extrapolating the edges of a bounding box (QGIS)

I woke up thinking about a fragment of a map the other day, and it occurred to me that what I was picturing could probably be made using geometry generators in QGIS. I was picturing something like this:

So I thought I’d have a whack at making it.

This was my first foray into crafting a geometry generator, inspired by some blog posts I read recently from BOGIND and Alasdair Rae.

My approach was something like:

browse the Geometry functions in the Expression Editor while pondering “how might I go about doing this…”
arrive at the idea of doing some maths to the coordinates of the centroid to produce two points to draw one line with
do that four times

After some fiddling around I arrived at the following geometry generator, which did the north-south extrapolation on the right edge of the bounding box:

# RIGHT

make_line(
  make_point(
    x($geometry) + bounds_width($geometry)/2,
    y($geometry) + bounds_height($geometry)*18
  ),
  make_point(
    x($geometry) + bounds_width($geometry)/2,
    y($geometry) + bounds_height($geometry)*18*-1
  )
)

north-south extrapolation on right edge of bbox

Some adjustments to plusses and minuses and negatives did the other edges:

# LEFT

make_line(
  make_point(
    x($geometry) - bounds_width($geometry)/2,
    y($geometry) + bounds_height($geometry)*18
  ),
  make_point(
    x($geometry) - bounds_width($geometry)/2,
    y($geometry) + bounds_height($geometry)*18*-1
  )
)

# TOP 

make_line(
  make_point(
    x($geometry) + bounds_width($geometry)*18,
    y($geometry) + bounds_height($geometry)/2
  ),
  make_point(
    x($geometry) + bounds_width($geometry)*18*-1,
    y($geometry) + bounds_height($geometry)/2
  )
)

# BOTTOM

make_line(
  make_point(
    x($geometry) + bounds_width($geometry)*18,
    y($geometry) - bounds_height($geometry)/2
  ),
  make_point(
    x($geometry) + bounds_width($geometry)*18*-1,
    y($geometry) - bounds_height($geometry)/2
  )
)

You may be wondering what the number 18 that repeats throughout is about. It is a multiplier that dictates how long the extrapolated lines are. I started off with a smaller number but increased it while playing around until the extrapolated lines extended out of the map area I was looking at, out of preference / what I was aiming for visually. (It didn’t occur to me there was a much simpler way of setting particular point coordinates to achieve this until I was recreating this in Leaftlet, doh! I’ll cover that later in a separate post…)

Tada! Job done:

Hmmm. Slightly wonky. This turned out to be related to the projection – how and why I don’t know, but switching from the typical local projection of EPSG:27700 (British National Grid) to EPSG:3857 (Pseudo-Mercator) made the problem vanish. Interestingly, before changing the projection, I found that increasing my multiplier to lengthen the lines would exaggerate the wonkiness and push the lines further away from where I expected them to be drawn… Something to ponder another day.

Anyway, here is the end result!