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Title
The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics
Author
Chen, Jun

ISPRS, Vol.34, Part 2W2, "Dynamic and Multi-Dimensional GIS’’, Bangkok, May 23-25, 2001
336
O n (geometry, t„)= uke{0,1,...,n} P k (geometry, t k , c)
Table 1 the steps of calculating OPH
Instant :
to
ti
12
t'J
tk
Observation:
Oo
0,
0,
Oo
Ok
calculate PH:
Po
p>
p,
Po
P k
update P:
Ho,,
update Po
H, r ,
Ho,,
update P,
update Po
H,,3
H.,3
Ho,:,
update P,
update P,
update Po
Hk-,.k
Hk-2, k
Ho.k
update P,
update Po
For arbitrary instant t n _k( k=1,2 n ), the observation
geometry O n . k can be anti-calculated with P and H:
O nk = ( uie{0,1 n-k} P, ) n ( D ie{0,1,...,n-k}
(□je{n-k+1 n} Hjj ))
3. Spatial-temporal topological model of MO
based on consistent topological relation
The temporal relations of two area objects have thirteen
cases according to Allen’s event based time relation[ Allen
J.F. 1983, ISO/TC211 1998].
The survival temporal period of area object is represented
as [t s ,t e ]. Given the appearing or start instant t s of A as As,
the disappeared or end instant teOf A as Ae, the temporal
relation © t of area object A and B is showed as table 2.
According to the spatial topological model of Max. J.
Egenhofer [ Max. J. Egenhofer, 1991 ], we can define spatial
topological relation 0 s between two MOs. Given the
boundary of area object geometry A ( such as observation
geometry O, present geometry P, and history geometry H)
as 6A, interior as A , the four intersection model which
describe the spatial topological relation of the two area
object geometry A and B is:
V4I =
ÖAHÖB
A U DÖB
öAnB"
A° n B°
If the element is true in the above matrix, the value of it is 1.
otherwise is O.The model describes eight kinds of spatial
topological relation 0 S :
During their evolving process, the spatial topological relation
of the two moving object is diverse. The change of the
spatial topological relation between two moving object at
different instant or in different period reflects the interaction
of two moving objects. But only the regular change of the
spatial topological relation reflects significative interaction of
two moving objects. We define the spatial topological
relation that maintains consistent during their evolving as the
significative relation, that is to say during the overlap period
[t m » t p ] of evolving of two moving objects, the spatial
topological relation of two moving objects maintains
invariant. In temporal relation 0 t , there are four relations,
before, after, meets and met-by, which have no overlap time
period, other nine relations have overlap time period.
We define spatial-temporal topological relation 0(© = @ s
x ® , )of two moving object based on consistent
topological relation during their overlap time period as
showed in table 3.
Given two arbitrary instant t it tj which belong to the overlap
time period, the spatial topological relation 0 sj and © sj of
observation geometry 0 (A) of A and observation geometry
0(B) of B maintains invariant.
In this model, the query of spatial temporal topological
relation of moving objects can be represented as : A0 S B
and A 01 B. For example:
select A from MO
where A during B
and A inside B