Ellipsoid-of-Revolution to Sphere and from Sphere to Plane - Map Projections: Cartographic Information Systems - page 286

9
Ellipsoid-of-Revolution to Sphere and from Sphere to Plane
Mapping the ellipsoid-of-revolution to sphere and from sphere to plane (the Gauss double
projection, the “authalic” equal area projection): metric tensors, curvature tensors, principal
stretches.
A special mapping, which was invented by Gauss ( 1822 , 1844 ), is the double projection of the
ellipsoid-of-revolution to the sphere and from the sphere to the plane .Theseare conformal map-
pings . A very ecient compiler version of the Gauss double projection was presented by Rosen-
mund ( 1903 ) (ROM mapping equations) and applied for mapping Switzerland and the Nether-
lands, for example. An alternative mapping, called “authalic”, is equal area, first ellipsoid-of-
revolution to sphere, and second sphere to plane.
9-1 General Mapping Equations “Ellipsoid-of-Revolution to Plane”
Setting up general equations of the mapping “ellipsoid-of-revolution to plane”: mapping
equations, metric tensors, curvature tensors, differential forms.
Postulate.
The spherical longitude λ should be a linear function of the ellipsoidal longitude Λ : parallel circles
of the ellipsoid-of-revolution should be transformed into parallel circles of the sphere.
End of Postulate.