Cross-multiplication: Difference between revisions
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[[File:Polyconic projection SW.jpg|300px|thumb|American polyconic projection of the world]] | |||
'''Polyconic''' can refer either to a class of [[map projection]]s or to a specific projection known less ambiguously as the American Polyconic. Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. This description applies to projections in equatorial aspect.<ref>''An Album of Map Projections'' (US Geological Survey Professional Paper 1453), John P. Snyder & Philip M. Voxland, 1989, p. 4.</ref> | |||
As a specific projection, the American Polyconic is conceptualized as "rolling" a cone tangent to the Earth at all parallels of latitude, instead of a single cone as 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 the time of its proposal by [[Ferdinand Rudolph Hassler]] in 1825 until the middle of the 20th century.<ref>''Flattening the Earth: Two Thousand Years of Map Projections'', John P. Snyder, 1993, pp. 117-122, ISBN 0-226-76747-7.</ref> | |||
The projection is defined by: | |||
:<math>x = \cot(\varphi) \sin((\lambda - \lambda_0)\sin(\varphi))\,</math> | |||
:<math>y = \varphi-\varphi_0 + \cot(\varphi) (1 - \cos((\lambda - \lambda_0)\sin(\varphi)))\,</math> | |||
where <math>\lambda</math> is the longitude of the point to be projected; <math>\varphi</math> is the latitude of the point to be projected; <math>\lambda_0</math> is the longitude of the central meridian, and <math>\varphi_0</math> is the latitude chosen to be the origin at <math>\lambda_0</math>. To avoid division by zero, the formulas above are extended so that if <math>\varphi = 0</math> then <math>x = \lambda</math> and <math>y = 0</math>. | |||
==See also== | |||
{{Portal|Atlas}} | |||
* [[List of map projections]] | |||
==References== | |||
{{reflist}} | |||
==External links== | |||
*{{Mathworld|PolyconicProjection}} | |||
* [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]. | |||
{{Map Projections}} | |||
[[Category:Cartographic projections]] | |||
{{cartography-stub}} | |||
Revision as of 14:39, 1 December 2013
Polyconic can refer either to a class of map projections or to a specific projection known less ambiguously as the American Polyconic. Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. This description applies to projections in equatorial aspect.[1]
As a specific projection, the American Polyconic is conceptualized as "rolling" a cone tangent to the Earth at all parallels of latitude, instead of a single cone as 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 the time of its proposal by Ferdinand Rudolph Hassler in 1825 until the middle of the 20th century.[2]
The projection is defined by:
where is the longitude of the point to be projected; is the latitude of the point to be projected; is the longitude of the central meridian, and is the latitude chosen to be the origin at . To avoid division by zero, the formulas above are extended so that if then and .
See also
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References
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External links
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Here is my web site - cottagehillchurch.com - Table of examples and properties of all common projections, from radicalcartography.net
- An interactive Java Applet to study the metric deformations of the Polyconic Projection.