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Bonne Projection

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BonneProjection

The Bonne projection is a map projection that resembles the shape of a heart. Let phi_1 be the standard parallel, lambda_0 the central meridian, phi be the latitude, and lambda the longitude on a unit sphere. Then

x=rhosinE
(1)
y=cotphi_1-rhocosE,
(2)

where

rho=cotphi_1+phi_1-phi
(3)
E=((lambda-lambda_0)cosphi)/rho.
(4)

The illustrations above show Bonne projections for two different standard parallels.

The inverse formulas are

phi=cotphi_1+phi_1-rho
(5)
lambda=lambda_0+rho/(cosphi)tan^(-1)(x/(cotphi_1-y)),
(6)

where

rho=+/-sqrt(x^2+(cotphi_1-y)^2).
(7)

The Werner projection is a special case of the Bonne projection.

See also

Heart Curve, Map Projection, Werner Projection

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References

MathWorks. "Mapping Toolbox: Bonne Projection." http://www.mathworks.com/access/helpdesk/help/toolbox/map/bonneprojection.shtml.Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, pp. 138-140, 1987.

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Bonne Projection

Cite this as:

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

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