The Tower of the Winds (Athens) - Restitution and Visualization 
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3.1 Initial data 
Outline with the approximate position of the station points of frames taking (approximates values of the external orientation 
parameters). 
- 8 tie points of well-known coordinates. (In each frame we are identified around 4 tie points). 
Pass points -around 10 points by frame- that complement the support. 
A coordinated system has been chosen with the plane parallel XZ to one of the faces. This way, the opposed face is parallel also to 
this plane, other tw o are parallel to the plane YZ and the other ones four, two at two parallel to the diagonal planes. The election of 
this system simplifies in great measure the restitution over plane elements, defining on the frames the position of the work planes, 
being able to restore on isolated frames. 
3.2 Orientation 
Starting from the internal orientation of each frame (distortions, crossings, main point) and of the approximate values of the external 
orientation parameters, the position and turns of each taking are calculated by resection. The model is formed by intersection and the 
pass point coordinated are calculated. Using the residuals of the used control points is deduced that they are adjusted exactly to the 
points pointed out in the frames, with what the supposition of the perfect octagonality of the plant is demostrated. 
Accepted the residuals of the control points, the adjustment bundle module compensates the whole cloud of points. In this case the 
first and last frames are coincident, for what the adjustment has a good compensation. The typical deviations, the errors means in 
X,Y,Z and the root mean square of unit weight give an idea of the precisions of the work. 
3.3 Restitution 
By means of the points and linestrings restitution in 3D, they are identified in successive layers the seat despieces, edges, cornice 
lines, as well as the most significant pathologies that the step of the time has left on the walls, like breaks, perforations, cracks and 
fissures, stains and erosions on the marble, etc. 
The main edges have been obtained by means of linestrings in 3D, with identification of their points in at least three frames, to obtain 
good intersections of epipolar lines. 
By means of pointing and definition of planes (parallel to the system of coordinated or in oblique addresses to 45 degrees) you can 
restitute on isolated frames, always on the surface of the defined plane. 
3.4 Rectification 
Each one of the sides of the octagonal prism has been rectified to obtain an orthophotomap to scale of the canvas of corresponding 
facade 6 . On these images, the relief of the frieze has been digitized, even with the error margin that supposes not being in the plane of 
the seat. - The restitution without vision in relief makes very difficult the work has more than enough non lineal contours - 
3.5 Edition 
The group of DXF files, of the restitution and digitalitation has been imported to Autocad VI4, to proceed to the termination and 
edition of the model in 3D. Mold details that were not identified correctly in the frames have taken their geometry of classic 
architecture treaties, incorporating them to the metric one that was obtained in our restitution. The base of steps on which the tower 
rises is not identified well in some frames and it has been completed starting from punctual determinations that have left connecting 
by means of segments. 
3.6 3D Viewer 
This viewer that the authors presented the last month of July of 2000 in a Congress of Mathematics applied in Athens, allows the 
visualization in 3D, of the model obtained by means of some simple glasses of red-green crystals (for its vision in white and black) or 
with active glasses (for its vision in color). It allows equally to move on the model and to obtain metric information of the point that 
points out the cursor. 
The oriented images of the tower have been converted to epipolar geometry to locate them in the position of the normal case so that 
the model in 3D is formed correctly. It can be observed this way a model 3D of The Tower of the Winds, not virtual, but real, starting 
from the work frames. If we had more frames and taken from in circle form around the monument you could generate a visit in 3D 
around our tower. The densificación of models would minimize the optic jump that is perceived between a model and the following 
one. 
Notes: 
J.Travlos. “Bildlexicon zur Topographie des antiken Athen. Verlag Ernst Wasmuth Tübingen. Berlin 1970 pp 281-288. 
( Rollei 35 metric 24x36mm k=41.91mm and reseau of 5x7 crosses 
Film KODAK Tecnical Pan, developer KODAK Technidol. 
J Tavlos op.cit.pp281 
6 Greece (Athens & the Mainland) 1997 Dorling Kindersley London 1997 
For the rectification we have used the programm PICTRAN (Technet)