I have a dataset in Mercator projection that spans the globe horizontally from -180 to +180 degrees longitude. However, it's more convenient for me to store and use the data in the range -170 to +190, since -170 degrees makes a better place to cut the map without slicing through features I'm interested in.
(I indicate the origin of -170 degrees through the xllcorner value in the .hdr file. The cells size in meters is set so that the width of the whole file at the equator comes out to 6378137.0, to match the WGS84 ellipsoid, so it should wrap around the globe perfectly and match on the east and west edges.)
All this works fine in Global Mapper as long as I stay with a cylindrical projection like Mercator. But when I reproject to Polar Stereographic, it looks to me like it only handles the range -170 to +180 longitude, leaving a 10-degree missing pie slice in the map. A similar effect occurs with Double Stereographic and other projections. For instance, Gnomonic projection with a 180-degree central longitude shows a missing vertical strip.
I can also envision the need in other situations to use a longitude range of, say, -190 to +170 (so some longitudes are less than -180) or 0 to 360, so that any longitude from -360 to +360 is probably possible.
I've attached an example as a low-resolution image file, which demonstrates the problem. Just load the file and change the projection to Polar Stereographic in the Configuration window.