Polygon partition

A partition of a polygon is a set of primitive units (e.g. squares), which do not overlap and whose union equals the polygon. A polygon partition problem is a problem of finding a partition which is minimal in some sense, for example a partition with a smallest number of units or with units of smallest total side-length.

Polygon partitioning is an important class of problems in computational geometry. There are many different polygon partition problems, depending on the type of polygon being partitioned and on the types of units allowed in the partition.

The term polygon decomposition is often used as a general term that includes both covering and partitioning.

Polygon decomposition is applied in several areas:

The most well-studied polygon partition problem is partitioning to a smallest number of triangles, also called triangulation. For a hole-free polygon with ${\displaystyle n}$ vertices, a triangulation can be calculated in time ${\displaystyle \Theta (n)}$. For a polygon with holes, there is a lower bound of ${\displaystyle \Omega (n\log n)}$.

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