XY 
—Py == 7 Aq — 
Z2 + Ya 
NE UR do, (X—b) Atq m Al 
Z 
      
    
       
   
     
144 RELATIVE ORIENTATION IN MOUNTAINOUS TERRAIN, VAN DER WEELE 
Z2 + ya Y (X—b) Y 
7 dat Edn + ds 45 —-——— Apt 
Y 
tz an (LD) 
(where X, Y and Z, are the respective coordinates of the point concerned). 
In this form the formula is related to an axis system as illustrated in Fig. II.a. 
11.2. 
The parallax formula contains ten elements of orientation, of which five are neces- 
sary to obtain a model free of parallax, and hence the five may be chosen arbitrarily. 
This may be demonstrated by writing the parallax formula, with a grouping of terms, 
in the following form: 
—Py — 
XY Z3 ys Y 
Luc LU dHo, dC*X4dDAaE NL) 
Where +44 = Ag — Agi 
AB — Ao, — Aog 
AC db. db. dgpn 0 dei TES) 
AD = Ax, — Any 
and AE = Ab — 4b, + dn 
If the quantities 44, AB, AC, AD, and AE, are considered as corrections to fictitious 
orientation elements, A, 
B, C, D and E, then by means of equations (II. 3) the values for 
the corrections to be applied to the elements which are actually used in any special case 
may be derived. 
This approach to the problem offers the possibility of derivation of methods of rela- 
tive orientation in a general way, without making repetition of derivation necessary for 
  
  
  
  
  
3 4 
/ = 2 
y 
5 6 
Fig. ILb. 
each of the fifty possible combinations of five elements which 
could be chosen from the ten available. 
11.3. Choice of points for parallax observation. 
If we consider, for the moment, that relative orientation is 
a mathematical problem, it will be obvious that we need five equa- 
tions of the form (IIL.2) in order to solve the five unknowns. 
The coefficients of the unknowns in these equations contain 
the coordinates of the points in which parallax observations are 
made. 
To obtain coefficients in the equations that show a maximum 
difference, the pattern of points is usually chosen as indicated in 
Fig. II.b. This pattern offers at the same time a convenient sym- 
metry as well as a check on the observations. 
For mountainous terrain this symmetry of position, if established on the plane of 
the negative, includes the relation: 
The parallax equations for the six points may thus be re-written as follows: 
Ys FK Y. Y. 
3 4 A 5 i ) it 
Za Z4 Zr Ze