OBJECT CONSTRAINTS ON AN OBJECT 
LINE STRING not intersecting itself 
CONNECTED area boundaries are closing line strings, 
AREA not overlapping, and with ordering property 
' DISCONNECTED component areas non-overlapping 
AREA 
AREA PARTITION set of non-overlapping areas 
with covering property 
  
  
  
Figure 2. Additional constraints on some geometrical objects 
AssociationObject and AggregationObject are both 
aggregations of ComponentDomain and Component. 
The Component attribute of each classes is constrained 
by the ComponentDomain, in which the possible 
components of the class are listed. ComponentDomain. 
provides a grouping mechanism for the objects that are 
the only possible building blocks of the aggregate. 
Geometrical objects of the model consist of geometrical 
base objects and geometrical complex objects. The 
geometrical base object classes are Point, LineString 
and ConnectedArea. Higher level geometrical objects, 
which are called geometrical complex objects, are 
formed by aggregating or associating the base objects. 
The geometrical base objects are aggregates themselves, 
for example, point is an aggregate of two or three 
coordinate values forming a tuple. In this modelling 
scheme, a distinction is made between the base objects 
and the complex objects is made to give an idea of the 
logical connection of this model to the geographical 
modelling conventions in general. Geometrical 
complex objects of the model are DisconnectedArea, 
AreaAssociation, LineAssociation, and AreaPartition. 
The object classes are described by their attributes in 
Figure 1. Figure 2 gives a listing of the implicit 
constraints on the object classes that are not included 
in the Figure 1. The implicit constraints on the object 
classes determine the implicit integrity of the object. 
For example, the boundary line string(s) of a connected 
area is constrained to be closing. On the other hand, 
the boundary line string is an instance of the 
LineString class whose instances are constrained so 
that they may not intersect themselves. In this case, the 
constraint of the component class propagates to the 
owner aggregate. 
The most complex object in the model is the 
AreaPartition object, whose components are areas and 
line strings. The semantics of AreaPartition lies in the 
covering property of the object, so that the subareas, 
that is, areas constituting the area partition may not 
overlap each other. This geometrical object type is used 
to define the geometry of a geographical phenomenon 
that is known to exist allover the geographical region 
to be modelled, for example, land use, or real estate 
division. Note the similarity of this geometrical object 
type with the consistency principle of a map database 
in general, presented in (White, 1984). 
460 
4.2 OPERATIONAL FEATURES OF THE MODEL - 
OBJECT METHODS 
The implicit integrity of the geometrical object model 
described above is enforced by the methods of object 
classes. The methods consist of procedures that 
determine whether or not the state of an object is 
consistent with respect to the class definition; the 
procedure can alsoaffect the state of an object so that it 
will reach the consistent state. For example, the 
consistency of an instance of the ConnectedArea class 
is enforced by a defining a method for the class that 
determines whether or not the boundary of a 
particular instance is closing. 
Constraint analysis is a possible design process for the 
object-oriented database design environment (Urban & 
Delcambre, 1990). In the process, the constraints on 
object classes are first specified using first-order logic 
representation, which is then converted to Horn clause 
form. The Horn clauses are numbered, and they are 
arranged to a graph based the dominating relationship 
between two clauses. The authors of the paper 
mentioned above propose that the constraint graph 
can be used as a help when specifying methods for 
object classes. 
In this study, the analysis of object methods is based on 
the idea of constraint analysis, but the handling of the 
problem is different. The analysis of object methods is 
performed based on the figure 3 which is a description 
of order between geometrical objects. The semantics of 
order between objects are the following. If an object 
class is defined as an aggregate (or an association) of 
other object classes, the aggregate (association) follows 
its component classes in the orderscheme. In figure 3, 
object B follows object A, if object A is in the head of 
the arrow connecting the two objects. For example, 
LineString follows Point, because the geometry of a 
line string is determined by points. Thus, LineString 
class should be provided by a method, that checks that 
the components of a line string instance do exist (as 
instances of the ComponentDomain of ConnectedArea 
class). Methods for the object classes are listed in Figure 
4 based on the structural features of the model (Figure 
1) and the order between the objects as in (Figure 3). 
POINT -«4— LINE STRING + CONNECTED AREA 
DISCONNECTED 
AREA 
LINE AREA 
ASSOCIATION ASSOCIATION 
AREA PARTITION 
Figure 3. Order between geometrical object classes. 
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