Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 178

Fig. 5.9 The meridian that
contains point P

Z
X 2

tan B 0 ﾼ p :

Y 2 þ

tanB 1 ; the
iterations can be repeated until the difference between the two values of B is less
than 0.0001 00 or the difference between the adjacent values of tan B is less than
5

The tanB on the left side (tanB 1 ) can be computed. Set tanB ﾼ

10 10 .
From Fig. 5.9 , in the right triangle PK p P 3 , it is apparent that:

p

X 2

Y 2

þ

cos B ﾼ

H :

N þ

Hence, we get:

p

X 2 Y 2 þ

H ﾼ

cos B

N : ð 5 : 22 Þ

Equations ( 5.20 ), ( 5.21 ), and ( 5.22 ) are the expressions for computing L, B, and
H with X, Y, and Z.
Such transformation can be easily understood. The problem is that ( 5.21 ) needs
iteration. There are many closed formulae for transformation between L, B, H, and
X, Y, Z (see Featherstone and Claessens 2008; Vermeille 2004).
An example of transformation between L, B, H and X, Y, Z is shown in Table 5.1 .