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SIGN CONVENTIONS IN PHOTOGRAMMETRY, SCHERMERHORN
We have in general three different coordinate systems:
a. terrain (survey or geodetic) coordinates;
b. model or machine coordinates;
c. plate coordinates.
The geodetic systems are different in different countries. Rosenfield [4] page 537 over-
looks that several European countries have the same geodetic system as the USA: X-
axis East and Y-axis North and Z up.
The proposal for the Stockholm resolution was not based on a relation with the
geodetic terrain system. It was only intended for the introduction of a right handed
system for the model as well as for the plate coordinates. Furthermore the title [5]
already shows that the proposal originated in particular from the desire to standardize
the formulae for numerical orientation in instruments. The considerations are related to
the practice in the plotting machines. Consequently the projection distance should be
represented in the simplest possible way. This is obtained with a coordinate zero point in
the left hand projection centre and with the positive Z-axis down.
In recent years, however, the numerical (analytical or digitized) treatment of photo-
grammetric problems, including in
particular that of aerial triangu-
lation, resulted in a more general
mathematical approach to these
problems. One consequence is that
we feel more free in the location of
the right handed systems we need
for models and images. Fig. 2 shows
an example. The zero point of the
plate coordinates is somewhere in
the negative. This corresponds with
normal practice in stereocompar-
ator measurements. The negative
cannot be centered with the preci-
sion of the coordinate measurement
itself. Therefore we read the coor-
dinates of the four fiducial marks
and in the computation we start
with the determination of x,y, and
of x,~x, ¥,~¥, Which values could
be introduced in the derivations as
x! and w,.
Ihe same consideration is ap-
plicable to the model coordinates
XYZ. It is not necessary to intro-
duce a system which has X, — Y,
Z, = 0. It is just as easy to use an arbitrary zero-point for instance in such a way
that all Z-values become positive. In case we need projection distances we can use
Xg — Xy — X9; Y, 7 Y, —Yq; Zy 7 Zg —Z,.
These formulae will automatically give us the proper sign of X,'Y,' Z,'. Whether
we assumed the Z-axes down or upward makes no difference. With the Stockholm con-
vention we have in the parallax formulae X,Y, Z,, in a system like in fig. 2 we have
X, Y, Z, and the sign of Z,' will automatically become negative. The assumption that
the zeropoint 0 is in the lefthand projection centre makes no other difference than that
Xp = X, etc. The change of the Z-axis by rotation of the system over 2008 about the X-
axis also leaves the final formulae for 4X, AY untouched.
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