> 
f 
f 
41 
Fig. 4.4:2. Transformation of rotated image coordinates x r , yr, c to the original system (x r ), (yr ), (c). 
For the two photographs the following expressions are found: 
(X') = ^ / COS^9 1 COSK 1 — j'cos^jsin«! — c SHlgOj 
(y) = tf'sinK! + y'cOSKi 
(c x ) = ^'sinr/^iCOSKi — j'sin^jSillK! + c COSCp x 
(x'')= x"cosq) 2 cos){ 2 — y // cos<p 2 sinK 2 — c sin<p 2 
(y") = ^ ,/ (sinaj 2 s i n <'/ ; 2 COSw 2 + cosco 2 sinK 2 ) + j' / ( co Sfo 2 cos «2 — sin6j 2 sing9 2 sinw 2 ) + (4.4:8) 
+ c sinf0 2 COS^ 2 
(c 2 ) = x"( — sinto 2 sinK 2 +cosa) 2 sing? 2 cosK 2 ) — y"(cosio 2 sin<p 2 sinK 2 -l-sin£o 2 cosK 2 ) + 
-|- C COSOJ 2 COS(^ 2 
Coordinates can be computed from formulas 4.4:1—4 for known values of the angles of the relative 
orientation of the model. Generally, the angles must first be determined and for this purpose the con 
dition 4.4:5 is used. Iterations are generally necessary and the method of least squares is of indispensable 
value for the unique treatment of redundant observations, i.e. more than five pairs of rays. 
For the case of dependent pairs of photographs all elements of the relative orientation must refer to 
one of the photographs only. The basic formula systems can be derived directly from fig. 4.4:3. 
(x")bz 2 
bx — 
(**) 
x z 
C 1 
yz = 
c i 
( c 2 ) 
(c 2 )6* 
c, — 
(c 2 )bx — (x")bzc. 
(c 2 )x' 
(x")bz 2 , 
(*")< 
Ji = 
(c 2 )x' — (x")c 1 
(c 2 )bx — (x")bz 2 
(4.4:9) 
v _ (/ 
J 2 — 
(* 
(c 2 )x' - 
— bz 2 ) 
( C 2 ) 
- (x")c 1 
— by 2 = 
y 
c x bx — x'bz 2 
(c 2 )x' — (x")c x 
(y") - by s