1 
The Future of Radial Triangulation | COMM ISS] 
Appendix to the 
by R. ROELOFS, Delft, Netherlands. PHOTOGRAMM 
   
   
The imposing development of instruments, methods and applications of spatial trian- 
gulation in the last twenty years has been accompanied by a decrease of int 
analytical radial triangulation, which, before and during the war, w 
of countries with considerable success. 
erest in the 
as applied in a number 
Various reasons can be given for this phenomenon; one of them is undo 
preference to instrumental methods, i.e. procedures which reconstruct more or 
ously the geometrical characteristics of the photo-flight by means of a 
ment, to give results which need only relatively little computational 
? 
In the present -period however, where an ever 
ubtedly the 
less rigor- 
plotting instru- 
working up. 
growing interest is shown in analytical 
methods of spatial triangulation, applying modern punch-card or electronic computing 
machines, this aspect of preference is fading away. The development of these machines 
and their introduction into photogrammetric laboratories for computing spatial triangula- 
tion, highly favours the possibility of their use for radial triangulation equally. Meanwhile, 
it should be realized that for analytical radial triangulation the availability of modern 
computers is not a ‘“‘conditio sine qua non” as it practically is for analytical spatial tri- 
angulation, the computations being less complicated. 
No doubt was ever raised about the high internal accuracy of radial triangulation ; 
observations are just elementary x- and y-parallax observations, all adjustments being 
made numerically; radial lens distortion and regular film distortion do not play any role; 
the instrument, the radial triangulator, is simple in principle and accurate. 
As to the external accuracy, radial triangulation has always been reproached with 
the occurrence of systematic errors in the directions or angles measured, due to inclination 
of the camera and non-flatness of the terrain. Many authors in former and recent years 
[1-6] have dealt with these errors, but most of them restrict themselves to studying the 
errors in the directions measured. 
It is much more important however to study the syste 
of measured directions which propagate and accumulate 
graphs: the scale transfer and the azimuth transfer. 
The author has made such a study and reference is made to the appendices to this 
paper which give the derivation of formulae. 
Naming the distance between the radial centres of two consecutive photographs a 
base, then the scale trans 
sfer is defined as the proportion between two adjacent bases, 
while the azimuth transfer is the angle between them. 
The accuracy of scale- and azimuth transfer was studied for tw 
the most important in practice: 
matic errors in those functions 
through the whole strip of photo- 
O cases, which are 
l principal point triangulation (radial centres in the principal points of the photo- 
graphs) 
2. nadir point triangulation (radial centres in the nadir points of the photographs). 
For principal point triangulation the systematic errors Ap and Aa in scale- and 
azimuth transfer were expressed as functions of the camera- and groundinclinations. 
(Appendix B, formulae (10) and (11). 
In nadir point triangulation the systematic error in the direction of a radial line is 
a function of the camera inclination only. If this inclination is known, the error can be 
tomputed and eliminated by applying the opposite value as a correction to the direction 
Measured. This correction being not however errorless, due to the camera-inclination 
being known with limited accuracy, the corrected direction is not errorless either. The 
standard errors mg and m, in scale- and azimuth transfer thus generated, were expressed