Calculating closest point referenced to centroid in QGIS

Question

I have a QGIS project in which I work with a polygon layer ('POLIGONS_TEST') and a point layer ('PUNTS_TEST').

I use the following Geometry Generator expression on the 'POLIGONS_TEST' layer to draw a line that joins the centroid of each polygon with the nearest points layer 'PUNTS_TEST'.

make_line(
    centroid($geometry), 
    closest_point(
        overlay_nearest('PUNTS_TEST', $geometry,limit:=1)[0],
        $geometry
        )
    )

As you can see in the screenshot, the result is correct but there is but there is a visual inconsistency. The closest_point function returns the closest point from geometry1 to geometry2. It seems that it considers geometry1 as the polygon's boundary and not as the centroid.

How could I solve this so that the proximity is calculated concerning the centroid, without having to convert the polygon layer to a point layer?

Example:

Unsatisfactory result after applying the expression proposed by the users @Erik and @Andrea:

Answer 1

You are conducting your overlay check on the polygons, not their centroids. Try changing the expression to

make_line(centroid($geometry), 
    closest_point(overlay_nearest('PUNTS_TEST',
    centroid($geometry),limit:=1)[0],
    $geometry)
)

Answer 2

The expression inside the overlay_nearest function is "an optional expression to evaluate on the features from the target layer". So the centroid function inside the other answers is evaluated on the point ('PUNTS_TEST') layer, not the polygon ('POLIGONS_TEST') layer, which is why it has no effect.

In this case you can avoid using the overlay_nearest function altogether by:

• creating a variable (@centroid) to hold the centroid
• using the aggregate function to create an array of points from the PUNTS_TEST layer
• use the collect_geometries function to turn that into a multipoint geometry
• find the closest point (closest_point) from the multipoint to the @centroid
• finally making the line from that point to the @centroid using make_line

with_variable('centroid',centroid(@geometry),
    make_line(
        closest_point(
            collect_geometries(
                aggregate('PUNTS_TEST',
                aggregate:='array_agg',
                expression:=@geometry)
            )
        ,@centroid)
    ,@centroid)
)