A photograph was taen of a building, with the x axis (canera 
base) making an angle & with the front-side of the building 
(Piz. %1).In restitution the floating mark is to.be moved.in 
the coordinate system (%,.3, 2). 
The following relations exist between the Two ccordinate 
eystens.(x, y,.2).anàd CE,.T7,.2): 
® Rog. X.cos« - Z.sin« 
y (4.9) 
ad - 2. d - 
7 Z4 Zesina Z COS 
NS X 
l 
From these relationships follow the partial derivatives 
COS X 0 -sin « 
Ug = 0 1 0 (4.10) 
-sine 0 cos & 
a 
and the transformation matrices 
o xn 
. 4 Cc 0 ^o -4 
X =F Um== = . ‚A -U- (4.11) 
x 
xv £T 0 5 y X 
BJ 
| 
= 0 
Hence, the calculation of x! and y' according to (4.0) with 
(4.10) and (4.11) represents a rigorous solution. The conclu- 
sion of Section 3 applies implying that the segments can be 
chosen arbitrarily large. 
4.4.2. ion-linear dependáences 
4.4.2.1. Consideration of earth's curvature 
‘The consideration of earth's curvature is usual on the imag 
as well as model coordinates. Correction on model coordi 
represents a rigorous solution, while the mene coordina 
correction rigorously applies only to near vertical phot 
graphs. 
According to Pig. 4.2 one obtains for (4.1) 
X + X = X 
BET FF 
Z = Z + (72 + $2)/2R (left image) 
2 
Z = Z + [(Z - p + (F - by) 1/2R (right image) 
Thus, the partial derivatives are 
1 0 0 
Uz = 0 1 0 (4.122) 
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