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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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