18 ANALYTICAL AERIAL TRIANGULATION, SCHUT 
triangulation with respect to an arbitrary coordinate system. In this case the six orien- 
tation elements of the first photograph will be chosen arbitrarily. The first model will 
then be obtained in both procedures by establishing the relative orientation of the second 
photograph from the condition that corresponding rays must intersect. An arbitrary 
scale will be assumed by assigning an arbitrary value to the base or to one of the base 
components of the first model. 
A transformation of the strip coordinates to the ground control system is then nec- 
essary. Leaving out of consideration a transformation which includes deformation of the 
strip by adjustment to redundant ground eontrol or with other extraneous data, the 
transformation consists of rotation, sealing and translation of the strip. 
This transformation is possible if three ground control points of which all three 
coordinates are known occur in the first photograph. This makes absolute orientation of 
this photograph possible and thus rotation and shift of the strip. For scaling at least one 
such point must occur in the second photograph. It is evident that in this case it is pos- 
sible to triangulate the strip directly in the ground control system. This is actually the 
practice in contemporary applications of the Herget Method. If more than one ground 
control point occurs in the second photograph it is possible to employ two or more of these 
points in the orientation of that photograph. However, in the second triangulation pro- 
cedure this is extremely undesirable. Identification errors will then affect the relative 
orientation of the photograph and, consequently, those of all following photographs. 
The transformation is possible also if the ground control occurs in different models. 
Very often not enough control will occur in any one photograph or model to enable this 
to be oriented separately. In this case, which may be expected to occur most often in 
practice, triangulation of the strip with respect to an arbitrary coordinate system is the 
only possibility. 
14. The coordinate system in which the ground control points are given will be an 
orthogonal three-dimensional system. Possible choices are: 
1. a geocentric system, 
2. a local system with its origin in or near the arca of the strip, with one of its axes 
approximately vertical and with a known relation to a geocentric system, and 
3. a map coordinate system consisting of plane map coordinates and terrain heights. 
Since map coordinates of the measured points are required ultimately, the choice of 
a map coordinate system is the most natural one. Local coordinates must be transformed 
to geocentric coordinates and geocentric coordinates must be converted to latitude, longi- 
tude and height above a reference surface. Latitude and longitude must in turn be con- 
verted to map coordinates. 
For long strips a local or geocentric system is often advocated. These systems have 
the advantage that neither earth curvature nor the use of different map projections for 
different parts of the strip causes complications. However, besides requiring the labo- 
rious conversion via latitude and longitude they have a second disadvantage. Very often 
either the plane position or the height of a control point is not known. Use of such points 
in a geocentric or local system causes complications. As yet therefore applications of the 
Herget Method have been confined to the case where all three coordinates of all control 
points are known. 
Because of these disadvantages of geocentric and local systems the author at the 
National Research Council of Canada has chosen the map coordinate system as the sys- 
tem in which to give the coordinates of the ground control points. 
The use of this system brings with it its own complications. In the first place the 
strip will follow the curvature of the earth while the map is a plane representation. 
Therefore the strip must be corrected for earth curvature either before transformation 
to the map coordinate system or during a direct computation in this system. 
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