“Ellipsoid-of-Revolution to Cone”: Polar Aspect - Map Projections: Cartographic Information Systems - page 451

19
“Ellipsoid-of-Revolution to Cone”: Polar Aspect

A 1 ,A 2

Mapping the ellipsoid-of-revolution to a cone: polar aspect. Lambert conformal conic

mapping and Albers equal area conic mapping.

E

Section 19-1, Section 19-2.

First, in Sect. 19-1 , we review the general equations of a conic mapping to the ellipsoid-of-
revolution , the polar aspect only. Second, in Sect. 19-2 , we treat a special set of conic mappings,
namely three types and special aspects. Indeed, the detailed computations are rather elaborate.

19-1 General Mapping Equations of the Ellipsoid-of-Revolution
to the Cone

Deformation tensor of first order, the meridian radius, the radius of curvature in the prime
vertical, the principal stretches.

The first postulate fixes the surface normal ellipsoidal coordinate as follows. The opening angle
half, representing the latitude Φ 0 of the cone, agrees to the latitude of the circle-of-contact.
For practical reasons, we use the polar distance Δ 0 = π/ 2

− Φ 0 . We refer to Fig. 19.1 .

Line-of-contact:

(19.1)

Δ 0 = π/ 2 − Φ 0 .