International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
  
[a] Both TTCs intersect at ZTC (Figure 2[a]): 
Create OTC (a2). TTC (2), and TCTs (c3 and c4). 
[b] OTC of TTC (1) intersects with ZTC of TTC (2) (Figure 
2[b]): 
Kill OTC (al), TTC (1), and TCTs (cl and c2). Create ZTC 
(n2), OTCs (a2, a3. and ad), TTCs (2 and 3), and TCTs 
(£3, €4,. 612). 
[c] ZTC and OTC of TTC (1 and 2) intersect (Figure 2[c]): 
Kill OTC (a1), TTC (1), and TCTs (cl and c2). Create ZTC 
(n2), OTCs (a2, a3, and a4), TICs (2 and 3), and TCTs 
(c2, €3,..: 5014). 
[d 
— 
OTC of TTCs (1 and 2) intersects (Figure 2[d]): 
Kill OTC (al), TTC (1), and TCTs (cl and c2). Create 
ZTCs (n2 and n3), OTCs (a2. a3, a4, and a5), TTCs (2 and 
3), and TCTsi(c2,'c3,...., c18). 
— 
ZTC and OTC of TTCs (1 and 2) intersect (Figure 2[e]): 
Kill OTC (a/), TTC (1), and TCTs (cl and c2). Create ZTC 
(n2), OTCs (a2, a3. and a4), TTCs (2 and 3), and TCTs 
(c2, €3,... cl). 
[e 
The configuration formed in Figure 2[a], [b], [c]. [d], and [e] is 
called a 2-temporal complex (2-TC) or 2D spatiotemporal 
object (TSTO). A 2-TC is a collection such that each TTC in 
2-TC is connected through a common face. 
5.1.2 Interior of TTC Intersects With Boundary-Interior 
of TTC' (TT-7): When the interior of TTC (1) intersects with 
the boundary of TTC (2), then the following actions are taken 
(Figure 3): 
Kill TTC (1) and TCT (c2). Create ZTC (n2), OTC (a2), 
and TCTs (c3, c4, and c5). 
TCT c2 is replaced by c3, because the co-boundary of OTC 
(al) is changed while the OTC (al) remains unchanged. At 
time T1, the co-boundary of a/ was <0,1> and at time T2 it was 
changed to <0,2>. This is one of the advantages of the implicit 
topology storage approach. If the topology is stored in an 
implicit fashion, then the object also has to be updated in order 
to update the topology, because topology is associated with the 
spatial object (e.g., in ArcGIS® the co-boundary [left and right 
polygon] information is associated with arc). 
T1 T2 
cit 1,011.) 
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m 60,170, T1") 
e4€2 0; 1,1; T1, T2) 
03.1, 1.3, T2, * 
c4 (2,2, 3, T2. * 
98.2,2.2, 12, *) 
  
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— 
  
  
  
  
  
  
  
  
ET 
Figure 3. Create TTC: Interior of TTC intersects with 
boundary-interior of TTC". 
10 
5.1.3 Interior of TTC' Intersects With Boundary- 
Interior of TTC (TT-9): When the boundary-interior of TTC 
(1) intersects with the interior of TTC (2), then the following 
actions are taken (Figure 4): 
Kill TCT (c2). Create ZTC (n2), OTC (a2). and TCTs (c3, 
c4, and c5). 
T1 T2 
  
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2 c4(272. 2; 32, 
c5(2.2,0. T2.) 
a1 
  
  
  
a2 
Figure 4. Create TTC: Interior of TTC' intersects with 
boundary-interior of TTC. 
In this case, TTC (1) remains unchanged but its spatiotemporal 
topology is adjusted (i.e., TCT c2 is replaced by c3). 
5.1.4 Boundary-Interior of TTC Intersects With 
Boundary-Interior of TTC' (TT-10): The operation rejects 
the TTC (2) because this cell is identical or the same as 
TTC (0 
5.1.5 Boundary of TTC Intersects With Boundary- 
Interior of TTC', and Interior of TTC Intersects With 
Boundary of TTC' (TT-11): 
Kill TTC (1), OTC (al), and TCT (cl and c2). Create ZTCs 
(n2, n3, and n4), OTCs (a2, a3, a4, a5. a6, and a7), TTCs 
(2, 3, and 4), and TCTSs (c3, c4...... c26). 
The process is shown in Figure 5. 
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tt 
  
  
  
  
  
  
c1 (1, 1, 3. T1, T2) c20|c19 ees e 
c2 (4. 1, 0, T4, T2) 
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c4 (1. 2, 0. T2. 7) 
c5 (3, 2, 2, T2. *) c25 ( 
c6 (3. 2, 0. T2, *) 
SSNNNNNNNN 
  
  
  
dod A A= 
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Figure 5. Create TTC: Boundary of TTC intersects with 
boundary-interior of TTC', and interior of TTC intersects 
with boundary of TTC". 
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