USGS Professional Paper 1395, "Map Projections - A Working Manual" by John P. Snyder.
2009-06-07
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See information source.
urn:ogc:def:method:EPSG::9834
Lambert Cylindrical Equal Area (Spherical)
This is the spherical form of the projection. See coordinate operation method Lambert Cylindrical Equal Area (code 9835) for ellipsoidal form. Differences of several tens of metres result from comparison of the two methods.
For the forward calculation for the normal aspect of the projection in which lat1 is the latitude of the standard parallel:
E = FE R (lon – lonO) cos(lat1)
N = FN R sin(lat) / cos(lat1)
where lat1, lat and lon are expressed in radians
R is the radius of the sphere and will normally be one of the CRS parameters. If the figure of the earth used is an ellipsoid rather than a sphere then R should be calculated as the radius of the authalic sphere using the formula for RA given in EPSG Guidance Note 7-2, section 1.2, table 3.
For the reverse calculation:
lat = asin{[(N – FN) / R] cos(lat1)}
lon = lonO {[E – FE] / [R cos(lat1)]}
where R is as for the forward method.
See information source for formulas for oblique and polar aspects and examples.