Fig. 4.4:3. Determination of model coordinates according to the dependent case of the relative orientation. 
The condition of the relative orientation can be found as before from the expression: 
yi—y% = 0 
From the y-parallaxes in at least 5 points the elements of the relative orientation can be computed, 
if necessary through iterations and the model coordinates can then be determined. 
The absolute orientation of the model to the coordinate system of the object is a coordinate transfor 
mation with at least 7 parameters, i.e., one scale change, three translations and three rotations of the 
model. 
For the more general case of three scale factors S x , S y , S z the basic coordinate transformation formulas 
are as follows: 
X = X 0 -f- xS x cost] cosa — yS y cos/y sina -f- zS z sin/y 
Y = Y 0 -(- xS x (sin^sinjy cosa + cos^fsina) + yS y (cos^cosa — sin£sin/y sin«) — zS z sin£ cos/y (4.4:10) 
Z — Z„ — xS x (—sin^sina + cos<$sin?y cosa) + yS y (coS($sin/y sina + sin<f cosa) + zS z cos^cos/y 
Formulas for analytical photogrammetry shown above were programmed for electronic computers 
by J. Talts, MSE, and a considerable number of practical tests have been made. The Oland test 
area has been used for these experiments because of the great number of very accurately measured, 
signalled, geodetic control points. The standard error of the geodetic coordinates in planimetry and ele 
vation is estimated at approximately 20 mm or less. 
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