The Method of T-Triangulation
T-triangulation is a procedure of plain triangulation from photographs, suitable for determining
points of minor control for the production of photoplans. In contrast to radial triangulation the
lengths of the polygon are measured in the photographs. The accuracy is greater than in radial
triangulation; for instruments are sufficient: stereomicrometer with reflecting stereoscope (Zeiss-
Aero topograph), a precise rule of glass and a goniometer by roll in the form of the »Strahl-
ordinator» (Ott). Differences of height and tilt influence the results in similiar manner as by the
radial triangulation.
The basis of the T-triangulation is the T-figure. Each T-figure whose foot coincides with the
principal point is a combination of distances with equal scales. If the T-figures are chosen according
to the following drawing in a sequence of photographs overlapping more than 50 % the scale
number M of the distance s' n “ ]) results from:
n—1, II
J ‘ J
S 23 S 34
Here J s[- •! and A q ( - signify the distance parallaxes in the photographs (measured by
stereomicrometer). The relations between parallaxes and distances are by any index 1:
¿j q(t i> t+1) — q(i+i).— q(i i)
In the formulas the upper indices in parentheses indicate the numbers of photographs, the lower
indices caracterize the distances in the photograph. If the number of photograph is replaced by an
apostrophe an approximate value for the distance in photograph is sufficient.
For calculating the polygon in the scale 1:M it is necessary to measure the angles at the
principal points. By means of 2 points of minor control the polygon can be calculated in definitive
coordinates.
M. Zarzycki (Canada) demande quel est le gain de précision de ce procédé par Discussion.
rapport à la triangulation radiale.
M. Sutor répond que pour un ruban de 4 clichés, les deux méthodes donnent
approximativement la même erreur moyenne quadratique, pour 9 clichés et 19
clichés respectivement sont les erreurs moyennes quadratiques de la triangula
tion radiale plus grande, notamment 30 % et 50 % resp. (utilisant un triangu-
lateur radiale).
Mr. Zarzycki asks about the gain in accuracy compared with normal radial triangulation.
Mr. Sutor answers that for a strip of 4 photographs the two methods give approximately the
same result, for 9 resp. 19 photographs the mean square errors of radial triangulation will be 30 %
resp. 50 % greater.
M. Buchholtz (Allemagne): »De la littérature russe je connais un procédé
semblable à la triangulation en T, la »photopolygonométrie», qui concerne aussi
la détermination analytique du cheminement polygonal donné par les points
radiaux d’une bande de clichés aériens. — Comme tels points radiaux on utilise
des »points nadiraux conditionnels» relatifs à une plaine de référence à peu près
horizontale. A l’aide d’un stéréocomparateur on mesure les angles et détermine
aussi — tout à fait indépendamment l’un de l’autre — les longueurs horizontales
des côtés du cheminement mentionné. Le procédé implique la connaissance des
altitudes sur le terrain des stations de prise, aussi de quelques éléments de l’ori
entation relative des clichés.
Mr. Buchholtz: From Russian literature I know a process, similar to the T triangulation, called
»photopolygonométrie» that concerns also the analytical determination of the polygon consisting of
the radial-centres of a strip of photographs. For these centres »conditionned nadir points» are used
with respect to a reference plane that is approximately horizontal. By means of a stereocomparator
the angles are measured and also — independent of each other — the horizontal distances of the