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the method of least squares — that gives maximum precision utilizing all points
— for every prepared model is determined:
— a scale-coefficient K
— three parameters that characterize the absolute orientation of the model
— three parameters Xo, Yo, Zo that fix the origins of the coordinates.
Compensation of the systematic errors and computation of the elements for
each model.
From the elements of the first model and the measurements made in the
instrument for any stereoscopic model (variation of Y-tilt and swing of the old
camera, comparison of coordinates of common points of two successive models)
one can derivate, step after step, the elements of scale and orientation of each
model. Several calculation methods are possible, giving equivalent results and
controlling each-other. In the next prepared model closing-errors in the elements
are found, linear repartition of the differences permits the canceling of syste-
matic errors. One may assume that after this linear repartition the elements
do not possess errors others than accidental ones. Next the terrestrial coordinates
of the passpoints can be computed by scaling and rotating.
Compensation of accidental errors and calculation of the coordinates of the
pass-points.
From the known coordinates of the first model step after step the quan-
tities Xo, Yo and Z,, that fix the origin of the coordinates of each model, are
derivated, followed by the coordinates of the pass-point of each model. In the
last model closing errors in the terrestrial coordinates are found. These differ-
ences are due to only accidental errors and are generally small. In the case of
short bridges the method of repartition is therefore of little importance, one
selects therefore the most simple method: the linear repartition,
This method practically applied since three years for the determination of
passpoints for plotting on scale 1 : 40.000 gives satisfying results: mean error of
about 2 meters and maximal errors of 5—6 meter in position and altitude, in the
case of short strips (one prepared model on five, in average; corresponding with
bridges of 20—25 km).
Case of long bridges. Compensation of blocks.
In the case of long bridges the compensation of systematic errors is princi-
pally the same, but the closing errors in the coordinates can have important
values and the simple linear repartition would give no sufficient results for this
reason. This is due to the influence of the pseudo-accidental errors, (accidental
deformations of the perspective bundles) the causes of which can be differing;
these errors bring about the ruptures in the traversings (in scale or in orien-
tation).
In the case of a single strip the only remedy to trace these errors and to
correct for them is the special method of relative orientation of Prof. Poivilliers.
In the case of a block of several strips these errors appear clearly in the
comparison of the coordinates of common points of two strips that have been
calculated in each of the strips apart after compensation of the systematic
errors.
A method, based on the theory of least squares and permitting to take into