QGIS – Voronoi Polygons

By David Crowther

Question:

What are Voronoi Polygons?

Answer:

The Voronoi Tool within QGIS enables you to create new Voronoi polygon objects from an input Point Layer…. but what is a Voronoi? -  well in mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects… see below!

In QGIS I have an input point layer and I would like to create a set of Voronoi Polygons around those points.

From the Processing menu choose > Toolbox > and open the Vector Geometry section.

Choose the Voronoi Polygons menu option.

The Voronoi Polygons Tool will open.

We will use the following settings:

• In the Input Layer choose the Points Layer.
• Choose the output file, this could be a GIS file or a Temporary Layer that you can save a copy of later.

If you now Run the Voronoi Polygons Tool, the output will be a polygon layer based around each input point, where any location in that polygon is always nearest to the input point location.

Note that the edges where there are no more input points will simply cut off the polygon as a straight line. If you wish to extend this area, in the settings choose to apply a Buffer Region e.g. 25%.

This time the output Voronoi polygons will extend beyond our boundary line.

To complete this task, we can use the CLIP tool to clip our Voronoi Polygon layer to the boundary line.

We now have a set of Voronoi Polygons around each input point which can then be used for performing spatial analysis. e.g. to identify all the Pupils that are closest (As the Crow Fly’s) to a specific School.