International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
EH To merge rectangular bases, if two rectangular bases B; 
and B,, share the same auxiliary point, they can union as 
a new base represented as B,, €- Bj, U Bj. Because the 
auxiliary point set is created during rectangulation, these 
auxiliary points have to be removed. 
2 Remove roof surfaces that contain auxiliary points. 
3 In addition to merge roof points, if bases Bj, and B; 
belong to primitive roofs, consider linking the roof points 
in B, and B,, if they have the same height and identical 
x value or y value. For example, Fig 2g shows y, = y,2, 
where P,€B, and P,eB, ; hence line pp, 
indicates a roof outline. 
660 + 
655 
  
  
  
  
650 + 
  
  
0 | 1 À 1 1 1 L 1 1 1 À 
215 320 325 390-335 340 345. 3580 355 360: 365. 370 
Figure 2f). Primitive roofs reconstruction. 
B75 + 
B60 
655} 
  
  
  
650r 
645 + 
  
1 | 
s L 1 À 1 1 A | 1 J 
15 320. 325 330: 335 340: 345 350 355 3600 265 270 
Figure 2g). Roof merging. 
After merging rectangular bases and roof points, we have to 
combining polyhedral roof surfaces in 3-D space. Reconstruct 
roof surfaces to the base that merge in step 1. The assumption 
here is the number of lines connected from each roof ridge point 
to the base points is determined by |B,|/|P| (Figure 2h). In this 
example, the number of base points is six and the number of 
roof ridge points is three. Therefore each roof point connects to 
two base points. According to this assumption, we rearrange the 
polyhedral surfaces as Figure 2i. 
After combining primitive models together, the building can be 
completed by projecting the boundary outlines of roof to the 
556 
ground. Here, operators measure one footprint point of the 
building on the ground to indicate the height (Figure 2j). 
685r 
660 
675} 
670} 
665} 
660 + 
655 
  
  
  
  
  
640 1 1 1 À L 1 1 À i À J 
Ji5- 320.325. 330. 335-340. 345 350 355 360.365 370 
Figure 2h). Rearrange polyhedral surfaces 
B85r 
680 
675 + 
670r 
  
  
645 + 
  
  
540 1 1 1 1 1 J 1 | 1 1 J 
315 320 325 390 335 Ct 345 350 355. 300 305 370 
Figure 21). Roof with labeling. 
  
205 
tt 
200 o EN 
195 % 
(0 A S 
u^ RC 
M N 
670 EN 2e 
N SL 370 
640 320 
Figure 2j). Project roof to the ground. 
After reconstructing the roof completely, the topologic data 
structure of this roof is described in Table 1. The data structure 
gives information about surface shapes, positions and how they 
are joined together. This table stores the 3-D topologic 
relationships among the points, edges and the polygons. The 3- 
D object is composed of labeling basic units including points 
and edges (Figure 2i). In this table, polygons are described by a 
sequence of edges, and edges are represented by two points 
without sequence. Based on this table, the roof can be 
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