A Lambert conformal conic projection (LCC) is a conic map projection used for aeronautical charts, portions of the State Plane Coordinate System, and many national and regional mapping systems. It is one of seven projections introduced by Johann Heinrich Lambert in his 1772 publication Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten (Notes and Comments on the Composition of Terrestrial and Celestial Maps [1] ).
Conceptually, the projection conformally maps the surface of the Earth to a cone. The cone is unrolled, and the parallel that was touching the sphere is assigned unit scale. That parallel is called the standard parallel.
By scaling the resulting map, two parallels can be assigned unit scale, with scale decreasing between the two parallels and increasing outside them. This gives the map two standard parallels. In this way, deviation from unit scale can be minimized within a region of interest that lies largely between the two standard parallels. Unlike other conic projections, no true secant form of the projection exists because using a secant cone does not yield the same scale along both standard parallels. [2]
Pilots use aeronautical charts based on LCC because a straight line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints for typical flight distances. The US systems of VFR (visual flight rules) sectional charts and terminal area charts are drafted on the LCC with standard parallels at 33°N and 45°N.
The European Environment Agency [3] and the INSPIRE specification for coordinate systems [4] recommends using this projection (also named ETRS89-LCC) for conformal pan-European mapping at scales smaller or equal to 1:500,000. In Metropolitan France, the official projection is Lambert-93, [5] a Lambert conic projection using RGF93 geodetic system [6] and defined by references parallels that are 44°N and 49°N.
The National Spatial Framework for India uses Datum WGS84 with a LCC projection and is a recommended NNRMS standard. Each state has its own set of reference parameters given in the standard. [7]
The U.S. National Geodetic Survey's "State Plane Coordinate System of 1983" uses the Lambert conformal conic projection to define the grid-coordinate systems used in several states, primarily those that are elongated west to east such as Tennessee. The Lambert projection is relatively easy to use: conversions from geodetic (latitude/longitude) to State Plane Grid coordinates involve trigonometric equations that are fairly straightforward and which can be solved on most scientific calculators, especially programmable models. [8] The projection as used in CCS83 yields maps in which scale errors are limited to 1 part in 10,000.
The Lambert conformal conic is one of several map projection systems developed by Johann Heinrich Lambert, an 18th-century Swiss mathematician, physicist, philosopher, and astronomer. [1]
Coordinates from a spherical datum can be transformed into Lambert conformal conic projection coordinates with the following formulae: [9]
where:
and:
If one standard parallel is used (i.e. ), the formula for n above is indeterminate, but then . [10]
Formulae for ellipsoidal datums are more involved. [10]
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The Mollweide projection is an equal-area, pseudocylindrical map projection generally used for maps of the world or celestial sphere. It is also known as the Babinet projection, homalographic projection, homolographic projection, and elliptical projection. The projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions.
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The Bottomley map projection is a pseudoconical equal area map projection defined as:
In cartography, a Tissot's indicatrix is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local distortions due to map projection. It is the geometry that results from projecting a circle of infinitesimal radius from a curved geometric model, such as a globe, onto a map. Tissot proved that the resulting diagram is an ellipse whose axes indicate the two principal directions along which scale is maximal and minimal at that point on the map.
The Albers equal-area conic projection, or Albers projection, is a conic, equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels.
The Collignon projection is an equal-area pseudocylindrical map projection first known to be published by Édouard Collignon in 1865 and subsequently cited by A. Tissot in 1881.
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