**By: Jason Davies**

JasonDavies.com

The globe is divided into a number of lunes, in this case six lunes, with the vertices of the lunes being at the projection’s origin (near Chicago) and its antipode.

The central portion is projected using the azimuthal equidistant projection, up to a given distance from the origin, in this case 30°. The remainder is cut along the lune boundaries outside this 30° circle, and the resulting gores are flattened.

The flattening of the lunes is the tricky (fun) part to implement. Gingery gives equations for the boundaries of the lunes in projected Cartesian coordinates. I have simplified them slightly by taking the origin to be the centre of the small circle, rather than the centre of the lune:

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