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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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