nbul 2004 
yundary— 
rof TTC 
following 
ICTs (c3, 
s with 
iotemporal 
ts With 
ion rejects 
e same as 
joundary- 
ects With 
reate ZTCs 
a7), [ICS 
WN BWW 
oq 
SAD AMID 
set 
ES NUT, n 7i 
NR es BROS 
M cS 
ORORBOROBMOMOMONM 
; — = = 
NN HNHNNS 
ooo090 
++ À 
SSNS 
ects with 
intersects 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. 
5.1.6 Interior of TTC Intersects With Boundary-Interior 
of TTC', and Boundary of TTC Intersects With Boundary 
of TTC' (TT-13): The boundaries of TTC 1 and 2 are their 
OTC. This can be considered as OTC-OTC intersections, 
where OTCs can intersect in many ways. Three cases are 
illustrated here. 
[a] Boundary of OTC intersects with interior of OTC (Figure 
6[a]). 
Kill TTC (1) and TCT (c2). Create OTC (a2), TTCs (2 and 
3), and TCTs (c3, c4, and c5). 
TCT c2 is replaced by c3 because the co-boundary of OTC (a7) 
is changed to 2 (at time T2) from 1 (at time T1). 
[b] Interior of OTC intersects with interior of OTC (Figure 
6[b]). 
Kill TTC (1), OTC (a1), and TCTs (cl and c2). Create ZTC 
(n2), OTCs (a2, a3, and a4), TTCs (2 and 3), and TCTs 
(c3, 64... .c12). 
[c] Both boundary and interior of OTC intersect each other 
(Figure 6[c]). 
Kill TTC (1), OTC (al), and TCTs (c1 and c2). Create ZTC 
(n2 and n3), OTCs (a2, a3. a4, and a5), TTCs (2 and 3), 
and TCTs(c3, c4,..., 018). 
These examples show that a different number of TCTs are 
generated depending on the geometric configurations of the 
temporal cells, although topologically they are all the same. 
c0 4 3. 14. 5 
c2 (1, 1,0, T1, * 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
S €i (1 1.11 12) e113 
  
1 5 , 
13.11.12) c1 (1, 1, 1, T1, T2) €20,10, T1, T2) c12í3. 5 2 x s 
c2(1 1.0 T1, T2) c2 it, 1,0. T1. T2) 63(2.2 0,72.) - c13(2,5.0.72.7 
8.1.0727 (1.2. 0, T2. *) 04(2.2.3.12 5 c4(0,52 T2 * 
080.1213, (1.2.2, T2. ") €5(.2.0.2 "1 — ci5(2.4,5, T2, ) 
c5 2,3 12.5 3,012, *) 080.2 3.72.7 — c16(2,4,2. T2. 7) 
61.2.2 13.7 3,212.) e7(1,3.0.12 °)  17(24372 7 
ET = m ) c8 (1,3, 3, T2. 9 c18 (3, 4, 2, T2, *) 
3.12.7) £9.(3.3.0. 12.5 
c10 (3.3.3. T2. *) 
[a] [b] [cl 
Figure 6. Create TTC: Interior of TTC intersects with 
boundary-interior of TTC", and boundary of TTC intersects 
with boundary of TTC. 
5.1.7 Boundary of TTC Intersects With Boundary- 
Interior of TT 
TTC' (TT-14): This is similar to the previous case (TT-13), 
except the TTC at time T1 is not killed (Figure 7). 
Istanbul 2004 
  
e 
  
  
  
  
  
  
  
  
c3 (5, 1.2, T2 
2 €4 (1.1, 1, T2, *) 
c5(1.3.0. T2.) 
c1(1.1,0, T1 T2) mn." 0403225 
£21 1.1, T1. T2 5 ! 
e341 1.2, 72:0 ) 
c4(1 1.1.1727) 3 
€5(1.2.0, T2. *) 4 
€6 (1.2.2, T2. *) 
  
  
  
  
  
  
[a] 
Figure 7. Create TTC: Boundary of TTC intersects with 
boundary-interior of TTC, and interior of TTC intersects 
interior of TTC". 
5.2 TTC Kill Operator (4) 
While applying Kill operators to TTC, two scenarios can be 
realized. 
[a] The face of TTC is not shared by other TTCs or isolated 
TTCs (Figure 8[a]): 
Kill ZTC (nl), OTC (a/), TTC (1), and TCTs (c1 and c2). 
All the faces and TTC itself are killed. 
[b] The face of TTC is shared by another TTC (Figure 8[b]): 
Kill OTC (al), TCT (1), and TCTs (c5, c6, c7; c8, c10, and 
c12). 
All the faces are killed except common face(s). 
c! c? ni c 
  
  
  
  
  
  
  
  
  
  
  
  
   
  
  
e114 . T :1 > 1" €7(1.1,0, T1.) 
TD peregre © Jo OT 
ALLE ned 04 2 23 co (12.2 T1, 
dice (012j011 c10(1.2, 1, T1, 
Se od ) c1(,22T7.5 
m c n2 d )  e12(2 24,11 9 
+ 1 
c à c S13 0.71" c7 (1, 1, 0, T1, T2) 
12) c2 c2(1,3 2 Tic! 
: c312.3.0. T1 
RIS 2 83 04032117 
542, 1.0. T1 T2) 
4 cote 
£ €5i2, 1, 1, T1, T2) 
«3 
  
    
Figure 8. Kill TTC: [a] Isolated TTC and [b] face shared by 
another TTC. 
5.3 Delete I) and Reincarnate (T) Operators 
The Delete operator is based on the Kill operator (i.e., the same 
algorithm is applied to the Delete operator as applied to the Kill 
operator). Once the objects (n-tcells) are killed, they can be 
purged from the database. The Delete operator purges the 
database by permanently deleting n-teells instead of making 
them inactive. Therefore, these cells are no longer available for 
the Reincarnate operator. The Reincarnate operator turns an 
inactive cell into an active cell by replacing the upper bound 
(ST Until) of the time interval with a null value. One example 
is considered here to demonstrate the function of the 
Reincarnate operator. This operator is pragmatic in retroactive 
changes. For example, at time T1, there was one TTC (A); at 
time T2, two new TTCs (B and C) were created. The TTC (A) 
has becn killed because of the Create operation at time T2. 
Scenario | is shown in Figure 9. At time T3, it was realized that 
the TTCs (B and C) had been wrongly created (wrong 
configuration). Actually they have to be created in the fashion 
shown in scenario 2, which is the actual configuration (Figure