Polyconic projection

Polyconic projection

A polyconic projection is a conical map projection. The projection stems from "rolling" a cone tangent to the Earth at all parallels of latitude, instead of a single cone in a normal conic projection. Each parallel is a circular arc of true scale. The scale is also true on the central meridian of the projection. The projection was in common use by many map-making agencies of the United States from its proposal by Ferdinand Rudolph Hassler in 1825 until the middle of the 20th century. ["Flattening the Earth: Two Thousand Years of Map Projections", John P. Snyder, 1993, pp. 117-122, ISBN 0-226-76747-7.]

The projection is defined by:

:$x = cot\left(phi\right) sin\left(lambda sin\left(phi\right)\right),$

:$y = phi + cot\left(phi\right) \left(1 - cos\left(lambda sin\left(phi\right)\right)\right),$

where $lambda$ is the longitude from the central meridian, and $phi$ is the latitude. To avoid division by zero, the formulas above are extended so that if $phi = 0$ then $x = lambda$ and $y = 0$.

References

* [http://mathworld.wolfram.com/PolyconicProjection.html Mathworld's page on polyconic projections]
* [http://www.radicalcartography.net/?projectionref Table of examples and properties of all common projections] , from radicalcartography.net
* [http://www.uff.br/mapprojections/Polyconic_en.html An interactive Java Applet to study the metric deformations of the Polyconic Projection] .

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• Polyconic projection — Polyconic Pol y*con ic, a. [Poly + conic.] Pertaining to, or based upon, many cones. [1913 Webster] {Polyconic projection} (Map Making), a projection of the earth s surface, or any portion thereof, by which each narrow zone is projected upon a… …   The Collaborative International Dictionary of English

• polyconic projection — [päl΄i kän′ik] n. a type of conic map projection in which the parallels are represented as arcs of circles having centers at different points along the straight central meridian and the other meridians are shown as curves …   English World dictionary

• polyconic projection — A map projection that is a combination of separate conic projections drawn for each parallel or latitude. In this projection, the central meridian is a straight line and other meridians are curves concave to the central meridians. Parallels are… …   Aviation dictionary

• polyconic projection — noun a conic projection of a map having distances between meridians equal to those distances on a globe • Hypernyms: ↑conic projection, ↑conical projection * * * noun : a map projection based on the development of a series of concentric cones… …   Useful english dictionary

• polyconic projection — noun Date: circa 1864 a map projection consisting of a composite series of concentric cones each of which before being unrolled has been placed over a sphere so as to be tangent to a different parallel of latitude …   New Collegiate Dictionary

• polyconic projection — Cartog. a conic projection in which the parallels are arcs of circles that are not concentric but are equally spaced along the central straight meridian, all other meridians being curves equally spaced along the parallels. [1900 05] * * * …   Universalium

• polyconic projection — pol•y•con′ic projec′tion [[t]ˌpɒl iˈkɒn ɪk[/t]] n. geo a conic map projection in which the parallels are arcs of circles that are not concentric but are equally spaced along the central straight meridian, all other meridians being curves equally… …   From formal English to slang

• polyconic projection — /ˌpɒlikɒnɪk prəˈdʒɛkʃən/ (say .poleekonik pruh jekshuhn) noun (in cartography) a conic projection in which the parallels are arcs of circles that are not concentric but are equally spaced along the central straight meridian, all other meridians… …

• international modified polyconic projection — A modified polyconic map projection chosen by an international committee in 1909 for construction of maps of the whole world, except polar caps, on one projection and on a scale of 1:1,000,000. The size of the sheet is 4° change of latitude by 6° …   Aviation dictionary

• Polyconic — Pol y*con ic, a. [Poly + conic.] Pertaining to, or based upon, many cones. [1913 Webster] {Polyconic projection} (Map Making), a projection of the earth s surface, or any portion thereof, by which each narrow zone is projected upon a conical… …   The Collaborative International Dictionary of English