great circles in QGIS and export in 3857 webmap

To create a great circle, you need either a custom azimuthal equidistant (aeqd) projection or a gnomonic (gnom) projection on one of your points.

In those projections, the great circle is a straight line, which you can densify to have a curved line in other projections. If the great circle crosses the 180° E/W line or the poles, it might be useful to cut the line on that line or point to avoid misplaced parts of the line in other projections.

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updated workflow

1. create a text file with your start coordinates

E N

7 51

2. In QGIS, create a custom aeqd projection around your start point

+proj=aeqd +lat_0=51 +lon_0=7 +x_0=0 +y_0=0 +a=6371000 +b=6371000 +units=m +no_defs

3. Load the text file as delimited text with WGS84 as CRS

4. Add the target points from any other backgrounds

5. switch the project CRS to your custom CRS

6. Create a new shapefile of type line and your custom CRS

7. Set snapping to your points layer with 10 pixels tolerance

8. connect your start point with all targets:

9. Densify the lines by 99 vertices

10. Switch the project CRS to EPSG:3857

Note that equidistant conic is a different projection, which does not show the great circles as straight lines:

A visualization of great circles in different projections can be found here:

http://www.progonos.com/furuti/MapProj/Normal/CartProp/Geodesic/geodesic.html