Geography Reference
In-Depth Information
8-3 Perspective Mapping Equations
Setting up perspective mappings “ellipsoid-of-revolution to plane”, the fundamental perspec-
tive graph, Space Photos.
In this section, we intend to present various
perspective mappings
from the ellipsoid-of-revolution
to the tangential plane, placing the
perspective center
arbitrarily. Let the position
P
c
be on the top
of the ellipsoid-of-revolution. Furthermore, let us use the orthogonal projection to locate the point
P
0
=
p
0
at
minimal distance
or
maximal distance
,namely
X
c
−
X
0
=minor
X
c
−
X
0
=max.
Alternatively, we can take advantage of an orthogonal projection of the ellipsoid-of-revolution to
the sphere, which passes the center
O
of the ellipsoid-of-revolution. The three variants of the
special perspective mappings “ellipsoid-of-revolution to plane” are illustrated by Figs.
8.6
,
8.7
,
and
8.8
.
Note that the perspective mappings from the ellipsoid-
of-revolution to the tangential plane are applied to map
points-in-space to the tangential planes of the ellipsoid-of-
revolution.
Examples are visions from a tower or from an airplane
and from an Earth satellite by eye or by a camera. A spe-
cial example are images of TV cameras showing clouds—
important information needed for weather reports.
For our introduction, we treat only the case of the mapping of minimal distance. The final
mapping equations, given the coordinates of perspective center (
Λ
0
,Φ
0
,H
0
) to the plane which
is located at minimal distance from the perspective center, are presented in Box
8.8
in terms of
the coordinates (
x
∗
,y
∗
)
p
in the tangential plane: see (
8.76
)and(
8.77
).
Box 8.8 (Perspective mapping equations, minimal distance, perspective center
Λ
0
,Φ
0
,H
0
).
South coordinates:
x
∗
=
x
∗
(
p
)=
=
H
0
(8.76)
E
2
)sin
Φ
cos
Φ
0
+
N
0
E
2
sin
Φ
0
cos
Φ
0
−
N
cos
Φ
sin
Φ
0
cos(
Λ
−
Λ
0
)+
N
(1
−
.
E
2
)sin
Φ
sin
Φ
0
+
N
0
E
2
sin
2
Φ
0
H
0
−
N
cos
Φ
cos
Φ
0
cos(
Λ
−
Λ
0
)+
N
(1
−
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