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This kind of measurements is included in the bundle 
adjustment with linearized formulas (1) given above. Again if 
one of the object points is a control point, partially known 
control point or homologue point the unknown coordinate part 
(dX and/or dY and/or dZ) has to be included in the. same way as 
explained before. If one of the terrestrial observations or 
conditions spans over several models, then linearized equations 
(1) are only generated for the image in which an observation or 
condition object point is seen. The same is done when a 
control point is only visible in one photograph. 
c.) Terrestrial observations. 
For terrestrial observations the following linearized 
formulas are used. 
Distance: 
zie al-iY m "d e ls 
ds. ; = s. [ 0 X. )dX, + Y. )df, E 1. )dZ, (2) 
+X; VX, HIT, ET AIS ] 
Azimuth? 
= - E - - —X.)dY.] 
dj 12% -Y. )dX. x X, )dY. ty Y,lax, + us X: j (3) 
51 
Height-difference: 
dil | 747, - AZ. (4) 
Angle in 3-D space (i ... Station point): 
non-linear form: 
= : - - 70, 4, 72.31 
cost, ; x i [X AK 7X.) * (Y, LES I 262,72; (5) 
: a. = —{X +} + 2%, 
linearized form: i jk 1 
8, = X, -X; 
5; 355s ne du = a; OX, * b, dY, * c. d2. * 8 3 d 
a,dk, + b d; + c,d, + for D. b, b, replace X by Y (6) 
a,CX, * b,dY, * c, dZ, + for c,, 05, 0, replace X by Z 
d.) Conditions for a straight line and a plane: 
Straight line: 
= A (cul . 
(XX) + (XX) or 0 Gd 
(2,71. 
- = = 
v. YA T1) Hr 0