Photogrammetria, XIX, No. 6 
B. Instruments in which the major function can be described as the (analogue) compu 
tations of corrections to photographic positions of points and lines. 
This distinction is not a very sharp nor does it provide an efficient or effective way of 
classifying instruments. It is, however, usefull because the projective transformation is a 
function common to many types of instruments (although not always the only analogous 
computation carried out by them) and therefore this function seems to warrant a separate 
treatment. 
In the next paragraphs we will deal, in a general sense, with these groups separately. 
II. 2. The 'projective transformation. 
II. 2.1. General. 
The common property of instruments which will be considered here is that of 
solving in one way or an other, equations related to a central-projection, which can be 
written in their well-known form: 
a^X + b^Y 4- C]Z + dj 
OgZ + b 3 Y + c 3 Z + d 3 
o^X + b 3 Y + c%Z + ¿2 
a 3 X + b 3 Y + c 3 Z + d 3 
where x and y are coordinates of points in a system connected to the plane of the photo 
graphs and X, Y and Z coordinates in the projection-space. 
The coefficients a, b, etc. are functions of the parameters involved, and for photogram- 
metric projections they are generally expressed in terms of the 9 elements of inner- and 
outer orientation of the projectors. However, these parameters are not necessarily equal 
or similar to those of the photograph at the moment of exposure. 
The test of ap instrument’s performance in the realisation of this projective-equation 
contains generally the following elements: 
1. The use of a grid plate in the place of the photographs in order to dispose automatically 
of a number of points with known coordinates x and y (including generally the assump 
tion that errors in those x and y coordinates are negligible). 
2. The setting of the orientation parameters on given values and the computation of 
expected values of X, Y and Z corresponding to those parameters. 
3. The measurement of X, Y and Z coordinates in the projection and their comparison 
with the expected values. 
4. The analyses of the differences between measured and expected values. 
According to the design of the instrument there will be differences in the practical 
application of the described procedure : 
A few items of major interest may be mentioned: 
a. Measurements are done for each projector separately or in a stereoscopic model. 
b. The nature of resultant information-digital (coordinates), graphical or both-affects 
the testing required. 
c. The projection-system of the instrument can be mechanical, optical, or optical- 
mechanical. In the latter cases special attention has to be paid to the influence of the 
distortion in the optical part. 
It will be clear that the arrangement and the number of measurements have to be 
adapted to the properties of the instrument. In this paper we will not attempt to give 
recommendations for every type of instrument separately since this would take us too far 
into details, but there are a few principles of general character that are worth to be con 
sidered in every case. 
x = 
V ~