i asl (11) 
X tanp, nl ra 
2.2 Analytical Representation of Lati 
tude 
From equation (4) we can get the first 
transformation equation of the latitude 
LAE 
K(x?^«v?) - (z--hY- s 
where 
K = (sinV,-h)/cosV, 
This equation represents the curve of 
intersection of the circular cone whose 
vertex is the center of projection C and 
its base is the latitude V, with the 
cylindrical surface of the film. By 
substitution in (8) and (9) we deduce 
the panoramic equation of the latitudes 
  
s. y* = = 
X sf cos? (=) (K2+1) -1 (12) 
2.3 Representation of The Panoramic Map 
Figure(6) shows the panoramic map in 
which the longitude and latitudes are 
illustrated according to the equations 
(11) and (12) respectively. The lati- 
tudes which satisfy the inequality: 
V, €& V, € n/2, where V. sin! (1/h) 
are represented on the map. The latitude 
which corresponds to V, is known as the 
envelope curve of the map. 
2.4 Location of Points From The Panoram- 
ic Map 
  
If the panoramic coordinates (X"',Y') of 
any point P' are known, then its corre- 
sponding point P,(U, ,V, ) on the globe can 
be determined from the equations (11) 
and (12) or approximately directly from 
the panoramic map. 
2.5 The General Panoramic Map 
  
In the general panoramic projection the 
axis of the camera is in arbitrary posi- 
tion w.r.t the geographical axis of the 
globe. To get the corresponding trans- 
formation equations in this case we have 
to change the direction of axes of ref- 
erence without changing the origin O. 
Let the new system of axes be (X',Y',Z') 
and the direction cosines of OX',OY', 
and e referred to the original axes be 
(L, » ,N, ) : (L ,M,,N,), and (L MN). 
Then the coordinates of the deu px 
Z") referred to the original sys em 
ive be; 
X LX FLY * L 2 
Y, = M x", * M, Y' + M, Zz’, (13) 
a Y ' Y 
Z -N X, *NY,tNZ, 
350 
  
  
  
  
  
  
  
  
  
  
h 
P 
9 >t 
Fig. 4. The panoramic mapping 
E. Ye 
X 
Y 
o* 5 
X 
i 
p* 
y 
x* 
Fig.5. The panoramic photograph.