# Map Projection Definitions for Land Surveyors

**map projection****–**^{1} A map relating coordinates of points on a specified surface (usually a rotational ellipsoid) to coordinates of corresponding points on a plane. The map depicts a relation between a coordinate system on a specified surface and a coordinate system on a plane. ^{2} Any systematic method of representing the whole or part of the cu surface of the Earth upon another, usually flat, surface. For maps of Earth, a projection consists of a network (graticule) of lines representing parallels of latitude and meridians of longitude, or a grid based on suet parallels and meridians. Map projections are classified 1) according to the characteristics which they preserve, e.g., as conformal or equal area; 2) according to the methods used in their development, e.g., polyconic, gnomonic, or stereographic; and 8) according to the names: their authors, e.g., as Mercator, Bonne, and Lambert. The latter may addition have their most prominent characteristic specified.

**map projection, Albers conical equal****–****area****–**^{1} An equal-area map projection from the sphere to a cone, which cuts the sphere at two latitudes. ^{2} map projection defined above, generalized to a mapping of the rotational ellipsoid onto the seam cone. To generalize, the differing radii at the latitudes must be taken into account. Straight lines radiating from a represent meridians; arcs of concentric circles represent parallels of latitude Along two selected arcs, called standard parallels, the scale is held Along the other arcs, the scale varies with the latitude but is constant along any given arc. The scale factor along an arc is the reciprocal of that along straight line, so that an equal-area map projection results.

**map projection, azimuthal****—**A map projection producing a graticule which the azimuths or directions of all lines radiating from a central point or pole are the same as the azimuths or directions of the corresponding lines on the ellipsoid. Also called “zenithal map projection” or “cent map projection.”

**map projection, Chebyshev’s****—**The most general map projection producing the least distortion in representing longitudinal distances was invented by Chebyshev in 1856.

**map projection, conformal-**^{1}Map projection producing a map the property that, at any point, the angle between two arbitrary lines through a point on the map is the same as the angle between corresponding lines on the mapped surface at the corresponding point. ^{2} Map projection where the scale at any point on the map is the same in all directions.

**map** **projection, conformal conical****—**A conformal map projection mapping a region on the rotational ellipsoid onto a region on a cone in such a way that at each point, the ratio of scales in two orthogonal directions is unity.

**map** **projection, conical****—**A map projection of the rotational ellipsoid onto a tangent or secant cone. In a conical map projection, the principal scale is preserved along the line representing the arc of a small circle or along the two lines representing the arcs of two small circles. Conical map projections may include cylindrical map projections (the apex of the cone is at an infinite distance from the sphere or ellipsoid) and projections onto a tangent or secant plane (the apex of the cone is at the center of the plane.) They will project onto a single cone tangent to the ellipsoid or, conceptually, the secant to the ellipsoid along two parallels; or they may project onto a series of tangent cones, all having the same axis which passes through the center of the ellipsoid but with apices at constantly increasing distances from the ellipsoid.

**map** **projection, cylindrical****–**^{1} A map projection whose scale is specified and constant along a line representing the arc of a great circle. ^{2} A map projection that first projects the geographic meridians and parallels of latitude onto a cylinder, either tangent or secant to the surface of a rotational ellipsoid, and then develops the cylinder into a plane.

**map** **projection, equal area****—**A map projection preserving a constant ratio between the area of a region on the surface being mapped and the area of the corresponding region on the plane. Often called “equivalent map projection.”

**map** **projection, gnomic-**^{1}A map projection from the sphere onto a tangent plane, with the point of projection at the center of the sphere. ^{2} The same as above. except that it involves mapping an ellipsoid onto a tangent plane, with the point of projection at the center of the ellipsoid.

**map** **projection, Lambert conformal conic—**A conformal map projection of the so-called conical type, on which all geographic meridians are represented by straight lines which *meet *in a common point outside the limits of the map, and the geographic parallels are represented by a series of arcs of circles having this common point for a center. Meridians and parallels intersect at right angles, and angles on the Earth are correctly represented on the projection. This projection may have one standard parallel along which the scale is held exact; or there may be two such standard parallels, both maintaining exact scale. At any point on the map, the scale is the same in every direction. It changes along the meridians and is constant along each parallel. Where there are two standard parallels, the scale between those parallels is too small; beyond them, too large. The Lambert conformal conic map projection with two standard parallels is the base for the state plane coordinate systems devised by the U.S. Coast *& *Geodetic Survey (now, National Geodetic Survey) for zones of limited north-south dimension and indefinite east-west dimension. In those systems, the standard parallels are placed at distances of one sixth the width (north-south) of the map from its upper and lower limits. See also *coordinate system.*

**map ****projection, Mercator—**A conformal cylindrical map projection in which the surface of a sphere or ellipsoid, such as the Earth, is conceived as developed on a cylinder tangent along the equator. Meridians appear as equally spaced vertical lines, and parallels as horizontal lines drawn farther apart as the latitude increases, such that the correct relationship between latitude and longitude scales at any point is maintained. The expansion at any point is equal to the secant of the latitude at that point, with a small correction for the ellipticity of the Earth. The Mercator is not a perspective projection. Since rhumb lines appear as straight lines and directions can be measured directly, this projection is widely used in navigation. If the cylinder is tangent along a meridian, *a *transverse Mercator projection results; if the cylinder is tangent along an oblique great circle, an oblique Mercator projection results. Also called “equatorial cylindrical orthomorphic projection.”

**map projection, oblique Mercator—**See *map projection, **Mercator.*

**map projection, polar—**Projection of points on the surface of a sphere to a plane tangent at its pole.

**map projection, polyconic—**A map projection with the central geographic meridian represented by a straight line along which the spacing for lines representing geographic parallels is proportional to the distances between the parallels. The parallels are represented by arcs of circles which are not concentric, but whose centers lie on the line representing the central meridian, and whose radii are determined by the lengths of the elements of cones which are tangent along the parallels. All meridians except the central one are curved. projection is neither conformal nor equal-area, but it has been much used for maps of small areas because of the ease with which it can be constructed. This map projection was used to construct early topographic maps of the United States (U.S. Geological Survey) and, in a modified form, it can be used for maps of large areas. This map projection was devised by F.R. Hassler, first superintendent of the U.S. Coast Survey (later, U.S. Coast & Geodetic Survey; now, National Geodetic Survey).

**map projection, sinusoidal—**An equal-area map projection mapping parallels of latitude into truly spaced, parallel, straight lines along which exact scale is preserved. The meridians are sine curves. The equator used as the standard parallel of latitude.

**map projection, stereographic—**An azimuthal map projection mapping hemisphere onto a plane by projecting from a point on the sphere on the plane tangent to the sphere at the opposite end of the diameter through the center of projection.

**map projection, transverse Mercator—**A map projection of the cylindrical type, being in principle equivalent to the regular Mercator projection turned (transversed) 90° in azimuth. In this project the central meridian is represented by a straight line correspond to the line which represents the equator on the regular Mercator map projection. Neither the geographic meridians (except the central meridian), nor the geodetic parallels (except the equator. if shown) are represented by straight lines. The transverse Mercator projection is a conformal projection used as the base in state plane coordinate systems for the grids of those zones whose greater dimension is in a north-and-south direction. See also *coordinate system.*

**map** **projection, universal polar stereographic—**A military grid system based on the polar stereographic projection, applied to maps of the earth’s polar regions north of 84° N and south of 80° S latitudes.

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Source: NSPS “Definitions of Surveying and Related Terms“, used with permission.

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