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The terrain objects occur at the lowest level of the
classification hierarchy. They can be seen as the elementary
objects within the thematic field represented by the
classification system. This implies that the decision, whether
certain terrain objects should be considered as elementary or
not, should always be made within the frame work of a
thematic field. Objects that are considered as elementary in
one thematic field should not necessarily be considered as
elementary in another thematic field.
AGGREGATION HIERARCHIES
The introduction of "elementary" objects implies the
existence of composite objects. They can be defined through
aggregation hierarchies which are quite distinct from
classification hierarchies.
An aggregation hierarchy shows how composite objects can
be built from elementary objects and how these composite
objects can be put together to build more complex objects
and so on. Suppose that we have houses, roads, parks,
factories, office buildings and shops as elementary objects.
From these several composite objects can be build as in
fig. 6:
industrial districts
factories roads
residential districts commercial districts
houses roads parks shops roads office
Fig. 6 Hierarchical relationships among elementary and
composite objects.
The composite objects of fig. 6 can be combined to build
towns or cities as in fig. 7, and these can be put together to
build urban areas.
City
oo industrial commercial
districts districts districts
Fig. 7 Hierarchical relationship between different
aggregation levels.
The aggregation hierarchy has a bottom up character in the
sense that starting from the elementary objects composites
objects of increasing complexity are constructed in an
upward direction. The composite objects inherit the attribute
values from their constituents parts.
The fact that elementary objects can be aggregated into
composite objects implies that also their attribute values may
be aggregated. If one of the attributes of houses is the
number of people living there, then it is easy to calculate the
total number of inhabitants of a residential district.
751
In literature on semantic modelling [Algic 1989] [Brodie
1984] [Brodie e.a.1984] [Egenhofer e.a.1989] [Oxborrow
€.a.1989] the upward links of the classification hierarchy
are labelled respectively as "ISA" links and those of the
aggregation hierarchy as "PARTOF" links. ISA links relate
particular objects to a class and to superclasses, where the
class and superclass will be defined by their general
characteristics i.e. attribute structures. The PARTOF links
relate a particular set of objects to a specific composite
object and on to a specific more complex object and so on.
Another distinction between the two hierarchies is that
elementary objects belong to exactly one class, whereas they
may belong to several composite objects. That means that
composite object types are not necessarily disjoint. A river
can be part of a hydrological system, which is a composite
of rivers, lakes and streams. That river can also be part of a
water traffic system consisting of rivers, lakes and channels.
But that river will be part of only one hydrological system,
i.e. an elementary object only belongs to one particular
composite object of one type.
OBJECT ASSOCIATIONS
Both hierarchies of the previous sections where clearly
defined. A classification hierarchy represents a stepwise
introduction of the attribute structure of terrain objects. An
aggregation hierarchy is defined by the generic models
describing how composite objects at one level are con-
structed from the objects of the next lower level. The levels
in the hierarchy represent objects of an increasing
complexity. Object association form a third type of object
sets, these are defined less sharply, they build no
hierarchies. They are just sets of objects which do have
something in common. This means that associations of one
type are not necessarily mutually exclusive. Their nature can
best be explained by some examples.
In a road network (which might be considered as an
aggregation), the route from town A to town B forms an
association. The route will consist of several roads, or
segments of roads. In its construction this association shows
similarities with aggregations. The difference is that
members of the route from A to B might also belong to
other routes. Hence these routes are not mutually exclusive.
Other examples are the set of all companies which do have
an office in Amsterdam and all cities in which a particular
company has an office. These two are typical examples of
associations based on m:n relationships.
DATA MODELLING
The previous discussion suggested that (elementary) terrain
objects should always be defined in the framework of a
classification system. Such a system will be defined within a
users context, which will have several aspects. The first
aspect is the discipline or disciplines of the users, i.e. are we
working in a cadastral environment, or soil mapping, or
demography etc. Each discipline will have its own definition
of terrain objects, classes and attributes. These definitions
depend also on the scale level or other aggregation level of
the mapping, i.e. a local level, a regional level, a national
level or even a continental level. At each level different sets
of elementary objects will be relevant. These different levels
may be linked by the fact that the elementary objects at one
level can sometimes be considered as aggregates of
