with respect to 
mown and an 
fy the result of 
iat one that has 
h starting from 
| smaller angle 
jints, an affine 
naps have been 
  
Balletti, Caterina 
  
1.1 Applications 
1.1.1 Perspective views 
The study presented has concentrated primarily one the perspective views, which, if on the on hand, these have the 
advantage of being easily understandable in so far as the perspective is among the methods of representation which is 
most widespread, on the other hand, it is in fact, not measurable, if not by resorting to tricks which implicate a deep 
understanding of the descriptive geometry. The choice to use the perspective views of Venice by Jacopo de^ Barbari 
was motivated not only by celebratory, but especially for the geometric and cartographic characteristics of this map that 
represents the most exciting example of the new method of representation of the city based on perspectives. For the 
actual reference cartography for referencing, the photoplane of Venice was chosen. The idea that the perspective 
construction of the view might have been realised beginning with a plan and using elevations is fascinating for those 
involved in cartography because it presupposes the existence of a survey of the city or at least, given the particular 
character of the urban structure of Venice, of a series of reference points probably positioned in bell towers and 
surveyed using triangulation or a polar coordinates. 
  
  
  
  
  
  
figure3. The perspective view of Venice of Jacopo de' Barbari 
The studies have been addressed to evaluating the shifting of the view with respect to a "correct" geometry. 
In the study of the view, the planimetric part was separated from the altimetric part, so that the information regarding 
the elevations were studied and evaluated separately. Even considering the view as a perspective construction based on 
geometric data surveyed directly or extracted from previous charts, the data on the elevations would result in not being 
easily worked with together with the planimetric data. 
the view of de" Barbari, relative to plane of the attachment of the buildings to the ground, of the canal side walkways 
and of the canals themselves, can be considered as the transformation of a planimetry of the city. Or rather, it is 
possible to obtain a view which corresponds geometrically to the city in the 1500's, taking an orthogonal projection of 
the city and modifying it according to a plane transformation. 
Among the various applicable and presented transformations (conform, polynomial, affine) the projective 
transformation with eight parameters has been chosen. This transformation is equal to the central projection of one 
plane on another, that is, in our case, to the placing in prospective of a planimetry. From this application, it was possible 
to evaluate the shifting of the view of Jacopo de' Barbari from a rigorous central projection. 
Superimposing a regular grid to the photoplane of Venice and mapping it onto the view through a transformation to 
finite elements, a representation of the current city of Venice is obtained with the geometric characteristics of the 1500s 
produced work. From the comparison with the correct prospective of the same photoplane (previously obtained from 
the projective transformation) the modifications by the author can then be seen. 
In an analogous way, it was possible to reconstruct the planimetric image of Venice from the 1500's, or rather, by 
mapping the view onto the photoplane. 
From the combined application of the transformation to finite elements and of the projective transformation, the 
elaborations have been realised which have led to modify the view, returning it, for the planimetric part, to a correct 
central projection. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 33