16 
the photogrammetric bundle vector/? to the corresponding 
vector Z in object space 
R (a,uu,K) 
(1) 
where/? o is the unit vector in the direction of p 
Z 0 is the unit vector in the direction of Z 
and /? (cc,'X',h) is the orthogonal rotation matrix linking 
the x,y, c coordinates of the camera system with 
the Z2, z^ system of the spatial triangulation. 
The photogrammetric bundle vector p has the following 
components: 
X 
x-x -h X +y. G 
p 
7 
- 
(y . y A y) . h 
V C y 
c 
. 
c 
Lx J 
(2) 
where (x, y) denote the measured plate coordinates; (x , y ) 
P p 
the coordinates of the principal point; c x and c two scalers; and 
e an angle expressing the deviation from perpendicularity of the 
x, y system. The quantities h x and hy represent the amounts 
of offset of the actual image from an idealized position, 
corresponding to the principles of central perspective, whose 
coordinates are x and y. The h x an d Ay are functions of the 
location of the image and are usually resolved into components 
of radial and decentering distortion. The parameters used to 
simulate the photogrammetric bundle are given in Figure 6 and 
the corresponding geometry in the plane of the photograph is 
shown schematically in Figure 7- These parameters are ob 
tained from a least squares solution using the cataloged 
coordinates of the photographed star images. The correspond 
ing 2 0 -vectors must be obtained by a rather complex up 
dating procedure which, mathematically expressed for a 
specific star, has the form shown with formula (3)«