Commission II Invited paper 155 
Sign Conventions in Photogrammetry 
by W. SCHERMERHORN 
1.T.C., Delft. 
The Stockholm Congress of the I.S.P. adopted a resolution on sign conventions. The 
intention of this was to solve difficulties experienced in the understanding of various 
publications in which different coordinate systems and different notations are used. Al- 
though it was not very likely that the factories would be willing to change the more or 
less arbitrary choice of the positive sense of the elements of orientation in the existing 
instruments, the resolution was meant as an effort to influence industry at least as far 
as new constructions are concerned. 
The resolution recommends the use of a right-handed rectangular coordinate system 
with its origin at the left hand projection centre and the 
z-axis downward. 0' +X 
This is, as mentioned by Schut [1], a rather vague and 
incomplete resolution. It does not indicate anything about 
the signs of the rotations about the coordinate axis and 
nothing about the positive sense of the graduations of the 
base components in plotting instruments. 
The Stockholm Congress, however, preferred to stand- 
ardize not more than a minimum. The consequences of the Fig. 1. 
accepted right-handed system are, that the angles of rota- 
tion are counted clockwise and that the signs of the base components are determined by 
the signs of all coordinates, since these are nothing else but differences in coordinates of 
the exposure station. 
Although there was not so much discussion at Stockholm, it seems that Commission 
II wants to put the question again on its agenda. We must know, however, that it does 
not regard only the instruments, but that at present also the digital computations in 
photogrammetry are influenced by these problems. Consequently this problem should also 
be discussed in Commission III. The importance of the problem, however, must not be 
overestimated. I agree in this respect fully with Thompson’s second paragraph of [3]. 
Therefore I will not make strong recommendations for additional proposals or changes, 
but will only introduce here a few problems which were raised after 1956 and offer my 
views on them. 
The first is the attack of Thompson on the usual notations b,, b b, for the base 
components. This notation originates from the period before the use of aerial trian- 
gulation. At that time it was only the base as such which entered into the various 
derivations. That was correct, but the same notations were transferred to the aerial trian- 
gulation in space. Therefore Thompson is right in making objections and consequently 
he prefers some special coordinate notations for the exposure stations as centres of 
perspectivity. I believe, however, that also this gives some complications as soon as the 
differentials of the base components must be indicated. Furthermore, the use of the clas- 
sical notation is so widespread in photogrammetric literature that a change would create 
some confusion. We propose a slight modification which, in some cases has already been 
accepted: to write bw, by, bz instead of b,, b,, b,. In the sense of the proposal of Thomp- 
son we could use for the base components AX, — X, — X, ,, etc. It can be considered as 
an acceptable compromise to replace 4 by b and to use small characters instead of capitals 
as would be normal in the system of the model. In this way we arrive from b,, b,, b, via 
AX, AY, AZ (as should be applied to aerial triangulation in the sense of Thompson) to 
bx, by, bz, in order to remain close to the usual notations. 
+Z 
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