as 
eat 
the 
hat 
an- 
A*, 
1), 
to 
ala, 
  
RELATIVE ORIENTATION IN MOUNTAINOUS TERRAIN, VAN DER WEELE 149 
where: Ax’ sin w — Ag’ cos w 
A w’ 
4b; 
AD** = —Ax' cos w — Ag’ sin w 
AB = An, 
  
Here again, the same principles as treated in the preceding sections offer an easy 
solution to the problem, and further elaboration on this subject should not be necessary. 
V. Model deformations. 
Model deformations in X and Y directions are, generally, of little interest for prac- 
tical purposes, as they will, nearly always, be smaller than the specified tolerances for 
planimetry in the map. The deformations of the model in Z-direction, however, are cri- 
tical, and there will be many cases in which the procedure of absolute orientation will 
involve a subsequent change of the relative orientation, in order to obtain a better cor- 
respondence between model heights and terrestrial heights. 
The influence of the elements of relative orientation, on the height of a point in the 
model is given, for vertical photography, by the formula: 
Z2 + X2 Z2 + (X—b)? XV (X—b)Y 
AZ, = — 5 lp’ 4 5 q" 3 ^ Aw’ — 7 dut + 
YZ YZ Z Z X (X5) 
T 5 1x’ — p 1x” — 5 15 7-4 5 45." + p 1b," — 5 db ^ 
which may be re-grouped as follows: 
  
Z2 + X? XY 1 1 ) 
7 = ( M ( , zs c a " i m 2 nt! Y: Z fes ; ” d- 
AZ, p — (49" — Ag) * = G Ao") * X|2 4" * , Ab — ,, Ab, 
YZ Z 
+ Y. 40" b (Ax' 12") ci i (Ab — 4h) + (b.44" + 40.1) when (VA) 
) 
To this influence of relative orientation, we have to add the effect of the absolute orien- 
tation, which is given by the formula: 
AZ, = X.49 - Y . AQ - Z,. 
a 
The addition of this effect to that of the relative orientation, changes the linear 
terms in formula V.1, and results in: 
(a) for mountainous terrain: 
Z2 + X? XY YZ Z 
AZ = |A + AB+ X.AC+Y.AD + AE + AKA AG. (V2) 
b b b b 
in which: [A Ip" — Ag’ 
1B 1e — Ao" 
1 1 
1C —2. lq ” 4 b 15, — b Ab," + AP 
(V.3) 
11) Aw I 10 
| F Ix! — Ax" 
  
and: