156 SIGN CONVENTIONS IN PHOTOGRAMMETRY, SCHERMERHORN
Regarding the rotations about the coordinate axis G. H. Rosenfield [4] raises the
question whether it would not be desirable to choose a primary and a secundary axis of
rotation. This is done in the plotting instruments resulting in the well-known angles of
orientation c, q, x. As Rosenfield states in the case of a photograph with a given orien-
tation, that means with a given value of the orientation matrix, we find different values
for w and ¢ in the matrices derived either with the X-axis or the Y-axis as primary
axis. It is evident that this is the same in the plotting instruments. There, however, we
normally can neglect this difference for near vertical photographs, as long as we are
dealing with differentials of these elements, for instance to compute the corrections to
the approximate values of these elements from the measurements of parallaxes. As soon
as we have convergent photography also the differentials are influenced by the choice
of the primary axis. In case we deal with absolute orientation, for instance if we wish
to impose the elements of absolute orientation as derived from a digital aerial trian-
gulation, to a plotting instrument, then even near-vertical photography requires the
choosing of a primary axis.
For digital triangulation there does not exist any preference between X- and Y-
axis. There exist, however, more plotting instruments with the X-axis as primary axis.
Therefore we propose to standardize on the X-axis as primary axis. We must realize,
however, that this is not convenient to terrestrial photogrammetry. Changing the Y- and
Z-axis there the rotation in azimuth should be the primary rotation which requires that
the Y-axis should be the primary axis. This is valid for the Zeiss Stereoplanigraph. Con-
sequently the transformation formulas, as far as the use in instruments is concerned
must be derived for both systems. The standardization on a primary X-axis is only in-
tended for the digital photogrammetry and can then in addition also be used for those
instruments which are designed with primary X-axis. We believe, however, that a
standardization of the primary axis is important, even more than that of the position of
the zero point and the direction of the Z-axis, on condition that we standardize on a
right handed system.
The subject which notwithstanding its limited importance gave rise to more discus-
sions than any other is about the direction of the Z-axis of the system. With my 1956
proposal I tried to remain as close as possible to the usual photogrammetric practice, also
in the instruments. In the instruments we distinguish between Z and H. The counter we
use for absolute orientation is a height counter and not a Z-counter. On the counter we
read the heights in the terrain with their zero in some reference plane. For the projec-
tion distance there exists a special Z-scale which counts in the opposite direction.
In particular those authors who object to the Stockholm resolution do not distinguish
between these two values in the proper way. Schut [2] on page 10 under 2a speaks about
the Z-readings which must be converted. Is he not thinking of height-readings since the
Z-scale is practically only read to determine a rough approximation of the model scale?
In which direction we take the positive Z is in this respect of no importance. In the case
of the Stockholm resolution we have: Height = H — Z, —Z (Z, = flying height over the
reference plane). In case we follow Schut and Rosenfield we have H Zo TZ.
There is not a great difference between the two cases from the point of view of the
relation between modelcoordinates and heights in the terrain.
More important however is that, since we use consequently a right handed system
for the image as well as for the model coordinates, the transformation formulae are in-
dependent of the position of these systems in space. Even for the parallax formulae we
obtain with Z upwards and down exactly the same equations. We can derive the formulae
for the case with Z up by realizing the opposite sign for Y, Z, y and K. Therefore more
important than the direction of the Z-axis, is that we standardize the primary axis,
because different primary axes yield different transformation formulae.
