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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
3.1 Cutting the planes 
All planes of the total set of detected roof planes and vertical 
wall planes created from the footprint are cut combinatively 
with each other, provided that the line of intersection is within a 
pre-specified minimum distance of the point cloud. This results 
in a potential huge amount of bounded faces, where all faces 
lying outside of the footprint are removed. 
3.2 Filtering faces 
The roof of the building is now represented by bounded faces, 
of which some are overlapping in the z-direction, typically 
when gable ends meet. Overlapping faces are removed if these 
are not represented by any points of the point cloud. If overlaps 
are still present, these faces are given probability priorities. 
  
Figure 6. Roof faces generated by cutting planes and filtering 
overlapping faces. The source point cloud is 
identical to that of figure 2. 
3.3 Removing degenerate parts of mesh 
When performing a weld operation on a mesh (connecting faces 
through edges), edges are only allowed to be connected to two 
faces — right and left. If an edge is bounding more than two 
faces, we call it a ^hot spot" edge. An example of such a hot 
spot is shown in figure 7, marked by a dashed line. 
By separating the mesh at the hotspot edge, two meshes are 
defined in figure 7. The face marked by the arrow defines the 
erroneous mesh which is excluded, and the other faces define 
the other mesh, which is then the true resulting mesh. 
Separate meshes can also be connected through a common 
vertex, which is then called a *hot spot" vertex. 
3.4 Fill holes in mesh 
Unfortunately, holes will appear in the mesh when removing 
degenerate parts. Filling holes is by no means trivial, but 
luckily it is a known discipline within Computational Geometry 
[Barequet et al., 1997]. 
3.5 Finalization 
In the final step of the reconstruction, all parallel adjacent faces 
are merged. Thereby faces might be concave, but the size of the 
BRep is reduced considerably. Furthermore, a RGB colour of a 
guaranteed “on the roof” spot is extracted from the ortho photo, 
and this colour code is added to the roof mesh. 
The resulting per building geometry is dumped in VRML 
format, of which there are standard loaders for various 
programming languages. 
4. RESULTS 
  
  
Figure 7. This mesh is erroneous, because the dashed edge is a 
hot spot edge connected to more than two faces.