block by robinhouston 6200770

A family of equal-area projections

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There is a family of pseudocylindrical equal-area projections that starts with the cylindrical equal area and ends with the sinusoidal, parameterised by t ∈ [0,1].

The formulas are:

x = λ cos^t φ

y = ∫_0^φ cos^(1-t) φ

where the integral has no closed form in general.

Update: It turns out this family was described, briefly, by Waldo Tolber in 1973: he calls it “a weighted geometrical mean of the meridians from the Lambert and sinusoidal projections”.

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