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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BS. Istanbul 2004 
  
  
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Figure 4. Composed building 
3.3.3 The successive steps of the process 
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3.3.3.1 Fusion of close points 
In a great number of cases, the 3D data contain "close" points 
(in fact, the same point with slightly different coordinates), 
which must be merged. This type of error can be really a trouble 
for building construction: two facets constituting a wall do not 
have a common edge (as it should be) but produce two 
superimposed edges. The space between both edges can be 
visible and disturbs the user, see Figure 5. 
  
1" 
Figure 5. "close" vertices instead of "merged 
To solve this problem, we set up a fusion method considering 
point neighborhoods. Two points meeting the following criteria 
arc automatically merged: 
e Both points are "close". 
e There is no edge between them. 
The difficulty consists in the definition of the concept of 
proximity between the points. If we had chosen a fixed distance 
criterion, applied with a cube or a sphere centered on the 
considered point, the resulting geometry modification wouldn't 
be known a priori. The criterion we chose is intended to 
preserve the initial geometry by eliminating the duplicated 
points. To avoid geometry modification. we chose an adaptive 
criterion. We consider a sphere of influence whose center is the 
given point. The problem is now to calculate the ray of this 
sphere of influence: 
e For each vertex of the model we calculate the length of 
all edges using it, : 
e The ray is calculated using the minimal length edge by 
applying a percentage of reduction, for example 5% of its 
shortest edge. 
Considering two points, “A” and “B”, if “A” belongs to the 
sphere of “B” and “B” belongs to the sphere of “A”, then both 
points are merged. 
Obviously the triangles defined by a merged point are updated. 
After this phase, all the degenerated triangles. it means non- 
made up exactly of 3 different points are deleted. 
3.3.3.2 Division into objects 
The available 3D data is not very often spatialized: the facets 
describing the objects are not organized in space. If we consider 
data source coming from CAD software, we can have data 
organized in a semantic way: facets are grouped by layers where 
the first one describes all the walls of the scene, another one all 
the roofs, etc. 
In order to optimize all the necessary processing, it is important 
to increase high-level information with special specific tiling. 
For this reason we organize the available scene in facet groups, 
which will constitute our basic working objects for all next 
processes. This group definition only considers the connexity of 
the final objects: for all facets constituting an object, there is at 
least another facet of the object sharing with it a vertex or an 
edge. 
  
  
  
  
  
  
  
  
  
Figure 6. Object example 
  
   
  
   
  
   
   
   
   
   
  
   
    
  
  
  
  
  
  
  
  
  
  
  
   
  
  
   
    
  
  
    
   
   
   
   
   
   
   
  
  
  
  
   
  
  
  
  
  
  
  
    
  
   
  
   
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