map projection

map projection transfer of the features of the surface of the earth or another spherical body onto a flat sheet of paper. Only a globe can represent accurately the shape, orientation, and relative area of the earth's surface features; any projection produces distortion with regard to some of these characteristics. The particular projection chosen for a given map will depend on the use for which the map is intended. Some projections preserve correct relative distances in all directions from the center of the map (equidistant projection); some show areas equal to (equal-area projection) or shapes similar to (conformal projection) those on a globe of the same scale; some are useful in determining direction. Many map projections can be constructed by the use of a light source to project the features of the globe onto a piece of paper (although in practice one performs the operation mathematically rather than with a light); other projections can be constructed only mathematically. Projections are classified as cylindrical, conic, or azimuthal according to the method of projection with a light source; many projections that can be constructed only mathematically are also classified according to this system.

Cylindrical Projection

In a typical cylindrical projection, one imagines the paper to be wrapped as a cylinder around the globe, tangent to it along the equator. Light comes from a point source at the center of the globe or, in some cases, from a filament running from pole to pole along the globe's axis. In the former case the poles clearly cannot be shown on the map, as they would be projected along the axis of the cylinder out to infinity. In the latter case the poles become lines forming the top and bottom edges of the map. The Mercator projection, long popular but now less so, is a cylindrical projection of the latter type that can be constructed only mathematically. In all cylindrical projections the meridians of longitude, which on the globe converge at the poles, are parallel to one another; in the Mercator projection the parallels of latitude, which on the globe are equal distances apart, are drawn with increasing separation as their distance from the equator increases in order to preserve shapes. However, the price paid for preserving shapes is that areas are exaggerated with increasing distance from the equator. The effect is most pronounced near the poles; e.g., Greenland is shown with enormously exaggerated size, although its shape in small sections is preserved. The poles themselves cannot be shown on the Mercator projection. Students using the Mercator projection obtain an incorrect impression of the relative sizes of the countries of the world.

Conic Projection

In a conic projection a paper cone is placed on a globe like a hat, tangent to it at some parallel, and a point source of light at the center of the globe projects the surface features onto the cone. The cone is then cut along a convenient meridian and unfolded into a flat surface in the shape of a circle with a sector missing. All parallels are arcs of circles with a pole (the apex of the original cone) as their common center, and meridians appear as straight lines converging toward this same point. Some conic projections are conformal (shape preserving); some are equal-area (size preserving). A polyconic projection uses various cones tangent to the globe at different parallels. Parallels on the map are arcs of circles but are not concentric.

Azimuthal Projection

In an azimuthal projection a flat sheet of paper is tangent to the globe at one point. The point light source may be located at the globe's center (gnomonic projection), on the globe's surface directly opposite the tangent point (stereographic projection), or at some other point along the line defined by the tangent point and the center of the globe, e.g., at a point infinitely distant (orthographic projection). In all azimuthal projections, the tangent point is the central point of a circular map; all great circles passing through the central point are straight lines, and all directions from the central point are accurate. If the central point is a pole, then the meridians (great circles) radiate from that point and parallels are shown as concentric circles. The gnomonic projection has the useful property that all great circles (not just those that pass through the central point) appear as straight lines; conversely, all straight lines drawn on it are great circles. A navigator taking the shortest route between two points (always part of a great circle) can plot his course on a gnomonic projection by simply drawing a straight line between the two points.

Other Projections

Among the other commonly used map projections are the Mollweide homolographic and the sinusoidal, both of which are equal-area projections with horizontal parallels; they are especially useful for world maps. Goode's homolosine projection is a composite using the sinusoidal projection between latitudes 40°N and 40°S and the homolographic projection for the remaining parts. Interruptions, or splits, are often made in the ocean areas in order to show land areas with truer shapes. The A. H. Robinson projection, now used by the United States Geographic Service, has gained acceptance because it accurately represents relative size.

Bibliography

See G. P. Kellaway, Map Projections (2d ed. 1970); F. Pearson, Map Projection Methods (1984).

map projection The representation on a plane surface of part or all of the surface of the Earth or a celestial body. Various projections have been used in the Earth sciences because of their particular suitability for certain work, e.g. equal-area projections for the global distributions of different sedimentary deposits, polar stereographic projection for the relationships within Gondwanaland, Mercator's projection for the absolute movements of the lithospheric plates, and conical projections for the Himalayan—Alpine fold belt. Projections based on Mercator's are most frequently used because of their general familiarity, unless the information portrayed is peculiarly distorted.

projection A mapping from one coordinate space to another, possibly of a lower dimension. It takes the points of an object onto the points of a fixed plane (the view plane) in such a way that each pair of points is collinear with a fixed point, the center of projection or eyepoint, which lies neither on the object nor the view plane. The main types of projection are parallel and perspective projections.