6. 
Z = Z.+w.k.=Z.+w.k. 
p 01 pi pi oj pj pj 
Z . + w .k . = Z , + w . k . 
oj PJ PJ ok pk pk 
(e) 
(f) 
in which (u, v, w) pi , (u, v, w) , (u, v, w) pk are rectified coordinates 
of the images of p in photos i, j, k and 
v = 01 P 1 v = PJ v = Qk P- k 
pi Oi p 9 pj Oj p ’ pk Ok p 
Using the image of p on photo i as an example, the rectified coordinates 
are related to measured plate coordinates X, Y, Z as follows: 
Pi 
u 
A 
A' 
D 
X 
X 
V 
w 
pi 
B 
C 
B* 
C 
E 
F 
i' 
^ 1* 
I 
pi 
A 
y 
z 
_ 
- 
r 1 
B 
PJ 
PJ 
J P k 
.. 2.02 
pk 
in which the elenents A, A’, D F of matrices A , B , and C* are 
functions of the respective rotations w, <f>, k of photographs i, j, k 
and z = -f the calibrated camera focal length. 
Referring to Figure 2.01, expressions for k . and k . can be derived from 
pi P J 
2.01 (a) and 2.01 (c) 
v .(X .-X .) - u .(Y .-Y . ) 
k = PJ °J 01 PJ °J -P- 1 - 
pi U .V . - U .V . 
F pi PJ PJ pi 
u .(Y .-Y .) - v .(X .-X .) 
k . „ PI °J 01 P 1 °J. 01 
PJ 
u .V . - U .V . 
PJ pi pi PJ 
(a) 
(b) 
2.03 
substitution of k . and k . into 2.01 (e) gives 
Pi PJ 
(X .-X .) (v .w .-v .w .) + (Y ,-Y .) (u .w .-u .w .) + 
v oj oi ' K pi pj pj pi' oj oi' pj pi pi pj 
(Z .-Z .) (u .v .-u .v .) = 0 
v oj oi 7 pi pj pj pi' 
2.011 (a) 
which is the condition equation for intersection of rays R . and R . . 
P-*“ P J 
Equations 2.01 (b) and 2.01 (d) can be used to determine expressions 
for k . and k 
PJ 
pk 
Capital letters A, B, 0, g, £, ...etc., underlined denote matrices