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Does anybody know a trick to create an antipodes map with QGIS?

That is a map of the world on one layer, and a map of the world on another layer, showing the antipodes of each point (practically a world map inverted north-south and east-west).

I did not find any shapefile with the inverted world in the net, so I guess I will have to play with the projection, which is a very complicated issue.

1 Answer 1

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Creating antipodes of points

To create the antipode of any point in QGIS, you have to switch it's coordinates using this expression:

make_point (
    if (
        x<0, 
        x($geometry)+180, 
        x($geometry)-180
    ),
    -y ($geometry)
)

Remark: See at the bottom of this answer for an explanation of the formula.

Dynamically create symbol for antipode of points

If you just want to dynamically create the antipode of any place you click on the map canvas, create a new point layer (be sure to have the CRS in EPSG:4326 for WGS84 projection), add a new Symbol Layer / Geometry generator / Geometry type: Points and paste the expression from above.

Now every time you click on the map canvas to create a new point (blue in the following screenshot), a second point (the antipode, red) will automatically be added: point 2 (New Zealand) gets the antipode in Spain, 4 in Australia gets the antipode in the Atlantic, 5 in China in Argentinia and so on: every time you click, the antipode will be generated automatically:

enter image description here

Creating antipodes of shapes (lines, polygons)

For any shape (line, polygon) you can extract the vertices and than apply this expression to get the "antipode shape" of your input by re-connecting the points.


Creating antipode world map

To create a whole world antipodes map, here is a little bit more detailed description (see the steps on the next screenshot):

  1. In QGIS, load a polygon of the world - I just introduced world to the coordinates field in the status bar to load the pre-installed World Polygon layer.
  2. Go to Menu Vector / Geometry Tools / Extract vertices. You get a new layer with all the vertices. In case you got a multipoint layer, apply Multipart to singleparts (in the same menu as before).
  3. Now, change the Symbol layer type of the extracted vertices from Simple Marker to Geometry generator / Geometry type: Points and add the expression from above.

Creating antipodes map with QGIS

What you get is the antipodes map you see on the next screenshot where I also added OpenStreetMap as additional basemap. The antipodes consist of vertices (red dots) - you could create lines and from these polygons again if you wish: Australia is on the Central Atlantic; Africa in the Central Pacific; India and Central Asia on the Southern Pacific (west of Southern America); North America on the Southern Indian Ocean; New Zealand over the Iberian Peninsula; South America stretching from Indonesia to China, Mongolia until eastern Siberia; and many small islands of the Pacific are dispersed all over Africa:

QGIS antipodes map

The formula to switch coordinates

The formula is simple:

  • The latitude just changes to its negative value (-y): 10 degrees North result in 10 degrees south.
  • For longitude, you get the antipode x-coordinate with x-value +/- 180 degrees, depending on it's original position East or West of the 0 degree meridian (London Greenwich). Thus: for x<0 (= degrees West), add 180 degrees, if it is to the East of Greenwich (x>0), substract from it 180 degrees.

That's what the expression above does.

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