406 19 “Ellipsoid-of-revolution to cone”: polar aspect
Φ 0
Φ 0
p
∆ 0 = π/2 − Φ 0
central point on the axis of the ellispoid
parallel to the equator
Fig. 19.1. Mapping the ellipsoid-of-revolution to the cone, polar aspect, line-of-contact.
19-2 Special conic projections based upon the ellipsoid-of-revolution
Normal mappings of type equidistant, conformal, and equal area. The mapping equations and the principal
stretches. Lambert mapping and Albers mapping.
In this section, we present special normal mappings of type equidistant, conformal, and equal area as
second postulates.
19-21 Special conic projections of type equidistant on the set of parallel circles
Let us transfer the postulate of an equidistant mapping on the set of parallel circles. As it is shown
in (19.9), we get a typical elliptic integral of the second kind.
Λ 2 = 1 and Λ 2 =
f
(∆)
M
⇒
f
(∆) = M
⇔
f
(∆) =
A(1 − E
2 )
(1 − E 2 cos 2 ∆) 3/2 ,
(19.8)
f (∆) = A(1 − E
2 )
(1 − E
2 cos
2 ∆)
−3/2 d∆
= A(1 − E
2 )
∆
0
(1 − E
2 cos
2 ∆
∗ )
−3/2 d∆
∗ .
(19.9)