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1 Generalisation of Spatial Databases
William Mackaness
1.1 The Importance of Scale in Geographical Problem Solving
‘All geographical processes are imbued with scale’ (Taylor 2004 p214), thus issues of scale are an essential
consideration in geographical problem solving. The scale of observation governs what phenomena can be viewed,
what patterns are discernible, and what processes can be inferred. We are interested in viewing the precise detail of
those phenomena, as well as the broad linkages across regional and global space. Choosing scales of analysis,
comparing output at different scales, describing constructions of scale (Leitner 2004) are all common practices in the
geosciences. We do this because we wish to know the operational scales of geographic phenomena, how
relationships between variables change as the scale of measurement increases or decreases, and we want to know the
degree to which information on spatial relationships at one scale can be used to make inferences about relationships
at other scales (Sheppard and McMaster 2004). What is always apparent when viewing geographic phenomena is the
interdependent nature of geographical processes. Any observation embodies a set of physical and social processes,
‘whose drivers operate at a variety of interlocked and nested geographical scales’ (Swyngedouw 2004, p129).
Both the scale of observation and of representation reflect a process of abstraction, an instantaneous momentary
‘slice’ through a complex set of spatio-temporal, interdependent processes. Traditionally it has been the
cartographer’s responsibility to select a scale, to symbolise the phenomena, and to give meaning through the addition
of appropriate contextual information. In paper based mapping, various considerations acted to constrain the choice
of solution (the map literacy of the intended audience, map styles, the medium and choice of cartographic tools).
Historically the paper map reflected the state of geographical knowledge, and was the basis of geographical inquiry.
Indeed it was argued that if the problem ‘cannot be studied fundamentally by maps - usually by a comparison of
several maps - then it is questionable whether or not it is within the field of geography.’ (Hartshorne 1939 p249).
Information technology has not devalued the power of the map, but it has driven a series of paradigm shifts in how
we store, represent and interact with geographical information. Early work in automated mapping focused on
supporting the activities of the human cartographer who remained central to the map design process. Current
research is focused on ideas of autonomous design – systems capable of selecting optimum solutions among a
variety of candidate solutions delivered over the web, in a variety of thematic forms, in anticipation of users who
have little or no cartographic skill. Historically the paper map reflected a state of knowledge. Now it is the database
that is the knowledge store, with the map as the metaphorical window by which geographic information is
dynamically explored. In these interactive environments, the art and science of cartography (Krygier 1995) must be
extended to support the integration of distributed data collected at varying levels of detail, whilst conforming to
issues of data quality and interoperability.
1.2 Generalisation
At the fine scale, when viewing phenomenon at high levels of detail (LoD), we can determine many of the attributes
that define individual features (such as their shape, size orientation), whilst at the broad scale, we see a more
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characteristic view - more particularly the regional context in which these phenomenon are situated (for example
their gestaltic and topolgical qualities, and various associations among other phenomenon). For example Journey
planning requires a broad scale view in order to gauge timeframes and alternate travel strategies, whilst a fine scale
detailed map is required to reach the final point of destination. It is not the case that one map contains less or more
information, but that they contain different, albeit inter related information. Thus maps are required at a range of
scales, in a variety of thematic forms, for delivery across a range of media. The term ‘map generalisation’ is often
used to describe the process by which more general forms of a map can be derived from a detailed form. In the
context of today’s technology, a vision is of a single detailed database, constantly updated in order to reflect the
most current version of a region of the world. For any given National Mapping Agency (such as the OS of Great
Britain or the IGN of France) that region is defined by their respective national boundaries. In such a context, the
process of map generalisation entails selecting objects from that detailed database, and representing them in various
simplified forms appropriate to the level of detail required, and according to some purpose (or theme). By way of
example, Figure 1 shows a series of maps at different scales, of Lanvollon in France. The goal remains the creation
of automated map generalisation techniques that would enable the derivation of such maps from a single detailed
database. This vision is driven by a variety of motivations: data redundancy (maintaining a single detailed database
rather than a set of separate scale specific databases - Oosterom, 1995); storage efficiency (recording the fine detail
of a feature in as few points as possible); exploratory data analysis (MacEachren and Kraak 1997) (being able to
dynamically zoom in and explore the data, and to support hypermapping); integration (combining data from
disparate databases of varying levels of detail); and paper map production (for traditional series mapping).
Figure 1: 1:25 000 1: 100 000 1: 250 000 (Copyright of the IGN).
Given the strong association of map generalisation with traditional cartography it is worth stressing its broader
relevance to spatial analysis and ideas inherent in visualisation methodologies. Though discussion will focus on the
cartographic, we are in essence dealing with the generalisation of spatial databases (Muller 1991; Smaalen 2003). In
this context we can view the fine scale, detailed database as the first abstraction of space – often called the Primary
Model or Digital Landscape Model (DLM) (Grunreich 1985). As a prerequisite the DLM requires the definition of a
schema that will support the explicit storage, analysis and characterisation of all the geographic phenomenon we
wish to record. A series of secondary models can be derived from this primary model via the process of ‘model
generalisation’. These abstractions are free from cartographic representational information, and could be used to
support spatial analysis at various levels of detail. Both primary and secondary models can be used as a basis for
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creating cartographic products (Digital Cartographic Models) via the process of ‘cartographic generalisation’. Figure
2 summarises the relationships between these models and the generalisation processes.
Digital
Landscape
Model (DLM)
Primary ModelSecondary Models
DLM’model generalisation
cartographic
generalisation
Digital
Cartographic
Model (DCMs)
Cartographic Model
Figure 2: Generalisation as a sequence of modelling operations (after Grunreich 1985).
Model generalisation may involve reduction of data volume, for example via the selection, classification or grouping
of phenomenon, or the simplification of phenomenon such as network structures. This may be required as a
prerequisite to spatial analysis, the integration of different datasets, or for computational efficiency. It is certainly an
integral step in the derivation of multi scaled cartographic products. Though it has important ramifications for
cartographic generalisation, model generalisation does not itself seek to resolve issues of graphic depiction such as
clarity or emphasis in depiction.
Cartographic generalisation describes the process by which phenomena are rendered, dealing with the challenges of
appropriate symbolisation, and the placement of text within the limited space of the medium (whether on paper or
the small screen of a mobile device). The symbology used to represent a geographic feature must be of a size
discernible to the naked eye. At reduced scale, less space is available on the map to place the symbols. At coarser
scales, the symbols become increasingly larger than the feature they represent. It therefore becomes necessary to
omit symbology associated with certain features, to group features, to characterise them in a simpler way, or to
choose alternate forms of symbology in response to this competition for space (Mark 1990). Figure 3 nicely
illustrates this idea, showing The Tower of London and its surroundings at 1:10, 000, 1:25,000, and 1:50, 000 scale.
At the finest level of detail we can discern individual walls, courtyards, pavements, trees and the buildings are
individually named. We can make many inferences drawing on our understanding and experiences of geographic
space, such as the function of buildings, and the components of the various fortifications. At a coarser scale we see
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less detail, in exchange for more of the context. For example we discern its strategic importance along the bank of
the river Thames, and text is used in a different way to label various features. At the coarse scale of 1:50,000 we see
how competition for space has presented further challenges for the cartographer. The thick red symbology used to
represent the roads has encroached upon surrounding features, which have had to be slightly ‘displaced’ or made
smaller in order to avoid overlapping and causing confusion among the represented features. We can also discern
more of a thematic edge to this representation, with the Tower highlighted as a tourist attraction. Overall then, we
can discern the processes of model and cartographic generalisation at work in the creation of such map designs.
Figure 3: Model and Cartographic generalisation acting in unison to reveal different qualities about The Tower of
London (Copyright OS).
1.3 Conceptual Models of Generalisation
Initial research in automated cartography began in the 1960s (Coppock and Rhind 1991) and sought to replace the
manual scribing tools and techniques used by the human cartographer, with their automated equivalent. Paper based
maps were digitised to create inherently cartographic, vector based databases – in essence the map became a set of
points, lines, areas and text to which feature codes were attached in order to control the symbolisation process. But
research soon highlighted the limits of this approach, and revealed the art and science of cartographer as a design
task involving complex decision making. There was a clear need for conceptual models (such as those presented by
Brassel and Weibel 1988 and McMaster and Shea 1992) as a basis for understanding the process of generalisation,
and developing automated solutions. McMaster and Shea (1992) presented a comprehensive model that decomposed
the generalisation process into three stages: definition of philosophical objectives (why generalise), cartometric
evaluation (when to generalise) and a set of spatial and attribute transformations (how to generalise). A
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complimentary view that reflects the potential of more complete solutions to automated generalisation is one in
which a variety of candidate solutions are considered (synthesis), based on cartometric and topological analysis
(analysis). This is followed by an evaluation phase that selects the most appropriate candidate based on both fine
scale and holistic evaluation techniques (Figure 4).
Analysis
Measuring many properties
(metric, topological and non
spatial) both within and
among classes of features.
Synthesis
Creation of a variety of
solutions using a
combination of model and
cartographic generalisation
techniques. Candidate
solutions in response to
analysis phase, constrained
by rules governing design.
Evaluation
Selection of optimal
solution according to
intended map use and task,
reflecting analysis at both
the fine and broad scale.
Figure 4: Generalisation in the context of automated solutions
1.3.1 Multi Scale Databases
Aligned closely to the topic of map generalisation is the idea of ‘multiple representation’, in which various
cartographic representations of a single object are stored for viewing or analysis at various levels of abstraction
(Kidner and Jones 1994; Devogele et al. 1997; Goodchild and Yang 1992; Kilpelainen and Sajakoski 1995). A
specific advantage being that their forms can be pre-cast and immediately presented to the user (thus avoiding the
time cost associated with creating solutions ‘on the fly’). Though the DLM (Figure 2) remains unchanged, a series of
multiple representations can be derived at any time, only needing to be recast when the central database is updated to
reflect changes in the real world. There are complicating issues in the management of the database, in particular
ensuring the seamless joining together of multiple representation after an update cycle. Ideas of multiple
representation mirror the idea of a single detailed database, from which other databases are derived using map
generalisation techniques.
1.4 Generalisation Methods and Algorithms
For any given conceptual framework, it is necessary to precisely define the methods by which we can analyse,
synthesise and evaluate solutions. Early research focused on reverse engineering the design process, observing the
human cartographer at work, and via a process of stepwise refinement, identify the discrete methods used by the
cartographer. In some instances the cartographer would omit selected features, or whole classes of features. Some
features were merged and enlarged and if space allowed, and where symbology overlapped, features were marginally
displaced in order to distinguish more easily between features. These and other methods can be divided into two
types of transformation: spatial and attribute transformation. The ten spatial transformation methods are:
amalgamate, aggregate, collapse, displace, eliminate, enhance, merge, refine, simplify, and smooth. The two
transformation methods are: classify and symbolise (Weibel and Dutton 1999).
Smaalen (2003) argues that in essence map features fall into one of three metaclasses (Molenaar 1998). Classes that
contain ‘network like’ objects, such as railways, rivers and roads; classes of relatively small, often rigid, ‘island’
objects – typically buildings, and a third class of mostly ‘natural’ area objects – often forming exhaustive
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tessellations of space, for example land parcels, lakes, forested regions, and farms. Each class has different
behaviours, and can be characterised in different ways. One can therefore envisage a matrix of these metaclasses
against generalisation methods. Each cell in the matrix containing a number of algorithms for modelling
transformations of that particular metaclass for varying levels of detail, and for a range of themes. A huge amount of
research has been devoted to populating such a matrix – developing methods that can be applied to various classes of
objects. By way of illustration, Dutton (1999) and other have worked on methods for generalising linear features
(Buttenfield 1985; Plazanet et al. 1998); finite element analysis and other techniques have been used to model
displacement among features (Hojholt 2000; Burghardt and Meier 1997). Considerable effort has been devoted to
methods for generalising buildings (Jiang and Claramunt 2004; Regnauld 2001), whilst other research has focused
on how space exhaustive tessellations of space can be generalised - for example as is found in geological mapping
(Bader and Weibel 1997; Downs and Mackaness 2002). Others have researched the problem of attenuating network
structures (Mackaness and Mackechnie 1999; Richardson and Thomson 1996) whilst others have proposed solutions
to the problem of text placement (Christensen et al 1995).
These methods have been framed in a variety of strategic contexts. For example Molenaar (1998) stratifies these
methods under four headings that reflect a need to model both individual and structural characteristics of the map.
Importantly he discusses the idea of functional generalisation – a generalisation technique used to group close
proximity, non-similar objects in order to create meaningful composites (Smaalen 2003). Figure 1 presents a nice
example of this whereby the various objects comprising the town of Lanvollon represented at 1:25 000 scale, have
been grouped and replaced by a single point symbol at the 1:250 000 scale. Functional generalisation is particularly
appropriate in the case of significant scale change.
1.4.1 Analysis
A strong recurrent theme in all the research into generalisation algorithms has been the need for techniques that
make explicit the metric and topological qualities that exist within and between classes of features. Effective
characterisation of geographic space requires us to make explicit the trends and patterns among and between
phenomenon, to examine densities and neighbourhoods, and to model connectivity and network properties, as well
as the tessellation of space. Thus the field draws heavily on spatial analysis techniques such as graph theory
(Hartsfield and Ringel 1990), Voronoi techniques (Peng et al 1995; Christophe and Ruas 2002) and skeletonisation
techniques (Costa 2000). The identification of pattern draws on regression techniques, and automated feature
recognition techniques (Priestnall et al 2003). These ‘supporting’ structures (Jones and Ware 1998; Jones et al. 95)
are used to enrich the database and enable the modelling of topological transitions (Molenaar 1998).
1.4.2 Synthesis and Evaluation
Research has also tried to model the process by which a combination of methods is used to synthesise various
solutions. For example a group of Islands may be merged, and enlarged in order to remain visible to the naked eye at
smaller scale. The process of enlargement may require marginal displacement to distinguish between the Islands.
Different results emerge according to the sequence in which the methods are applied, and the degree to which they
are applied (Mackaness 1996). The evaluation of candidate solutions must be graded against a set of criteria,
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themselves defined by the map task. For example, a map intended for tourists may accommodate greater
generalisation of the characteristic form than a map intended for sea navigation. In Figure 5 the two generalised
forms (hand drawn) are shown at the same scale as the original (in order to compare), prior to being reduced in size
to 30% of the original.
Figure 5: The choice, sequence and degree of application of various methods enable synthesis of different solutions,
but which one is ‘correct’?
Even in the very simple example of Figure 5, with a restricted set of considerations, it is easy to imagine a very large
set of permutations. But it is possible to define evaluation criteria. For example shape and area metrics can be used
to measure alignments (Christophe and Ruas 2002) or the degree of distortion from the original (Whang and Muller
1998; Cheung and Shi 2004). Topological modelling in surfaces and networks can be used to model neighbourhood
changes among a group of objects. Density and distribution measures can be used to determine trends in the
frequency of occurrence or the degree of isolation of a feature. Distance metrics can be used to assess the
perceptibility of an object (is it too small to be represented at the intended scale), and the degree of crowding among
objects. Evaluation also includes assessment of non-spatial attributes. For example is it a rare geological unit relative
to the surrounding region (Downs and Mackaness 2002), or a special point of interest in the landscape? Techniques
have also been developed to measure the content of map, and to evaluate levels of content as a function of change in
scale (Topfer and Pillewizer 1966; Dutton 1999). Many of the cartometric techniques used to analyse the properties
of a map as part of the synthesis of candidate solutions can also be used in this process of evaluation. In effect, each
and every one of these techniques makes explicit some property within or between classes of objects.
But a map in its generalised form reflects a compromise among a competing set of characteristics. There is very little
in the map that remains invariant over changes in scale. Indeed generalisation is all about changing the
characteristics of a map in order to reveal different patterns and relationships among the phenomenon being mapped.
Often the preservation of one characteristic can only be achieved by compromising another. Thus among a group of
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buildings do we give emphasis to the ‘odd one out’ because it is significantly larger than the rest, or preserve the
characteristic orientation shared among the group of buildings and the adjoining road? We know that the topology
among a set of objects changes if we remove, aggregate or functionally combine objects. But how do we ensure that
the new topology is a ‘valid’ one? And where we wish to combine data from different sources and scales, how do we
validate the quality of any given solution? There is no shortage of techniques for measuring the properties of an
object, but the challenge of defining tolerances and collectively prioritising those characteristics (linked to intended
use) remains a significant impediment to development of systems that are more autonomous in their operation.
1.5 A Rule Based Approach
More challenging than the development of generalisation methods, has been the formalisation of the procedural
knowledge required to trigger the use of such methods. At any instant in the design phase, there may exist a range of
alternate candidate solutions, whose creation and choice is based on rules of thumb (heuristics), to a goal state that is
somewhat hazy and hard to define (Starr and Zeleny 1977). Various attempts have therefore been made to use a rule
based approach to automated map generalisation (Richardson and Muller 1991; Heisser et al 1995; Keller 1995), in
which sequences of conditions and actions are matched in order to control the overall process. For example a small
remote building in a rural context has a significance much greater than its counterpart in a cityscape and is therefore
treated differently. A solution might be to enlarge the symbology in order that the building remains discernible to the
naked eye, according to those conditions:
IF a building.context = rural AND building.neighbourhood = isolated AND building.size = small THEN
building.generalisation = enlarge.
We can formalise both the <condition> and < action> part of such rules from observation of how features are
symbolised on paper maps at various scales. We observe how particular solutions operate over a band of scales (akin
to the idea of an ‘operational scale’ - Phillips 1997) and that beyond a certain threshold, a change in the level of
generalisation is invoked. Figure 6a illustrates the various representational forms of a cathedral and Figure 6b shows
the scale bands over which those representations might operate. These threshold points are determined by: 1) a
feature’s geometry and size, 2) its non spatial attributes, 3) its distribution and association with other features, 4) its
immediate proximity to other features, and 5) the resolution of the device on which the information is being
displayed or printed (Glover and Mackaness 1999).
d
c
ba
ab c d
1:1250 1:10,000 1:25,000 1:50,000
(a)
(b)
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Figure 6: a) Transformations with decreasing map scale; b) Corresponding scale bands for a topographic map
(Glover and Mackaness 1999).
Its treatment also depends on the feature’s importance in relation to the intended theme. For example castles and
visitor attractions in a tourist map will be given greater emphasis from those buildings deemed more general. Figure
7 is based on observations made from paper maps over a range of scales, and shows how key (or special buildings)
and general buildings are typically represented.
Scale 1:1250 1:10,0001:25,000
1:50,000 1:250,000
key building
(a) (b) (c) (d)
generalbuildings
CASTLE Castle
Figure 7. Examples drawn from paper maps of building generalisation at various scales.
Again from observation, we can identify the generalisation methods that can be applied at the fine scale, to derive
these various solutions - that their forms are simplified, or grouped, or collapsed and replaced with an iconic form.
For example derivation of the castle representational form at 1:50 000 scale can be formed by placing a minimum
bounding rectangle (MBR) around the group of ‘castle’ buildings (so deriving its convex hull), and substituting this
form for the group of individual buildings. One can envisage a similar process applied to each metaclass, and for
each scale band transition point (similar to the one illustrated in Figure 6). In this manner we can define a decision
tree that incorporates the various generalisation methods used, according to: the building type, its association with
adjacent features, and the operational scales of the various representational forms. Figure 8 is the decision tree for
‘key’ buildings intended for use in urban environments.
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Get source datasetgeometry
Building area< 150 ?
SIMPLIFY ENLARGE
YES
NO
radius search -single building?
PROPORTIONAL
MBR
get buildingcentre
get iconsymbol
SIMPLIFY
overlapsroad?
REGROUPconvex hulls
of subgroups
Get centre ofeach sub-
group get icon symbol
get convex hullcentre
get buildingcentre
get icon symbol
get convexhull or convexhulls of sub-groups
get convex hullcentre(s)
get icon symbol
Scale band 3
YES
NO
NOget icon symbol
YES
NO
CONVEXHULL
radius search -single building?
YES
ELIMINATE
�
�
H H
Scale band 1
Scale band 2
Scale band 4
Figure 8. Decision tree for key buildings.
These and other decision trees were collectively implemented in a GIS system that was able to derive different
thematic maps from a single detailed source (Glover and Mackaness 1999). The results (Figure 9) were compared
with their manual equivalent, as basis for identifying future work.
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Cas
Mu
Mu
Mu
UniSch
TOPOGRAPHIC TOURIST
SOURCE
Figure 9. Different products according to theme and scale derived from the same source.
Such a system works quite well for relatively small changes in scale. The system is limited by its inability to
generate alternate solutions to a design problem, and to automatically evaluate the correctness of the final solution.
The work also highlighted the need for cartometric tools capable of analysing both ‘local’ constraints (imposed by
surrounding objects), and ‘global’ constraints (ensuring consistency across the region including preservation of
trends). What was required was a system that would enable consideration of alternate designs that took into account
a shared view of of these and other design constraints. One such approach that has shown great promise in this
regard has been in the use of multi agent systems.
Multi Agent Systems
The idea of ‘agents’ came from the observation that complex processes can be modelled as a set of simple but
interconnected set of task. For example the complex task of sustaining an ant colony is achieved by assigning ants
(agents) to specific, defined tasks that collectively ensure the survival of the colony. Thus quite complex emergent
behaviour can arise from a set of connected but simple agent tasks (Weiss 1999). Thus one definition of an agent is
'a self contained program capable of controlling its own decision making and acting, based on its perception of its
environment, in pursuit of one or more objectives.' (Luck 1997, 309). Where more than one agent exists, we can
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define what are called multi-agent systems (MAS): Multi-agent systems are ones in which several computational
entities, called agents, interact with one another (Huhns and Singh 1998). In the context of map generalisation, it has
been possible to model various characteristics of features and to implement an agent based approach whereby agents
are assigned to manage the generalisation process across a geographic region (with a local perspective on the
problem), and to communicate with other agents at a more regional scale (a global perspective) in order to ensure
consistency in solution, and to ensure preservation of general trends across the map space (Duchêne 2003). This was
the methodology utilised in the AGENT project, a European Union funded project, comprising a consortium of
Universities, IGN (France’s NMA) and commercial enterprise (Barrault et al. 2001; Lamy et al 1999). The system
built on previous work undertaken among the consortium members (Ruas 1999), and was capable of analysing
various properties within and between classes of objects, of synthesising alternate candidate solutions and evaluating
the optimum choice against a set of design constraints. Where a solution was not forthcoming, a more radical or
broadscale solution was proposed and control passed from the local perspective to a more global one. Thus there
existed a hierarchical structure of mico, meso and macro agents, which, in effect, modelled both a fine scale view of
design, as well as the more general view of the problem. The project commenced in 1998, and its commercial form
is currently manifest in the CLARITY system from Laser Scan (www.laser-scan.co.uk), and continues to form the
basis of on going research among a consortium of national mapping agencies across Europe under the MAGNET
programme. Given its adoption by a number of European NMAs it is arguably the best solution to date to the
challenges of autonomous map generalisation, though a number of challenges remain. The first is in the development
of an interface that enables ‘tuning’ of solutions that arise from complex emergent behaviour and interactions. The
second is in defining the type of information that is passed among the hierarchies of agents, and how this
information is utilised in the various stages of decision making.
Conclusion
Generalisation holds an important position in the development of a theoretical framework for handling geographic
information ‘as it deals with the structure and transformation of complex spatial notions at different levels of
abstraction’ (Smaalen 2003, p1). As a modelling process, map generalisation is about characterising space in a way
that precipitates out the broader contextual relationships that exist among geographic phenomenon. It is about
making sense of things (Krippendorf 1995) and is intrinsic to geographic ways of knowing.
In essence, a database is a system of relationships – the process of generalisation is about abstracting and
representing those patterns of relationships inherent among phenomenon viewed at different levels of detail (similar
to the goals of scientific visualisation). The enduring vision is of a single detailed database from which such multiple
views can be automatically derived according to a broad range of tasks.
Over the years a variety of solutions have emerged in response to both a growing understanding of the complexities
of automated map design, and the changing context of use arising from developments in information technology.
Attempts at automation have highlighted the complexity of this task. It is certainly the case that the design of a map
(irrespective of medium) is a hugely challenging task, though the paradigm shift afforded by data modelling
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techniques has called into question the appropriateness of trying to mimic the human cartographer as a basis to
automation.
Developments in the field of generalisation continue to advance three key areas: 1) development of algorithms for
model generalisation with the focus on spatial data handling and analysis; 2) methods for creating and evaluating
candidate solutions for graphical visualisation and multiple representation; and 3) development of human computer
interaction models that enable integration of these methodologies in both the presentation and exploration of
geographic information. Research continues to reveal the subtleties of the art and science of cartography. For it to
remain relevant however, it must keep abreast of the changing environments of map use and analysis (including
interoperability requirements), and the broader developments in visualisation methodologies.
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