Gall Stereographic Projection
Meridians: Equally spaced straight parallel lines 0.77 as long as the Equator.
Parallels: Unequally spaced straight parallel lines, perpendicular to the meridians. Spacing increases toward the poles.
Poles: Straight lines equal in length to the Equator.
Symmetry: About any meridian or the Equator.
This is a perspective projection from a point on the Equator opposite a given meridian onto a cylinder secant at the 45º parallels. It is not equal-area, equidistant, or conformal. Scale is true along the standard parallels and constant between two parallels equidistant from the Equator. There is no distortion along the standard parallels, but it increases moderately away from these parallels, becoming severe at the poles.
For cylindrical projections, only one standard parallel is specified. The other standard parallel is the same latitude with the opposite sign. For this projection, the standard parallel is by definition fixed at 45º.
This projection was presented by James Gall in 1855. It is also known simply as the Gall projection. It is a special form of the Braun Perspective Cylindrical projection secant at 45ºN and S.
This implementation of the Gall stereographic projection is applicable only for coordinates that are referenced to a sphere. If you want to project coordinates that are referenced to an ellipsoid, using the
projinvfunctions, then create a
projcrsobject instead of a map projection structure. You can create a
projcrsobject for the Gall stereographic projection using the ESRI authority code 54016. For example:
Mapping Toolbox™ uses a different implementation of the Gall stereographic projection for displaying coordinates on map axes than for projecting coordinates using the
projinvfunction. These implementations may produce differing results.
landareas = shaperead('landareas.shp','UseGeoCoords',true); axesm ('gstereo', 'Frame', 'on', 'Grid', 'on'); geoshow(landareas,'FaceColor',[1 1 .5],'EdgeColor',[.6 .6 .6]); tissot;