THE PANORAMIC PROJECTION OF THE GLOBE FROM SATELLITES 
BY 
PROFESSOR WAGIH N. HANNA 
Faculty of Engineering 
Ain Shams University 
Abbasis , Cairo , Egypt 
WG IV/2 
ABSTRACT 
A panoramic photograph is a picture of strip of terrain taken transverse to the direction 
of flight. The exposure is made by a specially designed camera which scans laterally from 
one side of the flight path to the other. The lateral scan angle maybe as great as 180 , 
in which the photograph contains a panoramic of the terrain from horizon to horizon. The 
panoramic photograph is therefore considered a central projection of the globe on the 
cylindrical film in the satellite , which produces after development what is called "THE 
PANORAMIC MAP". When the axis of the camera coincides with the geographical axis of the 
earth joining the two poles N and S ,the map produced is called "VERTICAL PANORAMIC MAP" 
otherwise it is called "GENERAL PANORAMIC MAP". 
This paper deals with the geometry of the vertical panoramic photograph , the derivation 
of the transformation equations of the points on the globe and its corresponding 
projections on the cylindrical film and hence with its images on the panoramic map. The 
second part deals with determination of the panoramic equations of longitudes and 
latitudes and the illustration of the vertical panoramic map. For the general panoramic 
projection a simple and short discussion is given to determine the geographic and 
panoramic coordinates of any given point related to any arbitrary direction of the axis 
of the camera. 
KEY WORDS : Photogrammetry, Panoramic, Cartographic, Mapping, Satellites 
  
  
1. GEOMETRY OF THE PANORAMIC PHOTOGRAPH unity,i.e. r-l. 
Figure (1) shows an isometric view il- 1.2 First Transformation Equations 
lustrating the geometry of a vertical Figure(2) 
panoramic photo taken from exposure 
station C. The camera focal length is f This equation expressing the coordinates 
and the flying height above datum is h. (X, 1o 2,) in terms of either (X,,Y,:2,) or 
In this system the X axis is taken in (U, , Vi) are called the first transformation 
the direction of flight passing through equations.The equation of the cylinder film 
the center of the globe O. The Y-axis is D is 
taken through O perpendicular to the X 
axis in the equator horizontal plane. Y^*(z-h)?:f? (2) 
1.1 Notations and Representation Equa The equation of the projection ray B,CP, are 
tions 
X = xt 
r= radius of the globe 
Y = yt (3) 
PG Y any point on the globe 
zs h+t(Z,-h) 
c 
I 
longitude angle of P 
where t is a parameter. 
V, = latitude angle of P, Since P, lies on CP, and on the cylinder D 
then we have 
P, = image of P, on the cylindrical 
surface D X) = Xt 
From the figure we have the representa- Y, = Yıt 
tion equations; 
Zz = h+t(z,-h) 
X 7r cosV, cosU, 
Ya HZ. h) s f 
Y,sr cosV, SinU, (1) 
which yields to the parameter 
f 
+ (Z,-h)? 
zr sinV, 
t-- 
To simplify the calculations , the radi- 
us r of the globe is assumed to be equal 
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