GV-14 PHOTOGRAMMETRIC ENGINEERING 
With these data, the following equations are formed: 
a1Ax d biAy + cıAz = gn 
G3À X + b3A y 4 coAz — qo 
asAx + b3Ay + csÂz = qa 
where 
ll 
ll 
f'(m + mi) 
f'(ms + ns) 
a, = xam; + xbn, b, vam; + ybni C1 
as = xbms + xcns by = ybma + yen, C9 
as = xcmz + xanz bs = ycms 4- yan cs = f'(m3; + nj) 
La = (xa? + ya? + jf?) q = — LaLb sin aLb’A(aLb) 
Lb = (x0? + yi? + 22/2 q = — LbLc sin bLc'A(bLc) 
Lc = (x + yc? + f?) 1/2 qs — — LcLa sin cLa'A(cLa) 
Lb 
m = 1 — cos aLb’ n = 1 — cos aLb’ 
La Lb 
Le Lb 
ma = 1 — cos bLc' — ne = 1 — cos bLc' — 
I Lc 
La Lc 
m; — 1 — cos cLa' A3; — 1 — cos cLa' — 
Lc La 
xaxb + yayb + f* 
cos ull) = ei et 
LaLb 
xbxc + ybyc 4- f? 
cos bli) = — —nz 
LbLc 
; xcxa + ycya + f* 
cos cLa! = —— - 
LcLa 
A(aLb) = aLb — aLb 
A(bLc) = bLc — bLc' 
A(cLa) = cLa — cLa' 
and f' is the first approximation of f. 
The equations are solved simultaneously for Ax, Ay, and Az, which are 
applied as corrections to the x and y coordinates and f'. With the corrected 
values, new coefficients and constant terms are formed and a second set of 
simultaneous equations is solved for Ax», Ay», and Az». The forming of revised 
coefficients and constant terms coupled with repeated simultaneous solutions is 
repeated until the differential unknowns and constant terms vanish. 
Then, for any image a, 
xa. = xa + > Ax 
ya. = ya + $^ Ay 
f=f 4+ Az