Definition:Triangulation of Polygon
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Definition
Let $P$ be a polygon.
A triangulation of $P$ is a dissection of $P$ into a set of triangles $\family { \triangle_i }_{ i \mathop \in \II }$, where $\II$ is an index set.
If $P$ is a triangle, we consider $\family { P }$ to be a triangulation of $P$.
Fan triangulation
Let $A$ be a vertex of $P$.
Let $\triangle_i$ have a vertex equal to $A$ for all $i \in \II$.
Then $\family { \triangle_i }_{ i \mathop \in \II}$ is a fan triangulation of $P$.
Sources
- 1987: Joseph O'Rourke: Art Gallery Theorems and Algorithms: $\S 1.3$