Geography Reference
In-Depth Information
Fig. 8.7.
Perspective mappings of a perspective center
P
c
to the plane which is at the maximal distance from
an ellipsoid-of-revolution
E
2
A
1
,A
2
−
2
gh
cos
δ
or cos
δ
=
g
2
+
h
2
−
k
2
k
2
=
g
2
+
h
2
(8.85)
2
gh
(second equation),
=
±
√
4
g
2
h
2
−
(
g
2
+
h
2
−
k
2
)
2
tan
δ
=
±
√
1
−
cos
2
δ
cos
δ
(8.86)
g
2
+
h
2
−k
2
(third equation).
The height
h
=
H
0
of the perspective center
P
c
above the point
P
0
, which is nothing but an element
of the ellipsoid-of-revolution, is given. The distance
g
:=
X
c
−
X
P
the distance
h
:=
X
c
−
X
0
,
and the distance
k
:=
X
P
−
X
0
are given. In summary, the above equations lead to a special
formulation of
r
,namely
k
2
4
g
2
h
2
h
g
2
+
h
2
r
=
−
(
g
2
+
h
2
−
k
2
)
2
.
(8.87)
−
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