Geometry generator line from centroid to edge of irregular polygon

Question

I have a point layer styled with the following geometry generator formula for an irregular polygon. It is the union of (a) a circular buffer with (b) a tree canopy spread buffered by 1m (where that extends beyond (a)).

 union(buffer($geometry,"tpzbsrad_m"),buffer(make_polygon(make_line(
 translate($geometry,0,max("N",0.2)),
 translate($geometry,0.6*max("E",0.2),0.6*max("N",0.2)),
 translate($geometry,max("E",0.2),0),
 translate($geometry,0.6*max("E",0.2),-0.6*max("S",0.2)),
 translate($geometry,0,-max("S",0.2)),
 translate($geometry,-0.6*max("W",0.2),-0.6*max("S",0.2)),
 translate($geometry,-max("W",0.2),0), 
 translate($geometry,-0.6*max("W",0.2),0.6*max("N",0.2)),
 translate($geometry,0,max("N",0.2)))),1))

I would like to use the geometry generator to draw a 45° line from the tree point ($geometry) to the edge of this irregular polygon.

For most cases the following suffices - a line to the edge of the circular buffer.

make_line(
 $geometry, make_point($x + "tpzbsrad_m"*cos(radians(45)), 
                       $y - ("tpzbsrad_m"*sin(radians(45)))
))

But where the tree canopy extends beyond the buffer in that area it doesn't match up. See image below:

What expression can I use to get the line to be long enough to always touch the edge of the irregular polygon at 45°? shortest_line() results in angles all over the place, naturally.

(Looking for an expression that ideally works in QGIS 2.18 and 3.x)

Answer 1

Thanks for sharing your great work!

[Option 1]

An idea presented below would require:

• The irregular (sky-blue) polygon is saved as a vector layer ( your_polygon)
• refFunctions plugin (for geomwithin() function)

Then the expression is:

intersection(
    make_line(
             $geometry, make_point($x + 2*"tpzbsrad_m"*cos(radians(45)), 
                                   $y - 2*("tpzbsrad_m"*sin(radians(45)))
    )),
    geom_from_wkt(geomwithin('your_polygon', '$geometry'))
)

(A multiplier factor 2 to your "tpzbsrad_m" has no meaning but it ensures the line is extended long enough before it gets cut at the intersecting polygon boundary).

---

[Option 2] without refFunctions plugin:

Instead of using refFunctions plugin, there is an additional step to link your tree (point) and polygon.

• Join by Location to have identical id fields in both of your layers (point and polygon).

Now revised expression is:

intersection(
    make_line(
             $geometry, make_point($x + 2*"tpzbsrad_m"*cos(radians(45)), 
                                   $y - 2*("tpzbsrad_m"*sin(radians(45)))
    )),
    geometry(get_feature('your_polygon', 'id', "id"))
)

This expression uses get_feature() function which links 'id' field from the polygon (your_polygon) and the "id" field in the point layer (your tree locations).

Answer 2

Expanding on @Kazuhito's answer this is the expression I've used - simply an intersection() of the 45° line (extended x2) with the irregular polygon described in the original post.

Yet to test on larger datasets - I'm sure performance isn't optimal - but it's good enough for my use case and styling requirements.

intersection(make_line(
 $geometry,
 make_point($x + "tpzbsrad_m"*cos(radians(45))*2, 
 $y - ("tpzbsrad_m"*sin(radians(45))*2))),

union(buffer($geometry,"tpzbsrad_m"),buffer(make_polygon(make_line(
 translate($geometry,0,max("N",0.2)),
 translate($geometry,0.6*max("E",0.2),0.6*max("N",0.2)),
 translate($geometry,max("E",0.2),0),
 translate($geometry,0.6*max("E",0.2),-0.6*max("S",0.2)),
 translate($geometry,0,-max("S",0.2)),
 translate($geometry,-0.6*max("W",0.2),-0.6*max("S",0.2)),
 translate($geometry,-max("W",0.2),0), 
 translate($geometry,-0.6*max("W",0.2),0.6*max("N",0.2)),
 translate($geometry,0,max("N",0.2)))),1)))

See image below - always hits edge of the polygon now.