“Sphere to Tangential Plane”: Polar (Normal) Aspect - Map Projections: Cartographic Information Systems - page 212

Fig. 5.19. Line-of-sight, normal perspective mapping of the sphere to the tangential plane at the North Pole,
projection plane at minimal distance

5-245 The Gnomonic Projection

According to Fig. 5.20 ,the gnomonic projection is generated as a polar central perspective, where
O ∗ =0or D = 0 in the context of a normal general perspective mapping holds. In Box 5.15 ,the
items of such a mapping of the sphere to a plane (namely, (i) the parameterized mapping, (ii) the
left principal stretches of the left Cauchy-Green eigenspace, (iii) the left maximal angular shear,
and (iv) the inverse parameterized mapping) are collected.

Note that the gnomonic projection has been used in the
antiquity for the construction of a sundial (“gnomon”).

The basic results of the gnomonic projection or polar central perspective mapping of the sphere
S

2 R are collected in Lemma 5.4 .