B4. Istanbul 2004 
yundary relations. 
ces at time t. The 
+) cells incident 
poundary relations 
ps (ie, adjacency 
al objects can be 
ons between cells. 
encapsulated in a 
is an extension of 
cell tuple T is an 
vere any i-cell is 
a unique tuple-ID 
d TTC. Fach tuple 
zero or one TTC. 
encapsulates the 
mporal object. A 
me T oti € ST) 
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cell tuples to 
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d (re. static 
and 
system's state or the 
' operators calculate 
:o-boundary). These 
ITupleClass. On the 
tate of the system or 
'., creating, deleting, 
emporal GIS, three 
formed (ie. 
re associated 
TCellClass, 
create, 
with 
and 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
TwoTCellClass. Unlike in atemporal GIS, in a TGIS objects 
may die or be killed, but they remain in the database with a 
certain time stamp indicating their life span. As mentioned 
earlier, any n-tcell object can be born or can die. Therefore, 
four fundamental dynamic operators can be distinguished in 
spatiotemporal databases (i.e., Create, Kill, Reincarnate, or 
Delete [Destroy]). Thesc operators are associated with objects 
(ZTC, OTC, or TTC). In spatiotemporal databases, the Kill 
operation is different from the Delete operation, as the latter is 
merely a purge operation. Updating spatiotemporal objects is 
complex; any update operation affects the other objects, 
particularly in the unified approach. Any spatial change is the 
result of the creation (birth) and/or destruction (death) of an 
n-tcell. Kill is a protected operation, while the others are public 
or private. 
* The Create operator is equivalent to the usual insert 
operators. The task of this operator is to create a new 
object and/or update an existing object. This operator 
specifies the time stamp [start, *] of each spatial 
object, where the upper bound of the time interval is 
undefined (*). All objects with [start, *] time stamps 
are called active objects. 
e The Kill operator kills the spatiotemporal objects by 
defining the upper bound of the time interval. After 
being killed, objects are called inactive objects. These 
objects remain in the database only for the query 
purpose or Reincarnate operator. Therefore, the upper 
bound (*) is replaced by current system time. 
e The Delete operator permanently deletes the 
spatiotemporal objects from the database. Therefore, 
they are no longer available for any type of operation 
(static or dynamic). 
* The Reincarnate operator turns an inactive object 
into an active object by replacing the upper bound of 
the time interval to (*). 
5. OPERATORS FOR TWOTCELLCLASS 
  
5.1 Operation Create (Insertion of TTC) 
The Create operation for TTC is a recursive operation, starting 
from the insertion (creation) of the boundary of TTC (i.e., OTC 
and boundary of OTC, which is ZTC). This operation can be 
viewed from three perspectives (i.e., a TTC can intersect with 
ZTC, OTC, and TTC). The cases in which TTC intersects with 
TTC are discussed here; the other two cases (TTC-OTC and 
TTC-ZTC) are semisymmetric (because the geometry is the 
same, while the spatiotemporal topology is different) to the 
OTC-TTC and ZTC-TIC intersections. These cases are 
discussed earlier (Raza and Kainz, 2000a). 
Let TTC (A) and TTC' (B) be a TTC at time TI and T2, 
respectively. Using the point-set approach, a 2 x 2 intersection 
matrix can be constructed: 
CAndB' OAnm?B 
SAmÓeB ANB, 
Out of 16 possible intersections, only seven (TT 1, 7, 9, 10, 11, 
13, and 14) are valid, while the last one (16) is a 
nonintersection case and TT 11 and 12 are symmetric. 
TT = | 
\ 
1] GA intersects with cB 
7] “A intersects with AB 
9] B intersects with 7% 
10] 7A intersects with AB 
11] cA intersects with 8B and ?4 intersects with JB 
13] AB intersects with #94 and “4 intersects with B 
14] cA intersects with AB and % intersects with B 
Egenhofer (1993) derived binary topological relations between 
two regions using this approach. Figure 5 is a general 
illustration of TTC-TTC intersections; each intersection may 
have various combinations, some of which are associated with 
valid intersections and are discussed in the following sections. 
  
The aforementioned operators (Create, Kill, Delete, and 5.1.1 Boundary of TTC Intersects With Boundary of 
Reincarnate) are discussed and applied to the TTC in the TTC' (TT-1): Five combinations can be realized in this 
following section. intersection. 
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Figure 2. Create TTC: Boundary of TTC intersects with boundary of TTC.