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THE "AERIAL"
TRIANGULATION AND THE PLOTTING
OF THE EXTERNAL WALLS OF THE COLISEUM IN ROME
Giuseppe Birardi
Dipartimento di Idraulica, Trasporti e Strade
dell'Università di Roma "La Sapienza" - Italy
ISPRS Commission V
ABSTRACT
A particular procedure of "aerial" triangulation on the external walls of the Coli-
seum is necessary to insert in an unique reference system their plotting.
A paper on this subject was presented at the 1989 CIPA Symposium in Rome, but it was
not published, due to the inactivity of the CIPA organisation. The scientific and ope-
rative setup of this aerial triangulation, based on the projective bundles approach, is
now reported here; it presents some interesting peculiarity, due to the variable ellip-
tic curvature of the wall. Its results, characterized by a sub-centimetric accuracy, a-
re also reported.
The procedure is then described to plot the whole wall on an unique reference plane,
using a dedicated cylindric reference system.
plotting is finally annexed.
A table with a consistent portion of the
The present research is a part of the PROGETTO COLOSSEO of the University of Rome.
KEY WORDS: Coliseum, Aerial Triangulation, Plotting.
1. - Foreword
In a paper presented at the XVI Congress
of the ISPRS in Kyoto [Birardi et a.,
19881, the general setup of the photogram-
metric survey of the Coliseum in Rome was
introduced. We stated what follows:
1.1 - The plants of the external Northern
wall El, and of the first internal Sout-
hern wall E2 are perfect ellipses (see Ta-
ble 1).
This assumption was based on the gra-
phical measurement of a number of points
on the external borders of the walls, ta-
ken from a good pre-existing aerophoto-
grammetric map, scale 1:500. With the
program ELLIPSE, based on "best fitting”
techiques, we obtained hence reliable va-
lues of the parameters of the said elli-
pses, and of the adjustment residuals.
Nevertheless, for a further confirma-
tion of this assumption we have recently
re-computed the best fitting ellipses u-
sing a good number of control points, de-
termined on the walls by conventional ter-
rain procedures. We report here below the
comparison between the two sets of parame-
ters (schedule 1).
The little differences between the pa-
rameters of El and E2 mainly depend on the
fact that the map measurements were done
on the external border of the higher cor-
nices, while the terrain measurements are
effected on control points however placed
on the walls.
Furthermore, the mean residual of the
terrain E2 ellipse are almost halved as to
the El; in fact the surface of the E2 wall
is devoid of capitals, cornices etc., whi-
le the El wall has plenty of them, on
which the control points were located.
What above fully confirms the elliptic
hypothesis. We hope that with this the ve-
xata guaestio of the form of the Coli-
seum's plant is finally defined.
1.2 - To get a plane representation of
the whole wall on an unique cartographic
plane, it is opportune to use a special
Schedule 1
Ellipse Adj. Maj.semiax Min.semiax Excentr. Perim. Mean adj.
pts A e^2 L residual
nr.) (m) (m) (m) (m)
El (map) 27 95.505 78.910 0.317 549.23 0.30
nr pterr.) 7 94.631 77.545 0.329 542.14 0.30
E2 (map) 34 80.681 63.844 0.374 455.53 0.38
(terr.) 45 80.162 63
