Geography Reference
In-Depth Information
Solution.
In this case, the minor and the major distortions amount of (
18.43
), and det D
l
=
Λ
min
Λ
max
=1.
The matrix F
l
of eigendirections from the left diagonalization is provided by (
18.44
). As before,
F
l
C
l
F
l
=D
l
and F
l
G
l
F
l
=I
2
are satisfied.
D
l
:=
:= diag[
Λ
min
,Λ
max
]=
0
.
931 07 0
,
(18.43)
0
.
074 03
F
l
=
=
0
.
855 79 0
.
796 80
.
(18.44)
−
0
.
681 43 0
.
731 88
The Jacobi matrix J
l
reads
J
l
=
D
Λ
xD
Φ
x
=
−
.
0
.
973 14
0
.
783 11
−
0
.
270 98
0
.
343 70
−
(18.45)
D
Λ
yD
Φ
y
Λ
=29
◦
55
E
,Φ
=31
◦
13
N
,Φ
0
=60
◦
N
Finally, the orthonormal matrix of (right) eigendirections results to
F
r
=
0
.
918 11 0
.
396 32
.
(18.46)
−
0
.
396 32 0
.
918 11
F
r
C
r
F
r
=D
r
and F
r
G
r
F
r
=F
r
F
r
=I
2
, which enables us to orientate the Tissot ellipse in the
map.
End of Exercise.
The above two exercises close the discussion of the mappings “sphere to cone”. In the next
chapter, let us study the mappings “ellipsoid-of-revolution to cone”.
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