Select Polygons in layer A with a specific geolocation criteria in relation to each other and layer B

Question

I am trying to select Polygons from Layer A with the following rules:

1. Polygon in Layer A is smaller than 1 ha and further than 100 m from any other polygon in either Layer A or B that is greater than 2 hectares.

2. Polygon in Layer A measures between 1 ha and 2 ha and is further than 100 m from any other polygon in either Layer A or B greater than two hectares.

3. Polygon in Layer A measures between 2 ha and 3 ha and further than 100 m from any other polygon in either Layer A or B greater than two hectares.

4. Remove narrow corridors (less than < 50 m in width (see Fig 1)) from polygons in Layer A if the polygon is further than 30m away from any other polygon in either Layer A or B.

Figure 1

Narrow corridors are maximum 50m wide and can have any lenght. Not sure if it would work, but what about:

1. Create vertices along the polygon using 'extract vertices';
2. If necessary, create lat/lon of all points (if not skip to step 3)
3. Create lines between all vertices (x1, x2, x3) (use make_line? command) and measure line_length (use $length command) (Fig 2)
4. SELECT all lines <=50m
5. Create a new polygon around the selection and call “narrow_corridors”
6. Subtract narrow corridors from the original layer

Fig 2

Happy to have these run separate, as Layer B has hundreds of thousands of polygons and I can't think of a way around this.

Was thinking of using 'select by expression', but don't really know anything about coding yet.

Answer 1

With Virtual Layers, you can easily handle the first 3 items, the 4th item should be manageable with the same approach but the geometric requirement needs to be further defined.

Add a virtual layer with the SQL query below. Your Layers need to be in a CRS with units in meters and for which distance/area computations are correct (units in the query are in meters or square meters)

with min_distance_table as 
(select temp.geometry, temp.area, min(distance_a) min_a ,min(distance_b) min_b from 
(select a.*, st_area(a.geometry) as area ,st_distance(a.geometry,aa.geometry) as distance_a, st_distance(a.geometry,b.geometry) as distance_b from LayerA a, LayerA aa, LayerB b where st_area(aa.geometry)> 20000 and st_area(b.geometry)> 20000  and a.geometry != aa.geometry) temp

 where temp.area < 30000
 group by temp.geometry,temp.area)
 
 select *,
        case 
                when area < 10000 then '1ha'
                when area <20000 and area >=10000 then '2ha'
                when area < 30000 and area >= 2000 then '3ha'
                end area_category

from min_distance_table where min_a >100 and min_b > 100

A & B layers in green/pink:

Selected A layer geometries in red:

Selected layer attributes (categorizing the 1/2/3 Ha bins)

Someone even probably has a more efficient/elegant query to achieve the same result

For your 4th item, you should clarify how you would geometrically define a 'narrow corridor'