Topographie et Patrimoine Culturel 
38 av. Georges Clemenceau, 77400 Lagny sur Marne, France 
Phone : +33-164-30-38-35, E-mail: contact@topo-patrimoine.com 
KEY WORDS: Orthophotography, Architectural Survey, Cylindrical Structures, Digital Elevation Model, Surface Unwrapping, 
Antique Tower, Mediaeval Castle 
Because we, surveyors, architects and archaeologists, are used to describing objects in planar projections (planimetry, elevation), 
most orthophoto software have been designed to change a quasi-central projection into a true orthographic projection. This kind of 
projection is not really suitable for cylindrical surfaces. 
To enable the complete study of rotund tower surfaces, a specific process has been designed. The idea is to use the nearest cylinder 
as the surface of projection. Thanks to a motorised reflectorless total station, an accurate 3D point cloud is scanned. These points are 
used to calculate the best cylinder of projection (vertical axis co-ordinates, radius) and interpolated to produce a digital model of the 
real surface. For each digital image, the photogrammetric equations are calculated, derived from control points identified on the 
photo. It's then easy to link the orthophoto cylindrical co-ordinates to the pixel co-ordinates of the image to rectify it. The rectified 
images are gathered to produce a general view of the surface, as if the tower were unwrapped on the sheet. 
It's now possible to undertake an accurate analysis of cylindrical monuments: stone arrangements, distribution of windows, doors or 
chimneys. Any orthographic view can be produced automatically by choosing a direction of projection. The digital model can be 
used to get geometrical data: accuracy of the tower building , shifting of the centre between different floors. This method has already 
been used for several surveys: the antique tower in the Laudun oppidum, in the south of France, and the towers of the Blandy-les- 
Tours castle, near Paris. 
1. A CYLINDRICAL SURFACE OF PROJECTION 
The production of a single orthophoto that allows complete coverage of a cylindrical tower requires the use of a specific surface of 
projection. This surface must be the nearest cylinder, which means that the distance between the real surface and the mathematical 
cylinder must be as small as possible. It defines a new cylindrical co-ordinate system for the cartographic representation. By 
assigning the angular distance along the cylinder perimeter to the horizontal axis, and the elevation height to the vertical axis, the 
surface is mathematically unwrapped to produce a complete orthographic view. 
Fig. 1 : Geometrical unwrapping of a cylindrical surface 
In order to obtain geometrical specification about the real surface, to know if a cylindrical projection can actually be used, and to 
acquire enough data to determine the best cylinder, a 3D point cloud is measured with a motorised reflectorless total station (Leica 
TCRM or Trimble stations). 
Measurement and processing 
The determination of a digital model can provide an accurate description of the real surface. First, an irregular 3D point cloud is 
measured, dense enough to give back information about the tower geometry and its local deformation. The cloud density varies with 
the surface state: around embossments, fissures and architectural elements, 3d points are closer than in more regular areas. 
Proceedings 18" International Symposium CIPA 2001 
Potsdam (Germany), September 18 - 21, 2001