[GIS] Considering holes/constraints in Voronoi polygon creation in QGIS

maskingqgisvoronoi-thiessen

I am trying to create voronoi polygons in QGIS that would consider "holes" in the general domain. An example would be:

enter image description here

I actually created the Voronois in this image using QGIS through the GRASS command, then using the "Difference" tool to create the holes. A separate polygon shapefile, which contains the extents of the holes, was used as the "Difference" layer. An example application would be creating polygons around sampling points that were collected between structures that should be excluded from the analysis.

Two problems arise here:

The "difference" function does not appear to work 100% properly, with some polygon boundaries extending into the "holes". This can be fixed by finding row in the Attribute Table which do not have a polygon ID number (or ID of "0").
This type of after-the-fact "hole-punching" can result in discontinuous polygons, as shown by the red arrow in the image.

My question is: is there a Voronoi tool or plugin that can consider the presence of "holes" in the center of the domain, as a one-step process, and also eliminate the generation of discontinuous polygons? I envision that such a tool would extend a polygon boundary to the nearest intersection with another boundary, unless that other boundary slams against a "hole" boundary first.

Best Answer

This might be possible using rasters. First convert your points and boundary polygons into a high resolution raster. Set a mask for your boundaries using r.mask. Then, run r.grow.distance in GRASS and use the Value= output. This will give you for each pixel, which is the closest point. Convert this back into vector polygons. There might be extra steps needed to get rid of sliver polygons.

Related Solutions

QGIS Donut Polygons – How to Make Holes in a Polygon from Existing Smaller Polygons

If I have understood your problem properly I suggest you the fallowing steps:

Make a rectangular polygon the cover all your old paper map and call it a.shp
select from your previous work all the polygones that must make holes in te rectangle and save them all in another shape and call it b.shp
In vector menu use the geoprocessing function called "difference" and use as input a.shp and as difference b.shp > now you have the a.shp with holes from b.shp > call this layer c.shp
In vector menu use the geoprocessing function called "union" and use c.shp and b.shp I hope it'll help you

QGIS – Cropping Voronoi Polygons to Specific Distance from Input Points

Quick solution / principles

See below for variation with dynamic distance buffer

Create voronoi polygons from your points (as you already did).
Create a buffer around your points and be sure to check the dissolve option.
Intersect buffer with polygon layer.

Voronoi polygons (blue) of the white points; red: dissolved buffer around the points:

Green: voronoi polygons intersected with the buffers - everything outside of the buffer layer is clipped from the voronoi layer:

Variations

Make buffer with a dynamic distance, based on the density of the points (based on the nearest neighboring point). In the buffer tool, for Distance use data driven override and insert this expression (you can modify it to vary the buffer size even further):

length (
    make_line (
        $geometry, 
        array_first (
            overlay_nearest (
                'points',
                $geometry
))))

On the buffer layer, run Multipart to single parts before intersection.
After intersection, on the output layer check if there are any polygons that do not contain points (this is the case where the buffer of a points partially falls inside the voronoi polygon of another point - see screenshot). To select these "empty" poylgons, use Select by expression with this expression, where points is the name of the layer containing the points: overlay_contains( 'points') = false. Delete the selected polygons.

"Empty" polygons, highlighted in yellow; red: buffer with dynamic size, black lines: boundary of the voronoi polygons:

Green: resulting voronoi polygons, clipped with a buffer with dynamic distance:

Result, showing the whole result: voronoi-polygons clipped to a dynamic distance around the points, based on the density of the points (the closer points are, the smaller the voronoi polygons). Of course, there are no overlaps between polygons, but sometimes gaps between them:

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