ++(0,-2) node[below] {$mg$};
          \draw[force, rotate=26.57] (2.5,1.25) -- ++(0,1.5) node[above] {$N$};
          \node at (0.5,0.15) {$\theta$};
      \end{scope}
  \end{tikzpicture}
  ```

  ```latex circuit-diagram.tex theme={null}
  \begin{tikzpicture}[circuit ee IEC]
      % Simple circuit
      \draw (0,0) to[battery] (0,3)
            to[ammeter] (3,3)
            to[resistor={info=$R_1$}] (3,1.5)
            to[resistor={info=$R_2$}] (3,0)
            -- (0,0);
            
      % Parallel circuit
      \begin{scope}[xshift=5cm]
          \draw (0,0) to[voltage source] (0,3) -- (1,3)
                to[resistor={info=$R_1$}] (3,3) -- (4,3)
                -- (4,0) -- (0,0);
          \draw (1,3) -- (1,2)
                to[resistor={info=$R_2$}] (3,2) -- (3,3);
          \draw (1,2) -- (1,1)
                to[capacitor={info=$C$}] (3,1) -- (3,2);
      \end{scope}
  \end{tikzpicture}
  ```
</CodeGroup>

## Advanced Techniques

### Loops and Automation

<CodeGroup>
  ```latex foreach-loops.tex theme={null}
  \begin{tikzpicture}
      % Grid of nodes using foreach
      \foreach \x in {0,1,2,3,4} {
          \foreach \y in {0,1,2,3} {
              \node[circle, draw, fill=blue!\x0!green!\y0] 
                  at (\x,\y) {\tiny \x,\y};
          }
      }
      
      % Radial pattern
      \begin{scope}[xshift=7cm, yshift=2cm]
          \foreach \angle in {0,30,...,330} {
              \draw[thick, color=red!\angle!blue] 
                  (0,0) -- (\angle:2);
              \fill[color=red!\angle!blue] 
                  (\angle:2) circle (2pt);
          }
      \end{scope}
      
      % Connected graph
      \begin{scope}[yshift=-5cm]
          \foreach \i in {1,...,6} {
              \node[circle, draw, fill=orange!30] 
                  (n\i) at ({360/6 * (\i-1)}:2) {\i};
          }
          \foreach \i in {1,...,6} {
              \foreach \j in {\i,...,6} {
                  \draw[gray] (n\i) -- (n\j);
              }
          }
      \end{scope}
  \end{tikzpicture}
  ```

  ```latex calculations.tex theme={null}
  \begin{tikzpicture}
      % Using calculations
      \coordinate (A) at (0,0);
      \coordinate (B) at (4,0);
      \coordinate (C) at (2,3);
      
      % Midpoints
      \coordinate (MAB) at ($(A)!0.5!(B)$);
      \coordinate (MBC) at ($(B)!0.5!(C)$);
      \coordinate (MCA) at ($(C)!0.5!(A)$);
      
      % Draw triangle and medians
      \draw[thick] (A) -- (B) -- (C) -- cycle;
      \draw[dashed, red] (A) -- (MBC);
      \draw[dashed, red] (B) -- (MCA);
      \draw[dashed, red] (C) -- (MAB);
      
      % Centroid (intersection of medians)
      \coordinate (G) at (barycentric cs:A=1,B=1,C=1);
      \fill[red] (G) circle (2pt) node[below] {$G$};
      
      % Perpendicular lines
      \draw[blue, thick] (A) -- ($(B)!(A)!(C)$);
      
      % Circle through three points
      \node[draw, circle through=(A)(B)(C)] {};
  \end{tikzpicture}
  ```
</CodeGroup>

### Styles and Scopes

<CodeGroup>
  ```latex custom-styles.tex theme={null}
  \begin{tikzpicture}[
      % Define custom styles
      my node/.style={
          circle, 
          draw=#1, 
          fill=#1!20, 
          minimum size=1cm,
          font=\bfseries
      },
      my edge/.style={
          thick,
          ->,
          >=stealth,
          #1
      },
      important/.style={
          my node=red,
          drop shadow
      },
      normal/.style={
          my node=blue
      }
  ]
      % Use custom styles
      \node[important] (A) at (0,0) {A};
      \node[normal] (B) at (3,0) {B};
      \node[normal] (C) at (3,3) {C};
      \node[important] (D) at (0,3) {D};
      
      % Styled edges
      \draw[my edge={red, dashed}] (A) -- (B);
      \draw[my edge={blue}] (B) -- (C);
      \draw[my edge={green, bend left}] (C) -- (D);
      \draw[my edge={orange, bend right}] (D) -- (A);
      
      % Scope with different settings
      \begin{scope}[xshift=6cm, scale=0.8, opacity=0.7]
          \node[my node=purple] (E) at (0,0) {E};
          \node[my node=cyan] (F) at (2,2) {F};
          \draw[my edge={thick}] (E) -- (F);
      \end{scope}
  \end{tikzpicture}
  ```

  ```latex layers.tex theme={null}
  \begin{tikzpicture}
      % Background layer
      \begin{pgfonlayer}{background}
          \fill[yellow!20] (-1,-1) rectangle (5,4);
          \fill[blue!20] (1,0.5) circle (2);
      \end{pgfonlayer}
      
      % Main layer
      \draw[thick] (0,0) grid (4,3);
      \node[circle, draw, fill=white] at (2,1.5) {Main};
      
      % Foreground layer
      \begin{pgfonlayer}{foreground}
          \node[rectangle, draw, fill=red!70, opacity=0.8] at (3,2) {Front};
      \end{pgfonlayer}
  \end{tikzpicture}
  ```
</CodeGroup>

### Decorations and Patterns

<CodeGroup>
  ```latex decorations.tex theme={null}
  \begin{tikzpicture}[
      decoration={
          snake,
          amplitude=.5mm,
          segment length=3mm
      }
  ]
      % Different decorations
      \draw[decorate, thick] (0,0) -- (3,0) node[right] {snake};
      
      \draw[
          decoration={coil, segment length=4mm},
          decorate, thick
      ] (0,1) -- (3,1) node[right] {coil};
      
      \draw[
          decoration={zigzag, segment length=4mm},
          decorate, thick
      ] (0,2) -- (3,2) node[right] {zigzag};
      
      \draw[
          decoration={random steps, segment length=3mm},
          decorate, thick
      ] (0,3) -- (3,3) node[right] {random};
      
      % Text along path
      \draw[
          decoration={
              text along path,
              text={This text follows the curve!}
          },
          decorate
      ] (5,0) .. controls (6,2) and (7,2) .. (8,0);
      
      % Arrow decorations
      \draw[
          thick,
          decoration={
              markings,
              mark=at position 0.25 with {\arrow{>}},
              mark=at position 0.5 with {\arrow{>}},
              mark=at position 0.75 with {\arrow{>}}
          },
          postaction={decorate}
      ] (5,3) circle (1);
  \end{tikzpicture}
  ```

  ```latex patterns-fills.tex theme={null}
  \begin{tikzpicture}
      % Pattern fills
      \fill[pattern=horizontal lines] (0,0) rectangle (2,1);
      \fill[pattern=vertical lines] (2.5,0) rectangle (4.5,1);
      \fill[pattern=north east lines] (5,0) rectangle (7,1);
      \fill[pattern=grid] (7.5,0) rectangle (9.5,1);
      
      % Custom patterns
      \fill[pattern=dots] (0,2) rectangle (2,3);
      \fill[pattern=crosshatch] (2.5,2) rectangle (4.5,3);
      \fill[pattern=fivepointed stars] (5,2) rectangle (7,3);
      \fill[pattern=bricks] (7.5,2) rectangle (9.5,3);
      
      % Combining patterns and colors
      \fill[pattern=north west lines, pattern color=blue] 
          (0,4) rectangle (2,5);
      \fill[pattern=checkerboard, pattern color=red] 
          (2.5,4) rectangle (4.5,5);
      
      % Gradient fills
      \shade[left color=red, right color=blue] (5,4) rectangle (7,5);
      \shade[inner color=yellow, outer color=orange] (7.5,4) circle (0.5);
  \end{tikzpicture}
  ```
</CodeGroup>

## Best Practices

### Optimization Tips

<Tip>
  **TikZ best practices**:

  1. **Use styles** - Define reusable styles for consistency
  2. **Name nodes** - Makes connections easier
  3. **Use calculations** - Let TikZ compute positions
  4. **Layer wisely** - Background, main, foreground
  5. **Externalize** - Compile complex diagrams separately
  6. **Comment code** - Especially for complex diagrams
  7. **Use libraries** - Don't reinvent the wheel
  8. **Test incrementally** - Build diagrams step by step
</Tip>

### Common Pitfalls

<Warning>
  **Avoid these TikZ mistakes**:

  1. **Hardcoded positions** - Use relative positioning
  2. **Repeated code** - Use loops and styles
  3. **Complex paths** - Break into smaller parts
  4. **Missing libraries** - Load required libraries
  5. **Scale issues** - Test at final size
  6. **Memory problems** - Externalize large diagrams
  7. **Forgotten semicolons** - Every command needs one
</Warning>

## Complete Examples

### Network Diagram

<CodeGroup>
  ```latex network-diagram.tex theme={null}
  \documentclass{article}
  \usepackage{tikz}
  \usetikzlibrary{positioning, shapes.geometric, shadows, backgrounds}

  \begin{document}

  \begin{tikzpicture}[
      node distance=2cm,
      server/.style={
          rectangle, draw, fill=blue!20,
          minimum width=2cm, minimum height=1.5cm,
          drop shadow, font=\small
      },
      client/.style={
          rectangle, draw, fill=green!20,
          minimum width=1.5cm, minimum height=1cm,
          drop shadow, font=\small
      },
      database/.style={
          cylinder, draw, fill=orange!20,
          minimum width=2cm, minimum height=1.5cm,
          shape border rotate=90,
          drop shadow, font=\small
      },
      cloud/.style={
          cloud, draw, fill=gray!20,
          minimum width=3cm, minimum height=2cm,
          drop shadow, font=\small
      },
      connection/.style={thick, ->, >=stealth},
      label/.style={font=\footnotesize, fill=white, inner sep=2pt}
  ]
      % Core components
      \node[cloud] (internet) {Internet};
      \node[server, below=3cm of internet] (loadbalancer) {Load Balancer};
      
      % Web servers
      \node[server, below left=2cm and 1cm of loadbalancer] (web1) {Web Server 1};
      \node[server, below right=2cm and 1cm of loadbalancer] (web2) {Web Server 2};
      
      % Application servers
      \node[server, below=of web1] (app1) {App Server 1};
      \node[server, below=of web2] (app2) {App Server 2};
      
      % Databases
      \node[database, below right=2cm and 0cm of app1] (db1) {Primary DB};
      \node[database, right=1cm of db1] (db2) {Replica DB};
      
      % Clients
      \node[client, left=3cm of internet] (client1) {Client 1};
      \node[client, above left=1cm and 2cm of internet] (client2) {Client 2};
      \node[client, above right=1cm and 2cm of internet] (client3) {Client 3};
      
      % Connections
      \draw[connection] (client1) -- (internet);
      \draw[connection] (client2) -- (internet);
      \draw[connection] (client3) -- (internet);
      
      \draw[connection, <->] (internet) -- node[label] {HTTPS} (loadbalancer);
      
      \draw[connection] (loadbalancer) -- (web1);
      \draw[connection] (loadbalancer) -- (web2);
      
      \draw[connection] (web1) -- (app1);
      \draw[connection] (web2) -- (app2);
      
      \draw[connection] (app1) -- (db1);
      \draw[connection] (app2) -- (db1);
      \draw[connection, <->] (db1) -- node[label] {Sync} (db2);
      
      % Background regions
      \begin{pgfonlayer}{background}
          \fill[yellow!20, rounded corners] 
              ([shift={(-0.5,0.5)}]loadbalancer.north west) 
              rectangle 
              ([shift={(0.5,-0.5)}]db2.south east);
          \node[above] at (loadbalancer.north) {Data Center};
      \end{pgfonlayer}
  \end{tikzpicture}

  \end{document}
  ```
</CodeGroup>

### Data Flow Diagram

<CodeGroup>
  ```latex data-flow-diagram.tex theme={null}
  \documentclass{article}
  \usepackage{tikz}
  \usetikzlibrary{arrows.meta, positioning, shapes, decorations.pathmorphing}

  \begin{document}

  \begin{tikzpicture}[
      >=latex,
      node distance=2.5cm,
      process/.style={
          rectangle, draw, fill=blue!30,
          minimum width=3cm, minimum height=1cm,
          rounded corners, font=\small\sffamily
      },
      data/.style={
          trapezium, draw, fill=green!30,
          trapezium left angle=70,
          trapezium right angle=110,
          minimum width=2.5cm, minimum height=0.8cm,
          font=\small\sffamily
      },
      storage/.style={
          rectangle, draw, fill=orange!30,
          minimum width=2.5cm, minimum height=0.8cm,
          path picture={
              \draw ([xshift=0.1cm]path picture bounding box.north west) 
                  -- ([xshift=-0.1cm]path picture bounding box.north east);
          },
          font=\small\sffamily
      },
      flow/.style={thick, ->, >=stealth},
      label/.style={font=\footnotesize, above, sloped}
  ]
      % Input layer
      \node[data] (input) {Raw Data};
      
      % Processing pipeline
      \node[process, below=of input] (validate) {Validate};
      \node[process, below=of validate] (transform) {Transform};
      \node[process, below=of transform] (analyze) {Analyze};
      
      % Storage
      \node[storage, right=3cm of validate] (raw) {Raw Storage};
      \node[storage, right=3cm of transform] (processed) {Processed DB};
      \node[storage, right=3cm of analyze] (results) {Results Cache};
      
      % Output
      \node[data, below=of analyze] (output) {Reports};
      \node[process, right=of output] (visualize) {Visualize};
      \node[data, right=of visualize] (dashboard) {Dashboard};
      
      % Main flow
      \draw[flow] (input) -- node[label] {Stream} (validate);
      \draw[flow] (validate) -- node[label] {Valid} (transform);
      \draw[flow] (transform) -- node[label] {Clean} (analyze);
      \draw[flow] (analyze) -- node[label] {Insights} (output);
      
      % Storage connections
      \draw[flow, dashed] (validate) -- node[label] {Archive} (raw);
      \draw[flow, dashed] (transform) -- node[label] {Store} (processed);
      \draw[flow, dashed] (analyze) -- node[label] {Cache} (results);
      
      % Visualization flow
      \draw[flow] (output) -- (visualize);
      \draw[flow] (visualize) -- (dashboard);
      \draw[flow, bend right] (results) to node[label, below] {Query} (visualize);
      
      % Error handling
      \node[process, left=2cm of transform, fill=red!30] (error) {Error Handler};
      \draw[flow, red, bend right] (validate) to node[label, below] {Invalid} (error);
      \draw[flow, red, bend right] (transform) to node[label, below] {Failed} (error);
      \draw[flow, red] (error) |- (input);
      
      % Decorations
      \node[above=0.5cm of input, font=\large\bfseries] {Data Processing Pipeline};
      
      % Legend
      \begin{scope}[xshift=8cm, yshift=-3cm]
          \node[process, minimum width=2cm] (l1) at (0,0) {Process};
          \node[data, minimum width=2cm] (l2) at (0,-1) {Data};
          \node[storage, minimum width=2cm] (l3) at (0,-2) {Storage};
          \draw[flow] (3,0) -- node[above] {Flow} (4.5,0);
          \draw[flow, dashed] (3,-1) -- node[above] {Store} (4.5,-1);
          \node[above=0.3cm of l1, font=\bfseries] {Legend};
      \end{scope}
  \end{tikzpicture}

  \end{document}
  ```
</CodeGroup>

## Next Steps

Explore more LaTeX visualization:

<CardGroup cols={2}>
  <Card title="Mathematics" icon="chart-line" href="/learn/latex/mathematics/basics">
    Mathematical equations and graphs
  </Card>

  <Card title="Circuit Diagrams" icon="microchip" href="/learn/latex/specialized-notation/circuits">
    Electronic circuit drawings
  </Card>

  <Card title="Chemical Structures" icon="atom" href="/learn/latex/specialized-notation/chemistry">
    Molecular diagrams
  </Card>

  <Card title="Physics Notation" icon="cube" href="/learn/latex/specialized-notation/physics">
    Physics diagrams and notation
  </Card>
</CardGroup>

***

<Info>
  **Pro tip**: Start simple and build complexity gradually. Use the TikZ manual (texdoc tikz) as your reference - it's comprehensive with excellent examples. Consider externalizing complex diagrams to speed up compilation of your main document.
</Info>