International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
done. In order to present a certain level of detail, the tree has to 
be traversed down to the given scale level. 
AF.c 
EF. 0 
  
BC.O.. CEd 
AN 
A x 
/ N 
CD. 0 DE 0 
Figure 2: Original line (left) and corresponding BLG-tree 
(right); the scale levels are indicated in the nodes of 
the tree. At the leaves, the scale levels are zero. 
For the generation of the BLG-structure, the whole tree has to 
be generated in order to give the full zooming from coarse to 
fine. The transformation into the SO's is straightforward (confer 
Table 1): Starting point is a new line which appears at a certain 
scale level EPS, that corresponds to the length of the line sar. 
The line is generated by creating point 0 at position A (NPR), 
duplicating this point (DV) and moving it to the position F by 
increments dx4r. dyar. (MV). At scale level c a new point is 
inserted (EPS c). This is accomplished by duplicating point A 
(i.e. point 0 in the internal number scheme) and moving it to 
position c by increments dxac, dyac, All this information IS 
directly coded in the tree. The only issue is an appropriate 
sequencing of the insertion of the points, taking the respective 
scale levels of the nodes into account. 
   
pes 
  
gure 3: Screenshots visualizing increasing refinement of the 
Fig 
polygon-visualization (from top left to lower right). 
The following Figure 4 shows that the Douglas-Peuker 
algorithm is not appropriate for the generalization of structured 
objects such as buildings. Therefore, in the next section, an 
algorithm for building generalization and the corresponding 
decomposition into SO's is presented. 
    
   
    
    
Tim eee 
A NN, at 2 t Let ue 
Figure 4: Sequence of images of using DP-algorithm to buildin 
generalization — which is obviously not suited for 
the generalization of such structured objects. 
e 
e 
5.2 Building simplification 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Table 2: Coding Douglas-Peuker line simplification. 
Figure 3 presents some screenshots of the successive refinement 
of polygons using the SO-coding. The iterative refinement is 
clearly visible; the user can control the level of detail with the 
slider below. Furthermore, the transmission is organized in a 
way that only data in the current view will be loaded and 
refined. 
  
  
  
pov Create new object Building simplification is a special case of a point reduction 
EPS $1055) scale level EPS — distance method, where the specific properties of these objects are taken 
between points A and F into account. In this case the point reduction is more a structure 
NER RA YA Create point 0 with reduction, as properties like parallelism and rectangularity have 
coordinates XA and yA to be respected in the algorithm. Here, we used a method that 
Dv 0 Duplicate this point -> create analyzes the shape of the building and defines appropriate 
point 1 methods to eliminate too small parts of the ground plan, i.e. too 
MV 1 (xF-xA) (yF-yÀ) Move point 1 by dx and dy -> short facade elements (see [Sester 2000]). Three different kinds 
move it to point F of structures can be identified, for which appropriate reduction 
EPS c New event at distance c methods are defined: extrusion or intrusion, offset, and corner 
DV 0 Create new point after point 0 (see Figure 5). 
by duplicating point 0 S, 
MV 1 (xC-xA) (yC-yA) Move this point by dx/dy to Sn+t ouf 
point C Ses. edu Sa uu 
| Sp+2 | $2 E [23 ] 
Sn-2 | | Sn+2 | | 
| Sn+1 
c) 
offset, 
Elimination of short facade sn: 
intrusion/extrusion and corner. 
The decomposition of the changes in terms of SO's is 
straightforward. For the example of the offset it is the 
following: 
An offset consisting of 4 points is replaced by a straight line 
consisting of 2 points (see Figure 5a). The reduction process — 
which is done when eliminating or generalization this structure 
— extends the longest edge adjacent to the short edge s,, in this 
case it is line s... A new point is created at the intersection of 
the extended line and the predecessors predecessor line (in this 
case between line s,,, and line s,;). In order to code this 
process in terms of SO's, it has to be inverted, i.e. we start from 
the end situation with one line between points | and 4, then 
Figure 5: 
1296 
     
  
Internatic 
insert po 
duplicate 
3 new to 
EGO for ; 
In a simil 
two even 
Sester, 20 
presentati: 
(compare 
algorithm 
larger are: 
    
Figure 6: ] 
Fieure 7: T 
( 
5.3 Typific 
Typification 
new group \ 
occur betw 
eliminated 2 
terms of EG 
emerges. Th 
5.4 Displac 
The coding 
very simple,