Thiessen polygons or Voronoi polygons or Thiessen tessellation

Thiessen polygons, also known as Voronoi polygons or Thiessen tessellation, are a fundamental concept in GIS that define the spatial extent of influence or control of a set of points or observation sites. They are named after the American meteorologist Alfred H. Thiessen, who introduced the concept in 1911.

The basic idea behind Thiessen polygons is to partition a geographic space into contiguous polygons based on proximity to a set of input points. Each polygon is assigned to the nearest point, and all locations within that polygon are closer to that particular point than to any other point in the dataset.

The construction of Thiessen polygons involves connecting the midpoints between each pair of adjacent points, forming perpendicular bisectors. These bisectors are extended to create a network of lines that delimit the boundaries of the polygons. Each polygon encompasses the area that is closer to its associated point than to any other point.

The resulting Thiessen polygons have several applications in GIS:

1. Spatial interpolation: Thiessen polygons can be used to interpolate values between points. The value at any location within a Thiessen polygon is assumed to be equal to the value at the associated point.

2. Network analysis: Thiessen polygons can be used to determine the service area or coverage of specific facilities, such as determining which customers are closest to a particular store or service location.

3. Hydrology and catchment delineation: Thiessen polygons can assist in delineating watersheds or catchment areas by assigning each stream gauge or monitoring point to its nearest catchment.

4. Resource allocation and planning: Thiessen polygons can aid in allocating resources or planning infrastructure by identifying areas of influence or control for specific facilities or services.

To create Thiessen polygons in GIS software, you can typically find a specific tool or function that generates them based on a given set of points. Once generated, the polygons can be analyzed and used for various spatial analyses within the GIS environment.

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