because, the problem of crossing bridges (as in 
Morton order) is completely absent in row 
order. Also, the analysis required in 
determining which possible edges of the query 
window to search for the entry point is not 
necessary for orthogonal windows, since the 
entry point is always on the west edge of the 
window. With the row order, the search time 
does not seem to depend on the location of the 
window within the application space. It only 
depends on the magnitude of the window. 
  
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10| 18 17] 24 25 
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18119126127 
00 01 10 11 
: 16 17 24 25 
X 21-31 14 11 
0! 1|.8! 9 
  
  
(a) Morton Codes of 
3-Dimensional Space 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
layer 4 
545516216 
50191 |98|»2 [52 53]60]61 
ZZ |23|30|31||48|49|56/|57 eer ^ 
34| 35 | 42| 43 
oats 36 |37 | 44145 
6 | 7 |14|15||32| 33 40 41 
layer 3 
4.5 j12 13 
layer 2 
layer 1 
(b) The Layered Information of 
3-Dimensional Block 
  
  
Figure 2: Morton Ordering of a 3-Dimensional Block 
  
Figure 3: Coding in Row Order 
would seem to be less complex and more 
efficient than that using Morton order. For one 
thing, there would be no need for forming 
bounding rectangles, thereby eliminating the 
oversearches and possible inaccuracies which 
would otherwise be the case. 
The properties of row order also seem to enable 
better opitimization for rotated and irregular 
windows. Since the row codes are always 
sorted in increasing y, for any given layer, and 
the layers are also sorted in increasing 
dimensions, a search algorithm using row order 
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