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performed according to the presented solution, with the restriction however, 
that only such absolute given control. data are introduced as are necessary for 
a unique solution. The coordinates of the model thus obtained are then trans- 
formed in a second computational step by three translations, three rotations 
and a scaling factor in such a way that the sum of the squares of the residual 
distances between the model and all the given control coordinates becomes a 
minimum. Obviously, with such a method, the photogrammetrically obtained model 
. 18 being interpolated into the configurations of the given control coordinates. 
(Compare [3] ana [6] ) 
(b): Trend Conditional Equations ; 
Quite similar to the treatment of & metric conditional equation, it 
is possible to introduce & certain trend condition known to exist between the 
points to be triangul&áted, and which is mathematically expressed by & functional 
relation existing between the coordinates of such points. In a general sense, 
such conditional equations will resemble metric conditional equations, except 
that they will not necessarily have any absolutely giyen parameters. Moding 
on the mathematical character of a specific trend, the number of points involved 
in such a trend condition will vary. Correspondingly, the smallest possible | 
Subdivision in the process of establishing the final normal equation system by 
partitioning will be determined by the number of points combined by any one or 
several trend conditional equations. | 
E. A Solution for Triangulating Points not Included in the Least Squares 
Treatment for the Orientation Parameters 
Despite the possibility of incorporating any number of relative control 
points in the general analytical solution for a specific photogrammetric 
triangulation problem, it sometimes may be desirable to triangulate separately 
additional points of the model, Consequently, for those points, an independent 
coordinate determination becomes necessary. The positions of the corresponding 
rays are determined by the elements of orientation as obtained from an inde 
pendent preceding least squares adjustment and the corresponding plate measure- 
ments, It is obvious that these rays will not intersect due to unavoidable 
measuring errors. They must be made to intersect so that the sum of the squares 
of the corrections to be applied to the original plate measurements is a minimum. 
29