Motivation

• Guarding an Art Gallery

Triangulation

• Definition
• Triangulation Theorem
• Proof

Camera Placement

Strategies

Cameras at Vertices

3-coloring of a Triangulation

Art Gallery Theorem

Polygon Triangulation Algorithm

• Overview of Polygon Triangulation Algorithm
• Monotone Decomposition
• Definition of Monotone
• Overview of Monotone Decomposition
• Vertex Types
• Adding Diagonals
• Eliminating Split Vertices
• Eliminating Merge Vertices
• Plane Sweep Method
• Data Structures
• Running Time of Monotone Decomposition
• Triangulating a Monotone Polygon
• Overview of Triangulating a Monotone Polygon
• Adding Diagonals
• Running Time of Triangulating a Monotone Polygon
• Running Time of Polygon Triangulation Algorithm
• Conclusion

Notes and Comments

• Generalizations and Improvements
• Tetrahedralization
• Interesting Problems
• Polygon Triangulation Applet