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.

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.


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