“Eckert IV projection”的意思、由来-开放百科全书

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Eckert IV projection

释义

Formulas
Forward formulae Inverse formulae
See also
References
External links

The Eckert IV projection is an equal-area pseudocylindrical map projection. The length of the polar lines is half that of the equator, and lines of longitude are semiellipses, or portions of ellipses. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. In each pair, the meridians have the same shape, and the odd-numbered projection has equally spaced parallels, whereas the even-numbered projection has parallels spaced to preserve area. The pair to Eckert IV is the Eckert III projection.

Formulas

Forward formulae

Given a radius of sphere R, central meridian λ{{sub|0}} and a point with geographical latitude φ and longitude λ, plane coordinates x and y can be computed using the following formulas:

where

θ can be solved for numerically using Newton's method.^[2]

Inverse formulae

References

1. ^¹{{cite book | title = Map Projections – A Working Manual | last = Snyder | first = John P. | authorlink = John P. Snyder | year = 1987 | publisher = USGS | location = Denver | series = Professional Paper 1395 | isbn = 0-226-76747-7 | pages = 253–258 | url = https://pubs.er.usgs.gov/usgspubs/pp/pp1395 | accessdate = 2013-07-24 }}

^[1]
}}

External links

Eckert IV projection at Mathworld

2 : Map projections|Equal-area projections

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Formulas

Forward formulae

Inverse formulae

See also

References

External links