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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.Lee, L. P. "The Nomenclature and Classification of Map Projections." Empire Survey Rev. 7, 190-200, 1944.Schott, C. A. and Hunt, E. B. "Tables for Projecting Maps, with Notes on Map Projections." Appendix 39 in Report for the U.S. Coast Survey. Washington, DC: U.S. Coast Survey, pp. 96-163, 1854.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, France: Gauthier-Villars, 1881.

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Polyconic Projection

Cite this as:

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

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