Converting polygons to lines that are split depending on borders being shared in QGIS

Question

I have a file containing polygons that delineate the boundaries of municipalities within a specific region. I want to convert the polygon boundaries to lines. The resulting lines should be split depending on the line/boundary being shared with the neighbouring polygon. So each part of a line that is shared with a specific neighbour should be a separate LineString.

(Each polygon is accompanied by a unique "wikidata" field corresponding to each municipality.)

The image below shows the before state (3 polygons/closed MultiLineStrings) and the second image shows the desired state (3 closed MultiLineStrings, but consisting of 6 LineStrings). Each colour represents a different LineString. Shared nodes between two or more LineStrings are shown with grey dots.

Answer 1

It took some time but I found the solution. In case anyone needs it:

1. "Check validity" tool
2. "Boundary" tool
3. "v.clean" from GRASS Vector tools with only bpol tool

Answer 2

You can create this effect using Geomtry Genrator with this expression to create a separate line for each shared path between two polygons (to create actual lines with Geometry by Expression, see below):

collect_geometries(
    with_variable( 'my_id', @id,
    array_foreach(
        eval ('overlay_intersects (@layer, @id, filter:=@id<' || @my_id || ')'),
        line_merge( 
            intersection(
                boundary(geometry(get_feature_by_id(@layer, @element))),
                boundary($geometry)
            )
        )
    ))
)

To visually represent all in different colors, I used data driver override for the color -> Assistant... -> and inserted the following expression in Source:

@geometry_part_num ||   
array_find (array_sort (array_agg($id)), $id)+1

Select a color ramp, tweak values from/to and and maybe apply a transformation curve to really get clearly discernable, distinct color values as in the screenshot above.

---

To create actual lines with Geometry by Expression, use this expression (replace Layername with the name of the polygon layer), then run Multipart to single parts to get a separate feature for each part of the border:

collect_geometries(
with_variable( 'my_id', @id,
    array_filter (
        array_foreach(
            eval ('overlay_intersects (''Layername'', @id, filter:=@id<' || @my_id || ')'),
            line_merge( 
                intersection(
                    boundary (geometry (get_feature_by_id ('Layername', @element))),
                    boundary($geometry)
                )
            )
        ),
        @element is not NULL
    )
))

---

Now, to get different colors for neighboring lines, proceed as follows:

1. Create a (very tiny) buffer around the lines.
2. Use Topological coloring for the buffer.
3. Use Join attributes by location (lines form step 1 -> are within -> buffer from step 2) and selct the field color_id.
4. Then use Categorized layer style based on the attribute created in step 3 and you're done.

Based on topological coloring with only 4 colors to get clearly distinguishabel colors: