# Full text: The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics

```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).
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