and φ is the latitude, λ is the longitude from the central meridian, and φ1 is the given parallel of the projection which determines its shape, all in radians.
The inverse projection is then given by:
where
Parallels (i.e. lines of latitude) are concentric
elliptical arcs of constant
eccentricity equal to cos φ1, centred on the
north pole. On the central
meridian, shapes are not distorted, but elsewhere they are. Different projections can be produced by altering the eccentricity of the arcs, making it vary between the
sinusoidal projection and the
Werner projection. For larger values of φ1, it produces a heart shape.[2]
It was introduced by
Henry Bottomley as an alternative to the
Bonne projection to reduce the extent of extreme distortion at the edges and give a more satisfying overall shape.
Cybergeo article: Between the Sinusoidal projection and the Werner: an alternative to the Bonne (Une alternative à la projection cartographique de Bonne), Henry Bottomley, 2003