f 
Fig. 4.4:1 Independent pairs of photographs according to the normal case. Derivation of the relation between transformed 
image coordinates (x'), (y'), (x"), (y") and model coordinates x, y, z. The image coordinates of the right photograph are first 
transformed in scale to conform to the principal distance (c^, of the left photograph. Then the basic formulas 4.4:1 through 
4 can be derived from similarity. 
The condition for the intersection of corresponding rays is: 
Jl =J2 
or, according to the expressions derived: 
(?) ( C 2) = (?') ( c i) 
Ay-parallax is defined as: 
Py = Ji -J* 
Therefore, after substitution of (4.4:3—4): 
_ = (/) ( C 2 ) ~ (?') (Cl) j 
y (*0 ( c 2 ) - (*") (cj 
(4.4:5) 
(4.4:6) 
For y-parallaxes as functions of small errors the following expression is frequently used: 
Py = fyi ~ dy 2 
The coordinates (# r ), (y r ), (c) used above are functions of the rotated image coordinates x r ,y r , c accord 
ing to the following well known expressions (to primary, (p secondary and u tertiary): 
(#r) = X t COSCpCOSK — y r COS(J9SinK — C sint^) 
(y r ) = %t (sinojsin^COSK + costosin«) + y r (cOStoCOSK — sintosinq: sin«) + 
+ c sincocosq) (4.4:7) 
(c) = X T (— sintosinjt COSOjSinrfCOSn) — y r (costosint/sillit -j- sintOCOSit) -f- 
+ c COSCOCOSCp 
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