Polyconic projection

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 projection 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:

${\displaystyle {\begin{aligned}x&=\cot \varphi \sin {\big (}(\lambda -\lambda _{0})\sin \varphi {\big )}\\y&=\varphi -\varphi _{0}+\cot \varphi {\Big (}1-\cos {\big (}(\lambda -\lambda _{0})\sin \varphi {\big )}{\Big )}\end{aligned}}}$

where λ is the longitude of the point to be projected; φ is the latitude of the point to be projected; λ₀ is the longitude of the central meridian, and φ₀ is the latitude chosen to be the origin at λ₀. To avoid division by zero, the formulas above are extended so that if φ₀ = 0 then x = λ − λ₀ and y = 0.

See also

• List of map projections

References

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.

External links

• Weisstein, Eric W. "Polyconic projection". MathWorld.

• 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.