We are interested at the "Pole of inaccessibility" (https://en.wikipedia.org/wiki/Pole_of_inaccessibility) of our country.
Our approach is to use QGIS, and download coastline ([ngdc.noaa.gov]), and repeatedly create "contour lines of equal distance" until there is a point which is the farthest point away from the coastline.
Do you know how to generate a polygon which is an inner polygon and has equal distance the outer one?
An example of contour lines of equal distance on the Wikipedia page:
After a reminder from @underdark, I finally get the result. Here are my steps:
Get Mainland Coastline Shapefile
$ curl https://www.ngdc.noaa.gov/mgg/shorelines/data/gshhg/latest/gshhg-shp-2.3.5-1.zip -o gshhg-shp.zip
[action] use QGIS to add a field
valuewith value 1 to the polygon of mainland coastline
Rasterize the Polygon of Mainland Coastline
$ gdal_rasterize -a value -tr 0.003 0.003 coastline.shp mainland.tif
Proximity the Rasterized Mainland
$ gdal_proximity.py -values 0 -distunits GEO -of GTiff mainland.tif proximity.tif
Contour Based on the Proximity Result
$ gdal_contour -a distance -i 0.005 -f "ESRI Shapefile" proximity.tif proximity_contour.shp
You now have the contour lines of inaccessibility!