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Commission III Paper presented by the I.T.C. 77 
On the Adjustment of Rhomboids in Radial Triangulation 
by F. ACKERMANN 
I. T.C., Delft. 
1. Introduction. 
In radial triangulation the rhomboid is the basie computational unit with which 
strips or blocks are built up. It is formed by the radial centres of three successive photo- 
graphs and the wing-points of the central photograph which are intersected from the 
radial centres (see Fig. 1). As the geometrical shape of a rhomboid is determined by 
angles only, and the determination of scale can be done at any subsequent stage of the 
computational procedure, considerations about scale need not be taken into account for 
studies concerned with single rhomboids. 
  
  
  
  
  
  
  
  
  
  
Fig. 1. The rhomboid. 
For the computation of a rhomboid, and all adjustment questions connected with it, 
one can start with the assumption that the ten directional observations, measured in 
groups from the radial centres A, B, and E, are available. The directions 5 and 7 are 
both the result of a mean of two single observations. It is convenient to assume equal 
weight for the ten directions. 
As a rhomboid is fixed by nine directions, the tenth observation presents a closing 
condition. Hence the computation of a rhomboid is basically an adjustment problem. The 
procedure of computation which is probably most in use, and which for instance is 
taught at the International Training Centre in Delft as standard method, is the rhomboid 
adjustment according to the method of least squares, based on the one condition which 
corresponds to the one superfluous observation. Other methods are possible and have 
been used, but are not considered further in this paper. 
The aforementioned condition equation, with which the directions of a rhomboid 
are adjusted, is of such a shape that logarithmic linearisation makes the computations 
relatively easy. However, this method as applied normally requires the use of loga- 
rithmic tables which elsewhere in photogrammetric and geodetic computations are 
increasingly being replaced by desk computing machines. This reason alone would make 
it desirable to study the possibilities of modernising the rhomboid adjustment and te 
adapt it to the computing facilities available nowadays.