Find areas distant from any points

Question

I want to draw all areas that are far enough away from any single point of a layer, in this case they are Openstreetmap building=yes tags and I want to calculate the areas that are completely clear of buildings.

I don't know a QGIS plugin that specifically does this and I haven't found the sequence of algorithms suitable to have this result, in the image below the red points are my starting layer and the blue areas that I drew by hand are the ones I want to obtain, that is, islands that must be found in areas that do not contain points and all must have a minimum distance from any other points

Answer 1

You can convert the points to a raster and use Proximity to create an output where each pixel value is the distance to closest point:

1. Create an extent polygon to limit the analysis area. The entire polygon extent will be converted to a raster so make it as small as possible or the raster will be huge.

2. Rasterize the points, my area is large so I use 200 m pixel size (each house will become a pixel of 200*200 size with the value 1), choose a size as large as you can accept to limit the raster size.

3. Proximity:

4. Contour polygons. Then you can select/extract by attributes the polygons with certain distance. I use a contour interval of 1000 m.

My proximity raster have values of ~0-8000 m. So the most remote location (the whitest) is 8000 m from any point.

Answer 2

1. Create an extent polygon of your area of interest, e.g. via extract extent
2. Buffer the points by a distance you wish
3. Run difference and cut out the buffer from your area of interest

Answer 3

Use this expression with Geometry Generator (see also here how to use it):

case
when $id = minimum( $id)
then 
difference(
    bounds(collect($geometry)), 
    buffer(collect($geometry), 120)  -- change buffer distance here
)
end

Blue polygon created with the expression above: