Polyconic projection

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American polyconic projection of the world

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:

x = \cot(\varphi) \sin((\lambda - \lambda_0)\sin(\varphi))\,
y = \varphi-\varphi_0 + \cot(\varphi) (1 - \cos((\lambda - \lambda_0)\sin(\varphi)))\,

where \lambda is the longitude of the point to be projected; \varphi is the latitude of the point to be projected; \lambda_0 is the longitude of the central meridian, and \varphi_0 is the latitude chosen to be the origin at \lambda_0. To avoid division by zero, the formulas above are extended so that if \varphi = 0 then x = \lambda - \lambda_0 and y = 0.

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References[edit]

  1. ^ An Album of Map Projections (US Geological Survey Professional Paper 1453), John P. Snyder & Philip M. Voxland, 1989, p. 4.
  2. ^ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 117-122, ISBN 0-226-76747-7.

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