is, 
rom 
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ict 
‚he 
ral 
“hy 
th 
TT 
nd 
ids 
or 
1e 
1 
is 
We - oco». ux cce Uu w^ w pel 
Objectiz(ID4,81,M1) (11) 
Objectoz(1D2,85,M2) 
They are composed to form a new object: 
Object3-(ID3,83, Object; (Sy) ,Object2(S,) ,Ma) (12) 
Here SC 81, S.C Sg. 
2.3.3 Propagation The mechanism to describe 
such dependencies and ways to derive values is 
called propagation. It supports complex objects 
which do not own independent data and is based 
upon the concept that values are stored only 
once, i.e., for the properties of the components, 
and then propagated to the properties of the 
composite objects. For example, the number of the 
beds in a hotel is the sum of the beds of all 
bedrooms. The propagation model guarantees 
consistency, because the dependent values of the 
aggregate are derived and need not be updated 
every time after the components have been 
changed. 
The classification, generalization, association 
and aggregation enrich the semantic models so 
that the object-oriented approach supports 
multiple semantic functions, They are written as 
the following table of relations of the 
abstractions: 
classification instance of 
generalization is-a 
association member of 
aggregation parts of 
Comparisons between inheritance and propagation 
are made by the following: 
- Inheritance is defined in generalization (is a) 
hierachies, while propogation acts in aggregation 
(parts of ) or association (member of) 
hierachies. 
- Inheritance is a top-down approach, inheriting 
from the more general to the more detailed class; 
propogation, on the other hand, acts bottom-up. 
- Inheritance describes properties and 
operations; while propagation derives values of 
properties. 
- Inheritance is implicit, all  superclass 
properties are inherited from its subclass; while 
propagation is explict, i.e. only if specified. 
In addition; it must be stated for which 
relationship the propagation holds; which 
component properties are used; which composite 
property is derived and how the result is 
obtained. 
3 OBJECT-ORIENTED DATA MODEL 
IN GEOMETRY 
3.1 Introduction 
In geometry, there are four types of features: 
point-, line-, surface-, and complex features, 
which are considered as four superclasses of all 
features. Figure 4.3.1 shows the relationships 
between the four geometrical superclasses and 
various feature classes according to geographical 
properties. Therefore, in geometry, we can 
abstractly deal with point-, line-, surface-, 
complex features, when we define a feature class, 
besides defining geographical class, we must 
declare its geometric type. For example, when a 
building is being defined as a class of building, 
it is simultaneously defined as a surface 
feature, and it is automatically linked to the 
775 
data structure of surface features so that it 
inherits geometric information and the procedures 
to act on the data. 
The geographical objects will be identified and 
described by their geometric characteristics and 
their thematic attribute (non geometric). That 
means that two kinds of data need to be stored in 
GIS,and an identifier must be required to link 
them ( see Fig. 3). Here we discuss the object- 
oriented model of the geometric data. 
  
  
Spatial Features 
a) 
| Point feature | [Line feature] [surface feature] [Complex feature] 
  
  
  
   
| ) \ i | n | 
Fig. 3 relation between four geometric 
superclasses and geographic feature classes 
  
fittribute data 
Feature Il 
Identifier 
  
  
  
  
  
Geometry data 
  
  
  
Fig. 4 Link between geometric and attribute data 
3.2 Geometrical Topology, Data Sharing 
and Object-oriented Model 
Nodes and arcs play a central role in unified 
data structure, since they are the only geometric 
primitives which have position information 
directly associated with them. The terminal 
points of an arc share common "coordinate" 
information by pointers to their topological 
nodes (see figure 5). Line features are not 
defined in terms of geographical coordinates by 
identifiers to the arcs composing the line, and 
surface features are defined by identifiers to 
the arcs surrounding the surface. Actually, this 
topological data structure is implicitly 
represented by sharing the common nodes and arcs. 
On the other hand, that is like the aggregation 
implement of an object-oriented data model. 
  
ARCID S-node E-node Middle-point 
  
T 
Node ID. Mi M; z 
100 
20012 | 10020 08 432 3725 425 
  
  
  
  
  
10020 | 4285 2266 675 
  
  
  
  
Figure 5 Propagation of a component object 
The concepts of  object-orientation can be 
employed to build the geometric data models. In 
geometry, there are only four types of basic 
features and several primitive elements such as 
node, arc and "leaf node" in 2DRE (see Li & Gong, 
1992). A feature consists of one or more 
primitive elements, more than one feature may