The inability of the relational data model to represent 
semantics on data is one reason why other ways of 
modelling geographical, and other highly structured, 
data types have been considered during the last ten 
years. What is needed in application areas of this kind 
are data models which support higher level concepts 
than a simple relation. Higher level data models 
represent more types of constraints implicitly than 
lower-level data models ( Elmasri & Navathe, 1989, 
p-596). Thus the semantics of data are embedded in the 
database schema, not in the application program 
handling the data in the database. 
The technique of object-oriented (OO) data modelling 
is based on the concept of object, coming from object- 
oriented programming (Booch, 1986, Kim, 1990, pp.7- 
11). With a single object, it is possible to present both 
structural and procedural data about a real world 
entity. Object class definition presents an abstraction 
which has been made about a real world. The 
abstraction might be an association or an aggregation of 
classifications made before (Sowa, 1984, pp. 103-123, 
Nyerges, 1991, pp.76-82). Other abstraction techniques 
are generalization and specialization, which broaden 
or lessen (respectively) the meaning of an existing 
abstraction. These are the techniques for getting more 
semantics into the database schema, and which 
simplify the application programming. An object- 
oriented model is implicitly a constrained description 
of a real world, making it easier to understand the 
semantics of data. 
This does not mean, however, that the problem of data 
modelling can be forgotten. OO databases offer 
modelling concepts that are richer in semantic content 
than those of relational model, and the specification of 
data types might be more convenient, but the 
underlying problem still remains: What is the 
geographical knowledge that has to be captured in a 
particular problem area, that is, what are the 
geographical objects. 
3 OBJECT-ORIENTED GEOGRAPHICAL DATA 
MODELLING 
What can be required of a geographical data model? It 
should automatically provide answers to questions 
that can be answered by visual inspection of a map 
image (White, 1984, p.16). This requirement implies 
that the data model should provide concepts similar to 
the user's experiences of the world (Mark & Frank, 
1989), such as object, collection, part-whole, link, 
containing, near-far, etc. Geographical data modelling 
is a process whereby these experiental model concepts 
are mapped as mathematically defined concepts. 
The experiences described above can be formally 
modelled using concepts of geometry. The geometry of 
a map requires three geometrical base objects (0-cells, 
1-cells, 2-cells), two relations (0-1 incidence, 1-2 
insidence), and metrical descriptions of the objects 
(coordinates and shape) (White, 1984, p.16). The 
topological portion of a map geometry consists of base 
objects and incidence relations between them. The 
insidence relations constrain the touching of base 
458 
objects and, further, provide concepts with which the 
relationships between the base objects can be described. 
The concepts of the topological interior and boundary 
of a geometrical base object are derived from the 
incidence relation between the objects. For example, 
the boundary of a 2-cell is defined as a set of incident 
1-cells to the 2-cell. The mathematical formulation of 
the topological interior and boundary concepts has 
been discussed in (Egenhofer & Franzosa, 1991). The 
geometrical view of geographical modelling 
emphasizes the topological properties of geographical 
entities; the coordinates and shape of the base objects 
are metrical properties of these objects. 
Geographical data modelling is a process whereby an 
abstraction is made of a real world entity so that the 
geometrical properties of the entity are emphasized, 
and semantics are given to the geometrical abstraction 
by naming the abstraction and characterizing it with 
attributes. The neighbourhood of an entity, i.e. 
associated entities are modelled using concepts that 
emphasize the meaning of the neighbourhood. For 
example, neighbourhood inferred from the geometry 
of an entity might be modelled using the incidence 
relation, while other kinds of neighborhoods might be 
modelled as sets or tuples. 
Object-oriented geographical data modelling is defined 
here as a description of some portion of geographical 
reality using the concept of an object, as defined in the 
preceding section. Thus a geographical entity, along 
with its neighbourhood entities, can be described as a 
single object, resembling the conceptualizations 
humans make about reality. 
4 AN OBJECT-ORIENTED DATA MODEL FOR 
SPATIAL DATA 
This section gives an object-oriented data model for 
describing the geometrical structure of geographical 
entities. The model emphasizes the geometrical 
properties of geographical entities. Certain geometrical 
object classes are defined, which are then used as 
modelling primitives for geographical object types. 
The geometrical objects are independent of any 
application domain, and describing only the geometry 
of a geographical object. For example, line string is a 
geometrical object class, which can be used to define 
the geometry of a geographical object, say, ariver, ora 
boundary line of a river. Geometrical object classes are 
structural primitives of the model. Spatial 
relationships between geometrical objects are modelled 
using the concepts of topological interior and 
boundary. 
The model also includes operations on object classes, 
which change the structure of an object or derive a 
new object from an existing object. These operations 
are called object methods. For example, the method 
named boundary defined for a particular object class is 
a procedure that extracts the topological boundary of an 
object. 
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