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Transverse Mercator Projection
 A Transverse Mercator projection A Transverse Mercator projection is an adaptation of the Mercator projection. Both projections are cylindrical and conformal . However, in a Transverse Mercator projection, the cylinder is rotated 90° (transverse) relative to the equator so that projected surface is aligned with a meridian (or line of longitude) rather than the equator, as is the case with the regular Mercator projection. Image File history File links World map projection (source) File links The following pages link to this file: Map projection Transverse Mercator projection ...
Jump to: navigation, search The Mercator projection of the world up to a latitude of 86° N and S The Mercator projection is a cylindrical map projection devised by Gerardus Mercator in 1569. ...
Jump to: navigation, search The Mercator projection shows courses of constant bearing as straight lines. ...
Jump to: navigation, search The Mercator projection shows courses of constant bearing as straight lines. ...
In mathematics, a conformal map is a function which preserves angles. ...
The equator is an imaginary circle drawn around a planet (or other astronomical object) at a distance halfway between the poles. ...
On the earth, a meridian is a north-south line between the North Pole and the South Pole. ...
Jump to: navigation, search Map of Earth showing curved lines of longitude Longitude, sometimes denoted by the Greek letter λ, describes the location of a place on Earth east or west of a north-south line called the Prime Meridian. ...
In both the regular and transverse form of the Mercator projection, there is very little distortion of scale in the narrow region near where the projected surface is tangent, or secant, to the sphere or ellipsoid representing the Earth. The scale 5° away from the equator is less than 0.4% larger than the scale at the equator and is approximately 1.53% at an angular distance of 10°. This low level of distortion, combined with the conformal property which it inherits from the Mercator projection, make the Transverse Mercator projection ideal for mapping areas with a narrow longitudinal range, e.g., a nation such as Chile. A map is a hardcopy representation of part of the earths surface and it is essential that a scale bar and scale ratio be present on the map to convey the reduction factor. ...
In mathematics, the word tangent has two distinct, but etymologically related meanings: one in geometry, and one in trigonometry. ...
A secant line of a curve is a line that intersects two (or more) points on the curve. ...
A sphere is a perfectly symmetrical geometrical object. ...
Jump to: navigation, search Egg-shaped. ...
Jump to: navigation, search Map of Earth showing curved lines of longitude Longitude, sometimes denoted by the Greek letter λ, describes the location of a place on Earth east or west of a north-south line called the Prime Meridian. ...
Forms of the Transverse Mercator Projection The spherical form of the Transverse Mercator projection, which uses a sphere to represent the Earth, was first presented by Johann Heinrich Lambert in 1772. An elliptical form, which uses an ellipsoidal model of the Earth, was later presented by mathematician Carl Friedrich Gauss in 1822 and was further analyzed by L. Krūger in the early 20th century. In Europe, the Transverse Mercator projection is sometimes referred to as the Gauss-Krūger or Gauss Conformal projection. Johann Heinrich Lambert Johann Heinrich Lambert (August 26, 1728 – September 25, 1777), was a mathematician, physicist and astronomer. ...
Carl Friedrich Gauss (Gauß) (April 30, 1777 – February 23, 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. ...
The spherical form of the Transverse Mercator projection is conformal. The distortion of scale increases entirely as a function of distance from the central meridian. The ellipsoidal form is also conformal, but scale distortion is affected to some degree by parameters of the ellipsoid and this distortion is not entirely a consistent function of distance away from the central meridian.
The projected surface can be tangent to the model of the Earth in either case, which produces a map that is true to scale along this line. The scale factor can also be reduced in order to balance out the distortion over the mapped region. In this secant case, there are two lines of true scale on either side of the central meridian. These lines are parallel to the central meridian in the spherical model, but only approximately parallel in the ellipsoidal model.
The ellipsoidal form with a reduced scale factor is likely the most widely used projection in geodetic mapping, as it is employed by the U.S. Geological Survey in areas with a predominant north-south extent.
See also Jump to: navigation, search The Universal Transverse Mercator (UTM) projection system is a grid-based method of specifying locations on the surface of the Earth. ...
References Snyder, John P. (1987) Map Projections - A Working Manual. U.S. Geological Survey Professional Paper 1395, United States Government Printing Office, Washington, D.C.. This paper can be dowloaded from USGS pages |
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