Polygon triangulation

Summary

A polygon triangulation cuts a simple polygon into triangles by drawing diagonals between its vertices. Every simple polygon with $n$ vertices has one, and each triangulation has exactly $n - 2$ triangles and $n - 3$ diagonals. Triangulations reduce questions about a complicated polygon to questions about triangles. They are a basic tool of computational geometry, used for area computation, guarding problems such as the art gallery theorem, and graphics.