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3.5 Polyhedral 
Polyhedral is the part of the algorithm 
that uses the polygons the limit the 
contour of the object to construct the 
lateral polygons of the reconstructed 
shape. 
The feature of the polygonal routine that 
the lines are parallel to a side of a 
regular polygon let us compare the 
parallel lines of polygons in adjacent 
planes in order to link then in a 
quadrangle or in a triangle 
4. TEST 
4.1 Reconstructing a Lamp Shade 
The algorithm was tested reconstructing 
real lamp shade from four silhouettes 
taken from angle of 0, n/4, n/2 and 31/4 
rad 
The pre-processing digitalized the 
silhouettes in 127 x 127 pixel each and 
the reconstruction used all data. 
The reconstruction spend 10 minutes for 
the definition of the polygons and 3 
minutes for the polyhedral part in a PC/XT 
with mathematical co-processor. 
The silhouettes are shown in figure 3 and 
the reconstruction are shown in figure 4 
and 5. 
  
Figure 3 
5. CONCLUSIONS 
The algorithm introduced is easy to 
implement and the test showed that with 
approximations and the optimization, we 
can have good performance and good 
results. 
As mentioned before, the algorithm cannot 
reaonstruct concavities parallel to the 
image rays because the information is not 
contained in the silhouette image. The 
method can only reconstruct separate 
convex regions in the planes perpendicular 
to the rotational axis. 
  
  
  
  
  
  
  
  
  
339 
Figure 4. Reconstruction of the lamp shade 
after the definition of polygons. 
  
Figure 5. Complete reconstruction of the 
lamp shade.