Finding shortest distance from one point to each polygon and the distance from that point of the polygon to any of the points in the polygon in QGIS

Question

I'm trying to find the shortest distance from a point (point A uploaded as a CSV) to a polygon uploaded as a shapefile (polygon 1) and then the distance from that point of the polygon to any of the points in the polygon (e.g. point 1B, point 1C, point 1D inside polygon 1, uploaded as another CSV).

So the output expected is:
Point A -> closest point on Polygon 1 (P1): x km
P1 -> point 1B: x km
P1 -> point 1C: x km
P1 -> point 1D: x km

That's what I am trying to get to, also on a bigger scale, i.e. point A is always the same, but there are multiple polygons and multiple points in each polygon. At the end of the day, for each point I would like to have the shortest distance from the point A to the polygon that it sits within and then from there to the point itself.

Answer 1

I've assumed you have 3 layers called BasePoint (your point A), Polygon, and PointsInPolygon.

Depending on how you want the distance displayed, you can get the distance from each Polygon feature to BasePoint using the following expression:

with_variable('A',geometry(get_feature_by_id('BasePoint',1)),round(
    distance(
        closest_point(@geometry,@A),@A
    )/1000,2
)) || ' km'

And you can get the distance from each PointsInPolygon feature to its containing Polygon using the following similar expression:

with_variable('A',geometry(get_feature_by_id('BasePoint',1)),round(
    distance(
        closest_point(
            overlay_within('Polygon',@geometry,limit:=1)[0],@A
        ),@geometry
    )/1000,2
)) || ' km'

Output is as below.

If for some reason your BasePoint does not have a feature id of 1, you could replace this with get_feature eg get_feature('BasePoint',"name",'A')

If you add more polygons/points, the expressions continue to work:

Note: I used a geometry generator to create the lines joining the relevant features, and also for labelling. For example, the line from Point A to the Polygon layer can be visualised by:

with_variable('A',geometry(get_feature_by_id('BasePoint',1)),
make_line(closest_point(@geometry,@A),@A))

and labelled using rule-based labelling:

(The expressions are the same as for the distance and the creation of the line)