generalized Wagner

Parameters: Note, 0 << a, 0 << b, 0 << m ≤ 1, 0 << m₂ ≤ 1, 0 << n ≤ 1

Classifications

lenticular

Graticule

Meridians: Dependent upon parameterization.
Parallels: Dependent upon parameterization.
Poles: Dependent upon parameterization.
Symmetry: About the central meridian and the equator.

Scale

Dependent upon parameterization.

Distortion

Dependent upon parameterization.

Parameters

The five parameters are denoted a, b, m, m₂, n. They interact with each other in ways not easily describable. In order for the resulting projection to be equal-area, these relations must be enforced:.
m₂ = 1,.
a× b×m×n = 1.

Similar projections

Many projections can be represented as specializations of this very configurable projection, such as Aitoff-Wagner, Hammer-Wagner, Wagner VII, Wagner VIII.

Origin

Rolf Böhm, in 2006, published this generalized system encompassing Karlheinz Wagner’s many projections.

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