I've been experimenting with orthographic projections and I've run into a problem with the labels.

[![enter image description here](https://i.stack.imgur.com/2ETiu.png)](https://i.stack.imgur.com/2ETiu.png)

I would like to label the countries but I want the labels to run west-east along the country which isn't (currently) an option in the QGis labeling options.

So, I know I can place them along a line but I lack the patience to draw a line in each country. So I'm looking for an automatic way to draw a line through the centroid of a polygon and to the edges so that I can use it as a label placement line. 

By 'label placement line' I mean I need a line that crosses the country that I can use as the basis of my labels so that I can use follow line (parallel I think) in the labeling panel. (see for example this [question](https://gis.stackexchange.com/questions/32877/how-to-create-curved-labels-in-qgis)). So they will be a straight horizontal line in EPSG:4326 but nicely curved in my orthographic projection (`+proj=ortho +lat_0=51.470129 +lon_0=-0.452751 +x_0=0 +y_0=0 +a=6371000 +b=6371000 +units=m +no_defs`).

Ideally it would be a dense line so it curves when reprojected but I can always run a densify process on the output.