The Mollweide projection is a map projection also called the elliptical projection or homolographic equal-area projection. The forward transformation is
(1)
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(2)
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where is given by
(3)
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Newton's method can then be used to compute iteratively from
(4)
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where
(5)
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(Snyder 1987, p. 251) or, better yet,
(6)
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can be used as a first guess.
The inverse formulas are
(7)
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(8)
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where
(9)
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