geometrical object model. Modelling method is a 
metalevel concept in the model. 
The modelling methods of the geometrical base object 
classes are named Boundary and Interior. The action of 
these methods is to extract the topological boundary 
and interior of the instance of the class. Spatial 
relationships between geometrical base objects can be 
described formally with these concepts. The 
specification of binary spatial relations is given in 
(Egenhofer & Franzosa, 1991). According to them, the 
binary spatial relationship between two point sets can 
be determined by examining the intersection of the 
topological boundary and interior of these two point 
sets. In the paper mentioned above, the authors 
formalize the concepts that describe binary spatial 
relationships between two area objects, such as 
disjoint, touch, overlap, equals, inside, covered by, 
overlap with disjoint boundaries, and overlap with 
intersecting boundaries. Formal definitions for spatial 
relations are a starting point for the definition of 
arbitrary spatial relationships between any two 
geometrical objects. What is still needed is the 
development of the theories of the previous study to 
cover higher level geometrical object types, such as 
area partition proposed in this study. 
The action of the Boundary and the Interior methods 
is to extract the topological boundary and interior of 
the object class for which the methods have been 
defined. The binary spatial relationship between two 
object types is defined by the boundary and interior 
points sets of a particular class. An example might 
clarify the use of this approach: A user of the system 
might define a constraint on two different area types by 
help of the Boundary and Interior methods. Suppose 
that these two areas represent area type A and area type 
B. A constraint could be specified, whose semantics is 
the following: area type A must be disjoint from area 
type B. The method IsDistinct might enforce this 
explicit constraint: the input to the method are to 
instances of (for example) ConnectedArea class, and 
the method action is to determine whether or not an 
instance of a LineString class is shared by the two 
ConnectedArea instances. 
The constraints of this kind can be enforced by the 
sequencing of methods of geometrical base object 
classes given in Figure 5. 
5 GEOGRAPHICAL MODELLING BASED ON THE 
ABOVE MODEL 
On the basis of the model of geometrical objects 
defined above, the following is proposed concerning 
the geographical modelling for object-oriented 
databases: 
1) The geometrical structure of a geographical entity is 
modelled using the geometrical object definitions 
above, and other structural characteristics are described 
by additional attributes. The result of this modelling 
step is a geographical object class definition. 
2) The neighbourhood of a geographical entity is 
modelled by forming associations and aggregations of 
  
  
  
OBJECT OUTPUT FROM THE OUTPUT FROM THE 
BOUNDARY METHOD INTERIOR METHOD 
Point Point itself 
LineString Start point, End point Line string itself except its 
start point and end point 
Connected Bounding line strings Area itself except the 
Area boundary line strings 
  
  
  
  
462 
Figure 5. Description from the output of the modelling methods. The 
specification of output is based on (Egenhofer & Franzosa, 1991). 
geographical objects. Associations and aggregations are 
defined using the concepts of the topological boundary 
and interior of the geometrical objects underlying the 
geographical ones. The result of this processing step is 
the definition of a named neighbourhood of a 
geographical object class. 
The two definitions are then used in the 
implementation of the system. An example of the 
proposed modelling scheme is represented next. 
5.1 Example of geographical modelling using the 
geometrical object model 
The process of geographical modelling based on the 
geometrical object model presented in this paper is 
described using a simple example. Suppose that an 
application needs information on the areal extents of 
three land use classes, viz. mainlands, islands and 
water areas, in some study area. The dimensions of the 
study area are clearly defined, for example, by 
geographical coordinates, and it has been decided that 
the boundaries of the land use classes are digitized 
from topographic maps on a certain scale, say, 1:100 
000. It is now the job of the database designer to design 
an appropriate data model for this application, so that 
the information on the land use classes is correct with 
respect to the geographical reality of the map sheets to 
be digitized. 
On the basis of the semantics of the land use classes, 
the following constraints are put on database: 
1) The individual land use classes are represented as 
connected or disconnected areas. 
2) The three land use classes may not overlap. 
3) Every location in the study area must be occupied by 
some land use class depicting area. 
4) An area object representing mainland cannot touch 
(see section 4.3), that is, be the neighbour of an area 
object representing an island. 
The analysis of these constraints, and the geometrical 
object model represented in this paper leads to the 
following choices in the schema design. The study area 
geometry is defined as a reference to the AreaPartition 
class, because of the constraint of non-overlapping 
areas, which cover the whole study area. Constraints 1 
through 3 are implicit in the geometrical object model. 
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