5
-(1-23)3-2(1-2)? (1-coss) * (x -A) [1— coss)? 4 sin2# |
- (1 -3) ( (1-3)? - 2 (1-3) (1 - cos) 4 (1 — coss)? 4- sin?o- |
Since
4 (1 —cos®)? — 4 i (1 — cos 8)? + sin? 9}
is definitely negative it follows that A = 1 is the only real root.
3. Want of Correspondence along the Invariant Direction
and the direction of Tilt.
In the derivation of the expressions giving the want af correspon-
dence along and at right angles to the invariant direction it was assumed
that the x axis in the left hand picture lies on the principal-point base;
whereas the x axis in the right hand picture is swung about its principal
point to equalize the azimuths.
Omitting an appreciable amount of algebra, the ratio of the want
of correspondence at a point on the invariant direction (i) to its radial
distance turns out to be
Py. fPx—b tie Cr...
==); - cos. w, T (Px sin g— Py cos #) d t 5) 4 c; (9)
r
X
The cdrresponding ratio at a point on the direction of tilt (t)
is
P | fPx-b p :
C,
(e + €) +0 … … (19)
where, z
tan 7
Wo = f . ,
I — — tang sin d
b
C
Z
€: = } 52 > sing. @ (C../Cx)3 c; = #(C,/C,) — 1€? sing,
X
e = (f/b) e^ (1 4 Lo sing) - 8(C, ? sing
References
(1) A. M. Wassef, Photogrammetria, 1953-1954, No. 2.
(2) A.M. Wassef, Photogrammetria, 1955-1956, No. 2.
(3) A.M. Wassef, Photogrammetria, 1957-1958, No. 3.