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Ω =arcsin Λ 1
Λ 2
Λ 1 + Λ 2 ,
(F.62)
Λ 2 = (tr[C l G l ])
2 1 + Λ 2 = (tr[C l G l ]) + 2 .
Λ 1
(F.63)
End of Corollary.
Proof.
Λ 2 ) 2 and ( Λ 1 + Λ 2 ) 2 under the postulate of an equiareal
mapping Λ 1 Λ 2 = 1, namely by means of ( F.48 ).
( Λ 1 − Λ 2 ) 2 = Λ 1 + Λ 2 2 Λ 1 Λ 2 = Λ 1 + Λ 2 2= tr[C l G l ] 2 ,
For the proof of ( F.63 ) just compute ( Λ 1
(F.64)
( Λ 1 + Λ 2 ) 2 = Λ 1 + Λ 2 +2 Λ 1 Λ 2 = Λ 1 + Λ 2 +2= tr[C l G l ]+2 .
End of Proof.
Fig. F.1. Vertical weighted mean of the generalized Lambert projection and the generalized Sanson-Flamsteed
projection of the biaxial ellipsoid
E 2 A,B , squared relative eccentricity E 2 =0 . 1, weight parameters α =1, β =0 . 1
Fig. F.2. Vertical weighted mean of the generalized Lambert projection and the generalized Sanson-Flamsteed
projection of the biaxial ellipsoid E 2 A,B , squared relative eccentricity E 2 =0 . 1, weight parameters α =1, β =0 . 5
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