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
