Coordinates - Map Projections: Cartographic Information Systems - page 174

D = D ( A, B ):=cos A cos B cos Ω − sin A cos B sin Ω cos I +sin B sin Ω sin I ;

N ,A = − cos A sin B cos B sin I,

sin A cos 2 B sin I +sin A sin 2 B sin I, N ,B = − 2sin B cos B − (3.150)

M ,A = − sin A sin I, M, B =0 ,

N ,AA =+sin A sin B cos B sin I,
N ,AB =

cos A cos 2 B sin I +cos A sin 2 B sin I = N ,BA ,

−

(3.151)

2cos 2 B +2sin 2 B +2sin A sin B cos B sin I
+2 sin A sin B cos B sin I,

N ,BB = −

M ,AA = − cos A sin I, M ,AB =0 ,M ,BA =0 ,M ,BB =0 ,

D ,A = − sin A cos B cos Ω − cos A cos B sin Ω cos I,
D ,B = − cos A sin B cos Ω +sin A sin B sin Ω cos I +cos B sin Ω sin I,
D ,AA = − cos A cos B cos Ω +sin A cos B sin Ω cos I,

(3.152)

D ,AB =+sin A sin B cos Ω +cos A sin B sin Ω cos I = D ,BA ,
D ,BB = − cos A cos B cos Ω +sin A cos B sin Ω cos I − sin B sin Ω sin I ;

(tan Λ ) ,A = N

D 2 , (tan Λ ) ,B = M D 2 ,

(tan Λ ) ,AA = D 2 N ,A − 2 DD ,A N
D 4

, (tan Λ ) ,BB = D 2 M ,B − 2 D 2 D ,B M
D 4

,

(tan Λ ) ,AAA = D 4 (2 DD ,A N ,A + D 2 N ,AA )

8 D 4 D ,A N −

,

D 8

(tan Λ ) ,BBB = D 4 (2 DD ,B M ,B + D 2 M ,BB )

4 D 6 D ,B M

−

, (3.153)

D 8

(tan Λ ) ,AB = D 2 N ,B

− 2 DD ,B N

D 4

,

(tan Λ ) ,ABB = D 4 (2 DD ,B N ,B + D 2 N ,BB )

8 D 4 D ,B N

−

,

D 8

(tan Λ ) ,AB = (tan Λ ) ,BA , (tan Λ ) ,ABB = (tan Λ ) ,BAB = (tan Λ ) ,BBA .

In the following chapter, let us close a gap and introduce a classification scheme that is needed
in the remaining chapters.