Average of Hammer (Hammer-Aitoff) and Gall-Peters

[Sorea]

Please show me an example of the arithmetic mean of Hammer (Hammer-Aitoff) and Gall-Peters (cylindrical equal-area, std. par. 45°) projections (to resemble Winkel Tripel but equal-area)

[daan]

In general linear combinations of two equal-area projections do not result in an equal-area projection. Arithmetic mean is a simple case of a linear combination, and it will not yield an equal-area projection in this case.

Regards,
— daan

[Piotr]

I had a similar idea later, but with Smyth equal-surface instead of Hammer. There is an equal-area blending function now, but it produces a curved pole line, like in the Wagner projections. Swapping the projections (Hammer to Smyth) results in a pointed pole, with nearby areas being stretched to form more and more of a rectangle.

[Piotr]

Such a projection has low area distortion throughout the majority of Earth, however there is notorious area distortion near the poles.