(3) 
examined in a paper published in 1958 (2) in order to assess the attainable 
precision of various orders of approximation. The following is a brief 
summary of the main results, written with special reference to the practical 
aspects of design. 
Let the system of coordinates O' (x, y', z') attached to the right-hand 
photograph with origin at its perspective centre be rotated to O' (§ ,7,¢& ) 
parallel to O (x,y, z) of the left-hand picture; and let Cy, Cy, Cz be the 
components of the base O O'. The condition of correct relative orientation 
is that the plane containing the two perspective centres and the image 
(x, y, —1) of a ground point P on the left-hand picture shall also contain 
the image ($4 Cy, 7 Cy, 5+Cz) of P in the right-hand system. This 
leads to the system of equations 
Xx — X & - Ck 
xy - x7 =C, tms cmi] 
— X's = C, 
where 
C.¢.C roy -C...% 
Ns x5- 725 S and X-— 1:7 E. € ets) 
X624 £ X S+ ë 
Putting C, = b and C,/C, — C,, we obtain 
Eu 5 
x (-8)-5 
As shown in Ref (1) the coordinates ( £,77,§) may be derived from the 
photo-coordinates (x', y', —1) by applying to them the transformation matrix 
(1 — cos) sin" + cosA (1-cosŸ) sinv-sinA — sinŸ sin ÿ 
(1 — cos) cosnp + sin A —(1-cos®) cosp«cos^ — sin? cosy | ... (7) 
— sin sin @ sin? cos $ -cos 
X (6) 
where 9 p and $ are the Eulerian angles, and 
The exact expression of x given in Equation (6) is a function of (&, A, 
C'z; x, y) which may be expanded in a Taylor series with the remainder 
in Lagrange's form as follows : 
X(9,5,C'g)z X(o)tdx(o) t id^/X(o)-R | .. … … (9)