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Polyconic Projection

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PolyconicProjection

A class of map projections in which the parallels are represented by a system of non-concentric circular arcs with centers lying on the straight line representing the central meridian (Lee 1944). The term was first applied by Hunt, and later extended by Tissot (1881).

x=cotphisinE
(1)
y=(phi-phi_0)+cotphi(1-cosE),
(2)

where

E=(lambda-lambda_0)sinphi.
(3)

The inverse formulas are

lambda=(sin^(-1)(xtanphi))/(sinphi)+lambda_0,
(4)

and phi is determined from

Deltaphi=-(A(phitanphi+1)-phi-1/2(phi^2+B)tanphi)/((phi-A)/(tanphi)-1),
(5)

starting with the initial vale phi_n=A and defining

A=phi_0+y
(6)
B=x^2+A^2.
(7)

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References

Beaman, W. M. Topographic Mapping. Washington, DC: U. S. Geol. Survey Bull. 788-E, p. 167, 1928.Birdseye, C. H. Formulas and Tables for the Construction of Polyconic Projections. U. S. Geological Survey, Bulletin 809, 1929.Hunt. Appendix 39 in Report for the U.S. Coast and Geodetic Survey. 1853.Lee, L. P. "The Nomenclature and Classification of Map Projections." Empire Survey Rev. 7, 190-200, 1944.Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, pp. 124-137, 1987.Tissot, A. Mémoir sur la représentation des surfaces et les projections des cartes géographiques. Paris: Gauthier-Villars, 1881.

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Polyconic Projection

Cite this as:

Weisstein, Eric W. "Polyconic Projection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PolyconicProjection.html

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