3D MODELING AND REPRESENTATION OF “IDEAL CITY” 
PAINTED BY PIERO DELLA FRANCESCA 
Tomomasa SAEGUSA' ; Hirofumi CHIKATSU 
Tokyo Denki University, Department of Civil and Environmental Engineering, 
350-0394 Hatoyama Saitama, Japan 
saegusa@chikatsu-lab.g.dendai.ac.jp, chikatsu@g.dendai.ac.jp 
Commission Youth Forum 
KEY WORDS: Cultural Heritage, City, Modeling, Representation, Virtual Reality, Visualization, Geometry 
ABSTRACT: 
Recently, digital archives for cultural heritage or arts and crafts has received attention from possibility that people can appreciate or 
experience the archaeological objects, the past space or arts and crafts through the computer at any time and without going to the 
museum or the spot. In particular, 3D reconstruction and visualization of the lost objects or past word using antique maps or pictures 
have been receiving more attention since reconstructed 3D world gives important information for understanding those days. 
In these circumstances, 3D reconstruction for picture was investigated using “Ideal City” painted by Piero della Francesca at 1475 in 
this paper. 
1. INTRODUCTION 
3D reconstruction and visualization of the lost objects or past 
word using antique maps or pictures have been receiving more 
attention since reconstructed 3D world gives important 
information for understanding those days. 
From these viewpoint, 3D reconstruction of historical city 
Kawagoe where locate in Saitama Japan, and Palatitsa palace 
where was the residence of great Alexander’s father were 
investigated using antique maps and surveying maps by the 
authors (Sakamoto & Chikatsu, 2002, Suzuki & Chikatsu, 
2003). 
Similarly, 3D reconstruction of painted world as picture is 
interesting issue. With this motive, 3D reconstruction “Ideal 
City” painted by Piero della Francesca at 1475 was investigated. 
Ideal City was painted as ideal urban in those days using 
perspective geometry. 3D reconstruction using 
photogrammetric geometry, and visualization and landscape 
animation for the “Ideal City” are demonstrated in this paper. 
    
Figure |. 
153 
“Ideal City” 
2. PERSPECTIVE PROJECTION METHOD 
Piero della Francesca was famous Italian painter during 
Renaissance period but also he was a famous painter based on 
perspective geometry. Figure 1 shows “Ideal City” which was 
painted based on the perspective projection. 
The perspective projection is basic technique for expressing 3- 
dimensional object in 2-dimensional plane, and the method 
which was established in Italy in the 15th century is used in CG 
or architectural Perth. Figure 2 shows the concept of the 
perspective projection, and the basic points for the perspective 
projection are as follows. The scale and the object position are 
changed by the distance and the angle from the eye point, and 
the horizontal line is drawn as the straight line to show the 
height of the eye point. Moreover, even if the position of the 
eye point is changed, the horizontal line is drawn in the height 
of the eye point. 
There are some perspective method depend on number of the 
eye points, but the “Ideal city” painted by the one point 
perspective projection, and Figure 2 shows also the concept of 
the one point perspective projection. 
  
  
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