Feature

The Flattening Science

Cartographers are using a variety of methods to faithfully represent New Zealand and the world.

By Barry Bradley

Displaying our view of the world on a flat sheet of paper has always had its challenges. The basic problem is that the earth has a curved surface, and map makers have to represent this on a flat plane.

Map projections are used to represent part or the whole of the earth's curved surface, usually on a flat sheet of paper. The globe is the only representation that does not distort the Earth's geometry, except, of course, its size.

Despite its close approximation to the earth's true shape, the globe has distinct disadvantages for the viewer. If we want to look at the whole surface of the globe at any one time, measure distances or calculate constant directions, we come up against problems.

Transforming The Globe

An alternative is a map made by methodically flattening the globe's surface. Although this process may modify the globe's geometry, flattening makes it easier for cartographers to make maps and for users to file and use them.

A consequence of this flattening process is distortion. The term "distortion" is rather a misleading one, having connotations of undesireability. Many projections, however, turn these inevitable distortions into advantages.

For example, navigation routes can be transformed into straight lines, regions of greater interest can be enlarged, directions and distances from one point to all others can be shown clearly, and areas of interest can be centred. The most important consideration is matching the map projection to the need.

Is it important to retain the true areas of continents on a world map, or to preserve true shapes or exact distances between points? The answer hinges on what you want to display. Specially calculated projections are available to suit most display criteria.

Mapping New Zealand

The Department of Survey and Land Information (DOSLI) uses a wide variety of map projections in its mapping programme. These projections are carefully selected for their attributes in relation to the map purpose and type of data being displayed.

For the large scale topographic, cadastral and recreation maps, DOSLI uses the New Zealand Map Grid projection. This projection has been devised to minimise distortions over the land area. It was calculated in such a way that variations from the stated scale are at a minimum over the whole country, thus taking account of New Zealand's unique shape.

An Azimuthal Equidistant projection, which preserves true distances and bearings through the centre point, is used to map the world around New Zealand. Although the shapes of continents are progressively distorted as you move further from the centre point, accurate measurements are retained.

The Mercator projection is used by DOSLI in the preparation of plotting charts for the aeronautical industry. Any distortions in areas are traded off for the positive navigational properties of this projection. Courses can be plotted as straight lines, with correct compass angles between start and end points.

The Lambert Conformal Conic projection serves as a mapping framework for the vast areas of the Pacific Basin. Using this projection, the effects of area distortion are controlled.

Mapping The World

A recently published world political wall map, called "Nations of the World", is based on the Robinson projection.

The Robinson projection shows a more realistic view of the world than many traditional projections, better balancing the distortion of size and shape of land masses. Because of these features, the National Geographic Society recently adopted this projection for displaying world maps in its publications.

What is intriguing about the "Nations of the World" map is that the polar regions are mapped separately and printed as insets to the main map. These insets on the Azimuthal Equal Area projection are included because area distortion is at its greatest in these regions on the Robinson projection. Because the insets of the polar regions give the same nominal scale as the main map, specific areas can be easily compared.

For example, Greenland and Saudi Arabia aremuch the same size -- this is apparent on a world globe. However, the Mercator world map shows Greenland sprawling across the northern regions of the globe, making its land mass appear far larger than that of Saudi Arabia, whereas the Robinson projection shows them closer in size. The polar inset used in the Nations map is even more accurate.

Most of us have probably grown up with world maps constructed on the rectangular Mercator projection -- maps which were originally devised for navigation. Distortions on these maps were probably not recognised by us, leaving an erroneous impression of vast northern continents. Greenland, Canada and the USSR could be distorted in area by up to twelve times their actual size. The Antarctic continent was often omitted due to its embarrassingly exaggerated depiction.

Cartographers throughout the world have been entrusted with the "flattening science" and are partly responsible for people's perceptions of the world about them. Careful application of the wide range of projections will help restore fidelity and correct some of the misconceptions carried around in the human mind.

Barry Bradley is a senior executive officer for cartographic development with DOSLI.