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:

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

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

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

External links

* [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] .