Hierarchical Structures in Map Series
by Sabine Timpf
the different operations in Geographic Information Systems (GIS),
changing scale is crucial for the handling and analysis of multi-scale
data. The term multi-scale is used to indicate that there are data of
more than one level of detail in the database. Different levels of
detail are needed when dealing with spatial data. Current scaling
functions blow up and shrink the objects to display or change to a
radically different representation of the display.
research we investigate how to link map objects at different levels of
detail that represent the same real-world entity. We observe the
behavior of map objects at four levels of detail in eight case studies.
We apply an observation method derived from the method of abduction. It
relies on careful and controlled observation of phenomena, similar to
the method of reverse engineering in computer science. We define four
types of map objects to be observed:
a trans-hydro network, that is a combination of the street network, the railroad network, and the hydrographic network,
containers, that represent the regions between the links of the trans-hydro network,
areas, that represent the land-use areas and are contained in the containers, and
map elements, that are contained in the areas, representing buildings, symbols, and dead-end streets and railroads.
propose a hierarchical data structure that supports and describes the
behavior of map objects over four levels of detail. Hierarchical data
structures are best represented by trees or forests. The data structure
of the map cube model is a combination of three different trees,
representing three different types of hierarchies.
are defined according to the functions associated with the edges of
their trees: aggregate, generalize, and filter. The aggregation
hierarchy is built by aggregating objects. The generalization hierarchy
defines how classes relate to more generic super classes. The filter
hierarchy filters objects according to a filter criterion.
map cube model can be imagined as a three dimensional composition. Each
map is a level in a three-dimensional cube, the vertical axis
represents the level of detail. The hierarchical data structure for the
map series is a combination of the trans-hydro network, a tree of
containers including the information on areas and elements, an area
graph, and an element graph. The tree of containers stores which
container includes which areas and elements. It does not store how
these areas and elements are related to areas and elements on a lower
or higher level of detail. This information is encoded in the area
graph or element graph, respectively. We formalize the map cube model
in a functional programming language with an object-oriented paradigm.
our model the trans-hydro network is represented by a filter hierarchy,
the filter criterion is the relative importance of the link in the
network. The container tree is an aggregation hierarchy - the more
abstract the representation, the more containers are aggregated. The
area graph is a collection of area trees; each tree represents a
generalization hierarchy. The element graph is a collection of trees;
each tree is a constructed by several functions. Those functions are
‘omit’, ‘typify’, ‘merge’, and ‘continue’. The first three functions
correspond to the cartographic functions with the same name. Thus, the
model incorporates all three types of hierarchies.