topography
Or principal
1etres for x
y country I
or of about
3.5 metres.
hese errors
three cases
or x and y;
in x and y
to know in
purable one
refers to a
; in x and y
ngth of the
point trian-
or y 0.041
ation these
0 promille,
I assumed
en minutes
y, Is rather
e would be
eveloped a
DE
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.