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Temporarily Out of Stock Online Please check back later for updated availability. Overview Innovative review of map projection. Peters , also a pioneer in the work on finite distortion, optimised parameter values for various world map projections by minimising average distortion for 30, distances, connecting randomly chosen pairs of points with uniform probability distribution over the continental surface.

In Canters presented a new method for the development of world map projections with low distortion. Expressing the relationship between the co-ordinates in the map plane and the co-ordinates on the globe by the following two polynomials:. The attractiveness of the method lies in its use of polynomial type equations, which makes it very easy to impose useful restrictions on the geometry of the graticule shape of the parallels and the meridians, spacing of the parallels, ratio of the axes, length of the pole line,.

The Canters projection is used in Belgian geography textbooks and atlases, and has also been adopted for the production of wall maps by Belgian organisations that are active in development co-operation ABOS, NCOS. The easiest way to accomplish this is by a simple linear stretch of the graticule along one of the co-ordinate axes, followed by a compression of equal magnitude along the perpendicular axis to maintain the equal-area property. A good choice of the affine coefficient and a proper orientation of the axes will lead to less variation of scale and angular distortion for elongated areas.

Tobler presented examples of this simple equal-area transformation for areas of different size. A more complicated transformation of the oblique azimuthal equal-area projection that uses sine functions to alter the spacing of the original graticule in the x- and y direction was proposed by Snyder It allows the mapmaker to create equal-area graticules with oval, rectangular or rhombic isocols that have less distortion of angles and scale for non-circular regions.

Snyder presented examples with oval isocols of different eccentricity for the mapping of the Atlantic Ocean as well as a map of the conterminous United States with rectangular isocols. Canters proposed two simple polynomial transformations, with appropriate constraints on the value of the polynomial coefficients to make sure that the general condition for an equal-area transformation in the plane is satisfied. Applied separately or in combination these transformations make it possible to derive a variety of low-error equal-area graticules with alternative geometry, starting from any standard equal-area projection.

The proposed transformations were used for the development of various new equal-area graticules, useful for maps at the global as well as at the continental scale. Special attention was paid to the development of a new low-error equal-area projection for the fifteen member states of the European Union Canters and De Genst, ; Canters, Figure 3. Over the years a great number of map projections have been proposed. Even for the skilled cartographer, who has a good knowledge of map projection principles, choosing among this variety of existing projections is not an easy task.

Map projection selection interferes with several other variables in map design.

## Map Projections

As such it is not possible to compile a magic table telling us unambiguously what type of map projection is best for a given application. With the increasing use of geographical information systems and the development of new mapping software for personal computers cartographic tools are coming within the reach of an ever growing group of users that are unfamiliar with the principles of cartographic design. This has led some cartographers to determine what is currently known about map design from years of theoretical and practical research and to try to translate this knowledge into a set of rules that can be built into microcomputer-based software.

A few researchers have addressed the problem of automated or semi-automated map projection selection, taking into account the limitations imposed by the digital medium, as well as the new opportunities for map projection development that are offered by the computer see above. The area that will be covered, the ways in which the map is going to be used and the intended audience for whom the map is targeted are all major elements in the decision process.

Hence selection should start with the definition of a unique set of requirements that best suits the purpose of the mapping, and that can be translated into a set of map projection properties. Based on these properties a proper choice should be made. In spite of the practical importance of map projection selection only very few authors have treated the subject in any detail. Knowledge on map projection selection mostly appears as a heterogeneous and partly inconsistent collection of rules, repeatedly found in general textbooks on cartography or map projection.

Many authors only provide a summary of the map projections that are most frequently used for the mapping of various areas and for different map purposes.

These listings are of limited use to a novice cartographer, since they do not provide any insight in the reasoning that brings the cartographer to choose for a particular projection. To facilitate the selection process, he presents a decision tree that is based on: a size, shape, orientation and location of the region to be mapped, b special distortion properties conformal, equal-area, equidistant, correct scale along a chosen great-circle , and c application-specific considerations e.

Snyder also recognises that world maps cannot be satisfactorily represented by means of conic type projections, and that other selection criteria may be involved in global mapping than in continental or regional mapping e. He therefore makes a clear distinction between world maps and maps of smaller areas. For world maps many types of projections are listed, depending on the type of application. For smaller areas he recommends the use of conic type projections azimuthal, conical or cylindrical projections.

Maps of a hemisphere, which usually have a circular outline, are also treated as a separate class. For these maps Snyder recommends the use of azimuthal projections. MaPKBS, as it was presented in , cannot be regarded as a definite solution to the problem of automated map projection selection. It takes into account only a fraction of the criteria that may be involved in the selection process.

However, the development of the system proves that some of the trade-offs involved in map projection selection can be managed by an automated system if appropriate heuristics are defined, with or without the use of AI techniques. Two other attempts to develop expert systems for map projection selection have been reported, one by Smith and Snyder and one by Kessler The first attempt has not been described in sufficient detail to review it, the second has never been officially published. According to Snyder , p. For Mekenkamp the selection process consists of answering two fundamental questions: a what is the shape of the region to be mapped?

He distinguishes between one-point round , two-point rectangular and three-point triangular regions, leading to the choice of an azimuthal, a cylindrical and a conical projection respectively.

Mekenkamp only considers oblique aspects, since these produce the least distortion for a given area. This strongly simplifies the selection process. Mekenkamp also considers a functional argument in deciding on the type of region.

### Map Projections: Cartographic Information Systems

If attention has to be focused on one point e. Still the method has some important restrictions. While geometric properties are seldom mentioned in connection with map projection selection, they prove to be very important criteria that are often applied in cartographic practice, although mostly the mapmaker is not conscious of the fact that he or she is actually applying them see Canters, , pp. In their view the selection process consists of two parts figure 4. In the first part of the selection process map projection requirements are formulated, and a list of candidate projections is defined.

To reduce the complexity of the decision process the total number of map projections from which a choice can be made is kept to a strict minimum. Projections included in the selection procedure are chosen in such a way that each possible combination of map projection properties that can be set, is satisfied by at least one projection. This guarantees that, once properties have been stated, the list of candidate projections will be limited to one or maximally a few projections.

If the list contains more than one projection, all candidate projections are ranked by applying a simple set of decision rules. The projection that gets the highest score is selected. In the second part of the process the parameters of the projection that are free to choose are optimised, using an appropriate technique for error reduction.

Once the optimised projection is obtained the result is evaluated by the mapmaker, who ultimately decides if the projection is accepted or not. A quick visualisation of the graticule, with isocols showing the distribution of distortion, as well as a brief error report, is essential to allow the mapmaker to perform this evaluation. If parameter optimisation does not produce the expected result, the mapmaker can decide to apply a polynomial transformation to the obtained graticule to achieve a further reduction of distortion see also section on low-error projections.

If this does not lead to a major improvement the original map projection requirements are re-defined and the process is resumed. It is clear that in this approach map projection selection is seen as a dynamic process that can only be partly automated and still requires a great deal of human intervention. Sea Surface Salinity Remote Sensing. Earl F. Virtual Reality in Geography. Peter Fisher David Unwin. Geographic Information Management in Local Government.

Ian Gilfoyle Peter Thorpe. Spatial Data Quality. Patrick L. Environmental Modeling A Practical Introduction. Remote Sensing of Snow and Ice. Hassan A. Karimi Burcu Akinci. Spatial Information and the Environment.

## Map Projections - Cartographic Information Systems | Erik W. Grafarend | Springer

Julian W. Gardner Krishna C. Remotely-Sensed Cities. Computing in Geographic Information Systems. Narayan Panigrahi. Environmental Remote Sensing and Systems Analysis. Quality Aspects in Spatial Data Mining. Understanding Dynamics of Geographic Domains. Geography's Quantitative Revolutions Edward A.