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Cylindrical Equal-Area Projection

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CylindricalEqualAreaProjection

The map projection having transformation equations

x=(lambda-lambda_0)cosphi_s
(1)
y=sinphisecphi_s
(2)

for the normal aspect, where lambda is the longitude, lambda_0 is the standard longitude (horizontal center of the projection), phi is the latitude, and phi_s is the so-called "standard latitude."

Special cases of cylindrical equal-area projections are summarized in the following table (Maling 1993).

phi_smap projection
0 degreesLambert cylindrical equal-area projection
30 degreesBehrmann cylindrical equal-area projection
37.383 degreesTristan Edwards projection
44.138 degreesPeters projection
45 degreesGall orthographic projection
50 degreesBalthasart projection

The inverse transformation equations for the normal aspect are

phi=sin^(-1)(ycosphi_s)
(3)
lambda=xsecphi_s+lambda_0.
(4)
cyob

An oblique form of the cylindrical equal-area projection is given by the equations

lambda_p=tan^(-1)((cosphi_1sinphi_2coslambda_1-sinphi_1cosphi_2coslambda_2)/(sinphi_1cosphi_2sinlambda_2-cosphi_1sinphi_2sinlambda_1))
(5)
phi_p=tan^(-1)[-(cos(lambda_p-lambda_1))/(tanphi_1)],
(6)

and the inverse formulas are

phi=sin^(-1)(ysinphi_p+sqrt(1-y^2)cosphi_psinx)
(7)
lambda=lambda_0+tan^(-1)((sqrt(1-y^2)sinphi_psinx-ycosphi_p)/(sqrt(1-y^2)cosx)).
(8)
cytr

A transverse form of the cylindrical equal-area projection is given by the equations

x=cosphisin(lambda-lambda_0)
(9)
y=tan^(-1)[(tanphi)/(cos(lambda-lambda_0))]-phi_0,
(10)

and the inverse formulas are

phi=sin^(-1)[sqrt(1-x^2)sin(y+phi_0)]
(11)
lambda=lambda_0+tan^(-1)[x/(sqrt(1-x^2))cos(y+phi_0)].
(12)

See also

Balthasart Projection, Behrmann Cylindrical Equal-Area Projection, Cylindrical Equidistant Projection, Equal-Area Projection, Gall Orthographic Projection, Lambert Cylindrical Equal-Area Projection, Peters Projection Tristan Edwards Projection

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References

Maling, D. H. Coordinate Systems and Map Projections, 2nd ed., rev. Woburn, MA: Butterworth-Heinemann, 1993.Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, pp. 76-85, 1987.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 221-222, 1999.

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Cylindrical Equal-Area Projection

Cite this as:

Weisstein, Eric W. "Cylindrical Equal-Area Projection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CylindricalEqual-AreaProjection.html

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