[GIS] How to draw weighted voronoi polygons (thiessen) from points in QGIS

qgisvoronoi-thiessen

I have a shapefile of polygons which have an amount of population, I need to divide each of these polygons into small ones with nearly equal population. So I thought attributing points on each area inside each polygon and attributing a weight depending on its density.

After that I have to draw voronoi polygons based on the points drawn before and their weights to get these small areas that should be equally populated.

I tried to draw them in qgis but all I get is polygons with equal weights.

How to draw weighted voronoi polygons in QGIS?

Best Answer

Thanks to ArMoraer's suggestions I made a little python script based on PyQGIS and GDAL to generate a weighted voronoi diagram from a vector layer.

Here it is on github

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Please read How to build effective heat-maps?

It seems like you are looking for Distributions of attribute values rather than Concentration of points. Therefore, the QGIS heatmap plugin is the wrong tool for the job since it only does concentration of points.

Try Raster | Analysis | Grid (Interpolation) instead.

Another solution could be to first generate a vector grid - could be a hex grid if you like it fancy - and then calculate e.g. the average wellbeing score for each cell and map that.

Polygon – How to Insert Equally Distributed N Points into Polygons Using QGIS

I implemented Cyril's comment. This is the input test polygon:

Polygon to Lines

Split lines by maximum length using $length / 7 in the expression builder. (8 vertices)

Extract specific vertices (0 stands for start point)

Voronoi Polygons with 100% buffer to make sure that parts of the polygon do not lie outside the generated Voronoi (in theory they may still lie outside, but 100% is quite big)

Intersect Voronoi and test polygon

Point on surface (centroids could fall into holes)

The resulting 8 points look like this inside the test polygon:

~~I will now try to automate this procedure and edit my answer when I have results.~~

~~Update 5.12.2019: I haven't been able to automate this task.~~
Update 4.1.2022: Here is an implementation in Shapely:

from itertools import count, islice

from shapely.geometry import MultiPoint, Polygon
from shapely.ops import substring, voronoi_diagram


def _get_voronoi_starting_points(polygon: Polygon, point_count: int) -> MultiPoint:
    perimeter = polygon.exterior
    segment_length = perimeter.length / point_count
    segment_starts = islice(count(0, segment_length), 0, point_count)

    return MultiPoint([substring(perimeter, start, start) for start in segment_starts])

polygon =  # shapely.geometry.Polygon
point_count = 8

voronoi = voronoi_diagram(_get_voronoi_starting_points(polygon, point_count))
equally_distributed_points = MultiPoint(
    [part.intersection(polygon).representative_point() for part in voronoi.geoms]
)

Best Answer

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Polygon – How to Insert Equally Distributed N Points into Polygons Using QGIS

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