CIPA 2003 XIX th International Symposium, 30 September - 04 October, 2003, Antalya, Turkey 
figure 4 - Forward Intersection Combined with 
Trigonometric Levelling 
3.5 Coordinate transformation 
The coordinates computed in the arbitrary local 
coordinate system have to be transformed into the object 
system. 
As already stated, both sets of coordinates can be treated 
as plane ones- this arrangement simplifies transformation 
calculation. Different types of plane transformations were 
used. see(l, Albertz / Kreiling -7, Luhmann): 
- similarity transformation with 2 identical points 
- similarity transformation with over-determination 
(HELMERT - Transformation with 5 identical 
points ) 
- affine transformation with over-determination 
(HELMERT -Transformation with 5 identical 
points) 
Based on manual calculations the three transformations 
were programmed by the author Walter da Silva Prado, 
(see figure 5). 
We suggest the similar transformation with over 
determination to be the most adequate solution. Affine 
transformation is not necessary, because both systems are 
at the same scale. 
The comparison of the two similarity transformations 
shows insignificant differences. 
TRANSFORMADO PLANA DE SEMELHANQA COM EXCESSO 
TRANFORMADO DE HELMERT 
SISTEMA DE CAMPO 
SISTEMA OBJETO (FACHADA) 
PONTO 
V 
X 
v 
X 
PONTO 
PONTOS IDÉNTICOS 
PONTOS IDÉNTICOS 
103 
4969,552 
19981,197 
500,000 
1019,067 
103 
106 
4979,605 
20009,715 
507,067 
1048,443 
106 
100 
4967,584 
19962,213 
500,000 
1000,000 
100 
102 
4968,524 
19971,280 
500,000 
1009,110 
102 
107 
4980,654 
20019,866 
507,067 
1058,639 
107 
PONTOS A TRANSFORMAR 
PONTOS TRANSFORMADOS 
PONTO 
Y 
X 
Y 
X 
PONTO 
100 
4967,584 
19962,213 
499,997 
1000,000 
100 
101 
4967,638 
19962,285 
500,044 
1000,077 
101 
102 
4968,524 
19971,280 
500,000 
1009,108 
102 
103 
4969,552 
19981,197 
500,004 
1019,069 
103 
figure 5 - Similarity Transformation with Over 
determination 
3.6 Final comments about the two coordinate systems 
3.6.1 During the first days of the project, all 
measurements and computations were executed in the 
arbitrary local coordinate system. 
3.6.2 However, once having transformed the station 
coordinates of A, B and C into the object system, all 
further measurements and computations were carried out 
in the object system. The horizontal circles of theodolites 
and total stations were oriented in the object system; 
therefore we were able to measure azimuths in the field. 
3.6.3 A further check for two of the transformed station 
coordinates were obtained in the field by use of the 
program "Determination of Free Station Coordinates" of 
Total Station LEICA TCR 307. 
3.7 Precisions of ground control coordinates 
Derived from coordinate differences we calculated the 
standard deviations for the ground control coordinates as 
follows: 
standard deviations 
( mm ) 
Tolerances 
( mm ) 
± 8.8 
In X 
± 15 
± 8.3 
In y 
± 45 
± 3.4 
In z 
± 15 
These precisions are adequate to the scale 1:200 of 
orthophoto. 
3.8 Artificial points in the object coordinate system 
During processing orthophotos by PhotoModeler software 
we had to create about 16 artificial points in order to 
mark the edges of the orthophoto areas. These points, so- 
called QG (quebra galho), were defined in the y-plane by 
the intersection of horizontal lines (z = const, of known 
points) with vertical lines ( x = const, of known points). In 
order to proof such procedure, some coordinates were 
checked by field measurements. 
4 TAKING IMAGES 
A total of about 28 orthogonal and oblique images were 
taken with both cameras. 
Due to some obstructions such as trees, leaves, traffic, 
parked cars, etc, the cameras could not be placed in