On the fly reprojection in QGIS?

Question

I'm new to QGIS and trying to deal with on the fly reprojection. I have three layers :

• a shapefile in EPSG:4326
• a raster in EPSG:3395
• that same raster reprojected in EPSG:3857 (with QGIS via the "Save as..." contextual menu available when right clicking on the layer. I manually set the right extent in the options)

I want to show them in QGIS in EPSG:3857 and EPSG:4326. The three layers' CRS are set correctly in their properties window.

If I set the project CRS to EPSG:4326, the shapefile is shown correctly but the rasters are not (they are not visible at all).

If I set the project CRS to EPSG:3857 :

• the shapefile is correctly displayed
• the original raster is show at the right place, but not entirely (seems like the on the fly reprojection is not reprojecting the extent correctly) -> see screen 1
• the reprojected raster is displayed correctly -> see screen 2

If I set the project CRS to EPSG:3395 :

• the shapefile is correctly displayed
• the original raster is displayed correctly
• the reprojected raster is show at the right place, but not entirely (again, seems there is a problem with the extent)

Does someone know what's happening here? Is there any way to have everything displayed correctly in EPSG:3857? Is that normal that QGIS is unable to reproject (on the fly) from EPSG:3857 (and EPSG:3395) to EPSG:4326?

Screen 1 (shapefile and EPSG:3395 raster, the raster is cut):

Screen 2 (shapefile and reprojected raster, everything OK):

Answer 1

The Save As ... option only works good with vector layers. For rasters, use Raster -> Projections -> Warp.

The mercator projections are not able to display the North and South poles (they are in infinity). So if your shapefile includes +/- 90° N/S, the mercator raster files might go bananas.