Earth's Coordinate Grid

Gridding the globe with abstract lines has been put forward since the 2nd century BC, when Hipparchus suggested parallels of latitude and meridians of longitude constructed over a spherical model of Earth. Three hundred years later, Claudius Ptolemy refined these ideas and produced map projections with a graticule of longitude and latitude lines.

After the French-sponsored geodetic expeditions in Peru and Lapland in the 1730s, the ellipsoidal shape of the Earth became the basis for more accurate positioning of lines of latitude. After the International Meridian Conference of 1884 recognized the center of the transit instrument of the Royal Observatory at Greenwich, England, as the zero origin for longitude, the prime meridian, most nautical charts, and many maps agreed on the alignment of the longitude and latitude on small-scale charts and maps.

Spherical trigonometry is sufficient for distance and direction computations on the sphere, but the ellipsoidal shape of Earth makes these computations difficult. Additionally, the very meaning of distance is changed by different conceptions of appropriate paths from one point to another. Gerardus Mercator designed a map projection in 1569 that allowed one to plot a single compass bearing as a straight line on a map. The course followed by steering this single azimuth is not the shortest path from one point to another, but often the efficiency of steering a single bearing and the ease of course design makes the longer path worthwhile. On a spherical Earth surface, the shortest path is a great circle. On the sphere, the meridians of longitude all describe great circles. The parallels of latitude describe small circles, not the shortest path between points of the same latitude, unless they are both on the equator. The shortest path over the surface of an ellipsoidal Earth is the ellipsoidal geodesic. Following any great circle or geodesic other than along a meridian or the equator requires continuously changing the heading with respect to true north. On the ellipsoidal Earth, spherical trigonometry is not sufficient for computations of distance, direction, area, path intersection, and other practical problems. Software to perform geodetic direction and distance algorithms can require several pages of source code. Software for projecting the ellipsoidal Earth onto a flat plane can be complex and slow to execute for large geodatabases.

There are other global coordinate systems based on longitude and latitude. In the plate carrée projection, the lines of longitude and latitude are mapped as though they were orthogonal and equally scaled everywhere. The World Geographic Reference System and Maidenhead Grid Squares divide the surface of Earth into nested rectangles in longitude, latitude space described by alphanumeric characters. These are useful for pointing to positions or small regions, but dividing the world up into equal areas using longitude and latitude is as impossible as flattening Earth with a single map projection without introducing distortions.

While longitude and latitude are useful, especially for storing of database vertices, for index maps, and for point descriptions, there are major problems for mapping, navigation, and spatial analysis. Hundreds of useful map projections have been devised, resulting in local and regional coordinate systems with which distances, directions, areas, and shapes can be portrayed and measured. These map projections, based on the notion of flattening all or a portion of Earth's surface onto [Page 816]a flat plane, all fail to portray the Earth without distortion. Cylindrical, conic, and flat planes are geometric surfaces on which features on Earth's surface are projected. Cartographers can minimize one or more distortions of distance, directions, area, local shape, or global shape but never all of them. Small local regions can be portrayed on large-scale maps with reasonable fidelity, but tiling such maps to cover larger areas is not possible without overlaps or gaps. Global portrayals of Earth at smaller scales are often based on compromise projections that introduce minimal distortion of a few characteristics.

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