Is it possible to use the Goode Homolosine projection in QGIS? Both QGIS and GRASS seem to have trouble with the interruptions, squashing the higher latitudes together. I tried +proj=goode +ellps=sphere +datum=wgs84 as a custom CRS.
There has been a question on interrupted projections before: Discontinuous or Interrupted map projections?
The conclusion was that proj4 (which is used for projection handling in QGIS and GRASS) does not support interrupted projections.
With QGIS Lisboa, there is now a basic support for Goode Homolosine projection.
I downloaded IGH data from http://edc2.usgs.gov/glcc/fao/data_specifications.php
and set up this user CRS:
+proj=goode +lon_0=-100 +x_0=-11119487.43 +y_0=0 +a=6370997 +b=6370997 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
for North America.
lon_0 and x_0 are from Appendix 03 of this document: http://proceedings.esri.com/library/userconf/proc98/proceed/TO850/PAP844/P844.HTM
Overlaying natural Earth world boundaries_m, I get this picture:
Fitting good in North America (about 20km misplaced), and distorted in other regions.
Just noticed that proj knows interrupted goode homolosine by now:
+proj=igh +ellps=sphere +towgs84=0,0,0 +lon_0=100w +x_0=-11119487.43
gives me this picture of Natural Earths world boundaries and a 10-degree-vector grid:
I'm not sure which parameteres apart from
+proj=igh are necessary anymore.
QGIS 2.18 is nigh on fully supporting the Homolosine for rasters. You just need to be aware of issue #959: perform any raster warpping directly with GDAL using the
CHECK_WITH_INVERT_PROJ parameters and you are good.
Regarding vectors things are still complex. Some of the errors AndreJ shows in his answer prevail. The cause is simple: QGis is not aware that it is a Cartographic programme and considers the co-domain of any projection to be a finite space.
This has a simple fix: intersect any vector layer imported into QGis with the Homolosine co-domain. Some time back I made available a discrete co-domain vector defined at intervals of one degree longitude and latitude.