“Sphere to Tangential Plane”: Polar (Normal) Aspect - Map Projections: Cartographic Information Systems - page 197

Fig. 5.8. Spherical vertical section, equiareal mapping of the sphere to the tangential plane at the North Pole,
azimuthal projection

S 2 R onto the tangent space T N S 2 R Tissot ellipses, polar aspect, graticule Fig. 5.9. Equiareal map of the sphere

15 ◦ , shorelines

5-24 Normal Perspective Mappings

2

R of radius R to a tangential plane at
the North Pole, the South Pole, or an equatorial plane is of focal interest in Mathematical Car-
tography, in Photogrammetry, in Machine Vision as well as in Aeronautics and Satellite Geodesy.
Here, as soon as we have generated the general parameterized mappings of the perspective type,
we introduce more specific projections: the gnomonic projection ,the orthographic projection ,and
the Lagrange projection . Based on Figs. 5.10 , 5.11 ,and 5.12 , we design the elements of a first
perspective projection. At first, we locate the perspective center at O ∗ outside the sphere on the
southern axis of symmetry North-Pole-South-Pole. The perspective center O ∗ is the origin of

The general normal perspective mapping of the sphere S