Bonne Projection

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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.

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