ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
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We use Geometry representing spatial distribution of object. 
Observation geometry O n at instant t« Observation geometry Oj at instant Current instant c=t|+5. the Current instant c~t|+5 the 
A 2-dimension area object can be represented as: 
2Dobject (Geometry); 
Geometry — Agraphics c Geometry graphics. 
Geometry is a set of graphics, including polygon, circle, and 
rectangle, etc 
We define interior point set of Geometry A as A", boundary 
point set of Geometry A as 6A. 
The geometry of area object in spatial database is always 
closed, that is to say the geometry of an object includes it’s 
interior and it’s boundary. So in the operation based on point 
set of geometry, such as union, intersection, and difference 
of two geometries, the result geometry must be closed. We 
can define the point set based operation of two geometries. 
Give geometries A, B e 2Dobject (Geometry), the 
difference , union ,and intersection of A, B: 
Difference: A - B ={p|peA and p-’S B } 
Union: A+ B = { p | p£A or pe B} 
Intersection:AD B = {p|pGA and pe B} 
These operations will degenerate lower dimension geometry, 
such as swing point or swing edge, these degenerated 
geometries will be neglected in spatial database. 
We use instant and period represent the temporal of area 
object. The instant is a point in time reference system. In life 
time of an object, the observation instant of the object can 
be represented as :{t 0 ,ti, ,t„}.The period is closed section 
between two instant. Period = {[ t, t|] | t, fie {t 0 ,ti, ,t„} 
and ti<tj}. 
There are two kinds of change for area moving phenomena, 
one is continue change which occurs during period, the 
other is discrete change which occurs at instant. We assume 
that the time interval of observation sampling on continue 
change phenomena satisfies the rules which accord with 
dynamic change law of the phenomena. 
The observation instant of moving area phenomena or 
object (MO) is represented as t 0 , ti, t 2 , , t n , here t 0 is the 
first observation instant and t n is the latest observation 
instant. The arbitrary instant between two neighboring 
observation instant fi and fi +i can be represented as fi+5, 
here 6 is an increment of time granularity in time reference 
system. The current instant c of area moving object is 
represent as latest observation instant t n plus time increment 
6, that is c= tn+6„ In the next observation instant W the 
current instant c of phenomena will be updated. Before 
updating, the current instant c is replaced by c*, that is c*=c= 
t n +5, then the current instant c is updated by c= fi, + i+6. 
For the spatial-temporal data representation of MO, we 
consider the area geometry status in different time, and use 
two types of geometry object to describe the MO: 
object1( Geometry, instant) an observation snapshot of 
MO distribution in space at an instant. 
object2( Geometry, period) the fact of MO existing on a 
period. 
We use a series of geometry object with spatial geometry 
and time reference to represent moving object, that is using 
O, P, H to represent MO: 
MO = {(O, P, H) | Oe objectl A P e object2 A 
H e object2 } 
2. 2 The definition of OPH model 
In order to represent the spatial and temporal geometry of 
MO, we define three kinds of geometry object, named OPH 
model. First is observation geometry snapshot of MO at an 
instant, represented as O. Second is geometry object part of 
MO which is formed at past instant and continues existing at 
current instant, represented as P. Third is the geometry 
object part of MO which is formatted at past instant and 
disappeared at latter instant, represented as H, that is the 
history of MO during a period. Using the observation 
geometries Oi at different observation instant, we can 
calculate and update P, and H. Using the records of OPH, 
we can reappear spatial-temporal evolving of MO, reflect the 
developing process of MO, and execute spatial-temporal 
query, analysis of interaction and relationship between 
moving objects. Following we give the formal definition: 
Definition 1: At observation instant tj , spatial observation 
geometry of moving object represented as Oj, which is the 
snapshot of spatial distribution of MO. We named it 
observation geometry: 
Oi ( Geometry, fi) e objectl 
Example 1: At instant to , ti, observation geometry 
distributions of MO are O 0 (Geometry, t 0 )and Oi (Geometry, 
ti), showed in Figure 1(a) and (b). 
Definition 2: The geometry part of MO which appeared at 
instant fi and continuously existing at current instant c, 
defined as P|. We named it present geometry: 
Pi( Geometry , fi , c) e object2 
Example 2: The geometries which formed at instant t 0 , ti 
and continue existing at current instant c are P 0 ( Geometry , 
to, c ) and Pi( Geometry , ti , c ), showed in Figure 1(c).