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This question already has an answer here:

I have the coordinates for the police stations in a city, they are grouped close together at the center and sparse towards the suburbs.

Since I do not have the shapefile for the jurisdiction of each station, I want to do a rough estimate of the area by defining non overlapping variable size and dimension polygons with the police station as the center.

Is there a standard function in R or any other open source toolkit which will do this?

If a standard function is not available what algorithms is best suited for this task?

marked as duplicate by Simbamangu, PolyGeo Jun 13 '16 at 22:05

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • Is this really a duplicate? The linked question does nothing to describe what a Thiessen polygon is or how it relates to this question. Indeed, Thiessen polygons are only one possible solution to this question. – Jeff G Jun 14 '16 at 10:57
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Here's just one idea: Compute the voronoi diagram of the stations -- this is a partitioning of your city into polygons (also called Thiessen Polygons) where exactly 1 station is in each one. From here you can compute the area of each of the polygons.

There are a couple R packages that will compute these polygons: see R function for Thiessen Polygons

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