UniServe Science News Volume 14 November 1999


Understanding Map Projections

William Cartwright
Department of Land Information, RMIT University

Understanding Map Projections logo.

The spatial sciences rely on graphic descriptions of data to enable map users to visualise geographic data. As the data refers to positions on the curved surface of the Earth (latitude and longitude), the map (plane surface) needs to have certain characteristics, such as equivalence of areas, retention of shape and equidistance. For instance, when calculating areas on a map it is essential that complementary points on a map and the Globe contain the same area. For topographic mapping it is essential that the correct shape of mapped features be retained. Also, for navigation purposes, as the sailing line of a ship on the Earth's surface remains constant, it should be projected as a straight line on a map.

An understanding of the problems of map projections, apart from the superficial, can only be gained by studying the mathematical nature of projections and in particular, the problems of determining the size and shape of the Earth (the science of geodesy) and displaying portions of the Earth's surface as a map.

The development of an appreciation of the properties of map projections is an important component of the study program of tertiary students, who on the completion of their undergraduate degrees, expect to enter the surveying and mapping professions in Australia. The theory behind these properties is based on certain mathematical principles. These principles can be employed to derive equations linking latitude and longitude to Cartesian coordinates of map projections. By altering various parameters in the equations, the properties of a map projection can be shown to change. Students in the spatial sciences need to be aware of and appreciate these changes in map projection properties.

Understanding Map Projections is a computer based simulation teaching package for students of mapping that approaches the teaching of the concepts of map projections using visual methods to depict properties usually specified using mathematical formulae. It allows students to view graphic portrayals of various map projections and to explore how the continental shapes distort as projection variables are altered in equations.

After using the package, students who previously had little or no knowledge about map projections should have a much greater appreciation of map projections and their use to depict the Earth (3-dimensional) on a plane (2-dimensional) paper map or computer monitor. Students should be better able to identify particular projections and choose the appropriate one to use for the display of particular parts of the Earth and different mapping themes.

Understanding Map Projections presents students with a 'pseudo' and interactive image of the spherical Earth, a two-dimensional representation that depicts the choice of projection methods (one of which will determine the Earth's representation) and a set of indicators that define the properties of the map for certain applications. They are presented with a set of scenarios, guiding them in an exploration of the connections between projection method, the graphic image and its various properties.

The interactive course can be used in any educational program in the spatial sciences offered in Australia. It can also be used in secondary schools in geography and graphics communication subjects where students have elected to undertake studies in map-related topics.

The package has been developed as a 'generic' product and provides teaching support resources, rather that offering a monolithic course. Instructors can build their own teaching activities around the package and use the various elements to construct applications that suit the student group using the package. This has been designed to ensure that it can be used at both early tertiary levels and advanced post-primary levels.

Upon starting the package users are presented with an initial choice of four options:

  • Overview;
  • History;
  • Projections; or
  • Tutorials.
  • Figure 1.

    Figure 1. 'Entry' page

    At the bottom of each page are interactive controls that allow users to navigate through the package.

    Moving the cursor over the 'Overview' hot spot changes the arrow cursor to a hand and clicking on either the icon or text takes the user to the overview selection page. This page provides links to information that supports the effective use of the package. A general introduction to the package, the comprehensive 'Glossary of Terms' and production team information can be accessed from this page. The Glossary contains a generous coverage and explanation of the terms used throughout the package.

    By clicking the 'Globe' icon in the control panel the user can move back to the Overview page.

    Figure 2.

    Figure 2. Overview page

    Let's explore the 'History' option. A mouseclick over the icon or 'history' text moves the user to this page. The history of map projections and associated developments is treated in two ways:

  • Introductory Text; and
  • Interactive Timeline.
  • Figure 3.

    Figure 3. History access page

    The introductory text provides a treatise on the history of map projections. Map projections expert, Rod Deakin, who has also developed the exploratory map projections components of this package, has written the text.

    Figure 4.

    Figure 4. Text describing the Origins of Map Projections

    The Interactive Timeline covers four 'periods' of the development of map projections - from simple graphical depictions to more accurate mathematically-derived constructions. The timeline can be 'moved' by 'grabbing' the background of the image area and 'pulling' it from left to right. Throughout the timeline certain interesting developments are highlighted when the cursor travels over the text. By clicking on one of these hot spots, further descriptions of the particular development or 'key' event can be exposed. A typical information screen is depicted in Figure 6.

    Figure 5.

    Figure 5. Interactive Timeline

    Figure 6.

    Figure 6. Detailed information

    The third element of the package is the 'Projections' sections. Users are able to explore the elements of the three types of map projections:

  • Cylindrical Projections;
  • Azimuthal Projections; and
  • Conical Projections.
  • Two 'special' map projection cases are also expanded upon.

    Figure 7.

    Figure 7. Map Projections

    By clicking on one of the hot spots the user can move to explore one of the map projection types in more detail. By clicking on 'cylindrical projections' the user moves to a simulation of how this type of projection 'works'. In this case, as illustrated in Figure 8, the resultant map produced by wrapping a virtual cone around the globe illustrates the basic principles of the projection. This is in fact a very general description of the projection and its mathematical basis, the 'starting point' for producing the graphics needs to be appreciated. By clicking on the icon in the bottom left corner another executable package is launched and the user can explore how the graphical depiction of a particular projection will change when its specifications are altered (see Figure 9 for a typical output). This can be printed for later discussion and evaluation. Students can explore the many different types of cases and then return to the main package by exiting this section.

    Figure 8.

    Figure 8. Simulation of the Cylindrical Projection basics

    Figure 9.

    Figure 9. World outline on a Cylindrical Projection

    Finally, the Tutorials allow students to explore the attributes of map projections and discover how to choose one to minimise certain distortions. These distortions can be in area, distance or azimuth (angles).

    Two tutorials are included:

  • Why Have Projections; and
  • Projection Attributes.
  • The 'Why Have Projections' section has three scenarios that students can work through to see how maps and charts that are constructed from selected projections can be used for sea and air navigation and as a tool for interpreting natural and environmental issues like global warming. Figure 10 depicts the first page of the scenario that explains the use of charts for sea navigation.

    Figure 10.

    Figure 10. 'Why Have Projections' scenario

    The second tutorial provides a number of check boxes that allow a number of desired attributes to be selected and then the appropriate map projection that meets these specifications can be depicted. This tutorial has been designed to enable students to appreciate how the correct selection of map projection can ensure that a map or chart is drawn with minimal errors for certain applications. Students also discover that certain attributes, equal area and equidistance, are mutually exclusive. Figure 11 shows this part of the package.

    Figure 11.

    Figure 11. Projection attributes check boxes and resultant map projection example

    Understanding Map Projections is a multimedia package allowing students to develop a visual 'sense' of a map projection and understand how changes in projection attributes affect the appearance of the map projection. Students can create their own visual image of a chosen map projection. They can also use the package to create a 'checklist' of projection attributes that would reinforce the correct choice of a projection that allowed the depiction of particular thematic information at the appropriate scale and accuracy for a specific mapping project. The key elements of map projections can be explored and manipulated, enabling users of the package to be able to better appreciate a particular graphic portrayal and how changes to parameters alter the appearance of the final map.

    Further information:
    Dr William Cartwright
    Department of Land Information
    RMIT University
    GPO Box 2476V
    Melbourne Victoria 3001
    Telephone: (03) 9925 2423
    Fax: (03) 9663 2517
    Email: william.cartwright@rmit.edu.au

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    UniServe Science News Volume 14 November 1999

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