Polyconic projection
Encyclopedia
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.
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.
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 
.
Map projection
A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...
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.
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
Ferdinand Rudolph Hassler
Ferdinand Rudolph Hassler was a surveyor who worked mostly in the United States and also in Switzerland. He headed the United States Coast Survey and the Bureau of Weights and Measures.-Biography:...
in 1825 until the middle of the 20th century.
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 .