projected
This identifier is as used by the information source but has been superseded by the INSPIRE identifier.
European Commission Joint Research Centre "Map Projections for Europe". http://www.ec-gis.org
2012-11-26
true
false
http://www.foodie-cloud.org/def/crs/EPSG/0/3035
ETRS89 / LAEA Europe
Use ETRS89 / LCC (code 3034) for conformal mapping at 1:500,000 scale or smaller or ETRS89 / UTM (codes 25828-37 or 3040-49) for conformal mapping at scales larger than 1:500,000.
Europe - onshore and offshore: Albania; Andorra; Austria; Belgium; Bosnia and Herzegovina; Bulgaria; Croatia; Cyprus; Czech Republic; Denmark; Estonia; Faroe Islands; Finland; France; Germany; Gibraltar; Greece; Hungary; Ireland; Italy; Latvia; Liechtenstein; Lithuania; Luxembourg; Macedonia; Malta; Monaco; Montenegro; Netherlands; Norway including Svalbard and Jan Mayen; Poland; Portugal; Romania; San Marino; Serbia; Slovakia; Slovenia; Spain; Sweden; Switzerland; United Kingdom (UK) including Channel Islands and Isle of Man; Vatican City State.
-16.1
39.65
32.88
84.17
OGP
2014-05-01
false
false
http://www.opengis.net/def/area/EPSG/0/1298
Europe - ETRS89
Single CRS for all Europe. Used for statistical mapping at all scales and other purposes where true area representation is required.
conversion
European Commission Joint Research Centre "Map Projections for Europe". http://www.ec-gis.org
2010-03-01
true
false
http://www.opengis.net/def/coordinateOperation/EPSG/0/19986
Europe Equal Area 2001
LCC (code 19985) used for conformal mapping.
Europe - European Union (EU) countries and candidates. Europe - onshore and offshore: Albania; Andorra; Austria; Belgium; Bosnia and Herzegovina; Bulgaria; Croatia; Cyprus; Czech Republic; Denmark; Estonia; Faroe Islands; Finland; France; Germany; Gibraltar; Greece; Hungary; Iceland; Ireland; Italy; Latvia; Liechtenstein; Lithuania; Luxembourg; Macedonia; Malta; Monaco; Montenegro; Netherlands; Norway including Svalbard and Jan Mayen; Poland; Portugal including Madeira and Azores; Romania; San Marino; Serbia; Slovakia; Slovenia; Spain including Canary Islands; Sweden; Switzerland; Turkey; United Kingdom (UK) including Channel Islands and Isle of Man; Vatican City State.
-35.58
44.83
24.60
84.17
OGP
2014-05-01
false
false
http://www.opengis.net/def/area/EPSG/0/2881
Europe - LCC & LAEA
Single projection for all Europe. Used for statistical mapping at all scales and other purposes where true area representation is required.
USGS Professional Paper 1395, "Map Projections - A Working Manual" by John P. Snyder.
2007-01-12
false
true
For Projected Coordinate Reference System: ETRS89 / ETRS-LAEA
Parameters:
Ellipsoid:GRS 1980 a = 6378137.0 metres 1/f = 298.2572221
then e = 0.081819191
Latitude of natural origin (latO): 52°00'00.000"N = 0.907571211 rad
Longitude of natural origin (lonO): 10°00'00.000"E = 0.174532925 rad
False easting (FE): 4321000.00 metres
False northing (FN) 3210000.00 metres
Forward calculation for:
Latitude (lat) = 50°00'00.000"N = 0.872664626 rad
Longitude(lon) = 5°00'00.000"E = 0.087266463 rad
First gives
qP = 1.995531087
qO = 1.569825704
q = 1.525832247
Rq = 6371007.181
betaO = 0.905397517
beta = 0.870458708
D = 1.000425395
B = 6374393.455
whence
E = 3962799.45 m
N = 2999718.85 m
Reverse calculation for the same Easting and Northing (3962799.45 E, 2999718.85 N) first gives:
rho = 415276.208
C = 0.065193736
beta' = 0.870458708
Then Latitude = 50°00'00.000"N
Longitude = 5°00'00.000"E
http://www.opengis.net/def/method/EPSG/0/9820
Lambert Azimuthal Equal Area
This is the ellipsoidal form of the projection.
Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.
Oblique aspect
To derive the projected coordinates of a point, geodetic latitude (lat) is converted to authalic latitude (ß). The formulae to convert geodetic latitude and longitude (lat,lon) to Easting and Northing are:
Easting, E = FE + {(B . D) . [cos ß . sin(lon ? lonO)]}
Northing, N = FN + (B / D) . {(cos ßO . sin ß) ? [sin ßO . cos ß . cos(lon ? lonO)]}
where
B = Rq . (2 / {1 + sin ßO . sin ß + [cos ßO . cos ß . cos(lon ? lonO)]})^0.5
D = a . [cos latO / (1 ? e2 sin2 latO)^0.5] / (Rq . cos ßO)
Rq = a . (qP / 2)^0.5
ß = asin (q / qP)
ßO = asin (qO / qP)
q = (1 ? e^2) . ([sin(lat) / (1 ? e^2 sin^2(lat))] ? {[1/(2e)] . ln [(1 ? e sin(lat)) / (1 + e sin(lat))]})
qO = (1 ? e^2) . ([sin(latO) / (1 ? e^2 sin^2(latO))] ? {[1/(2e)] . ln [(1 ? e sin(latO)) / (1 + e sin(latO))]})
qP = (1 ? e^2) . ([sin(latP) / (1 ? e^2 sin^2(latP))] ? {[1/(2e)] . ln [(1 ? e sin(latP)) / (1 + e sin(latP))]})
where *P = p/2 radians, thus
qP = (1 ? e^2) . ([1 / (1 ? e^2)] ? {[1/(2e)] . ln [(1 ? e) / (1 + e)]})
The reverse formulas to derive the geodetic latitude and longitude of a point from its Easting and Northing values are:
lat = ß' + [(e^2/3 + 31e^4/180 + 517e^6/5040) . sin 2ß'] + [(23e^4/360 + 251e^6/3780) . sin 4ß'] + [(761e^6/45360) . sin 6ß']
lon = lonO + atan {(E-FE) . sin C / [D. rho . cos ßO . cos C ? D^2. (N-FN) . sin ßO . sin C]}
where
ß' = asin{(cosC . sin ßO) + [(D . (N-FN) . sinC . cos ßO) / rho]}
C = 2 . asin(rho / 2 . Rq)
rho = {[(E-FE)/D]^2 + [D . (N ?FN)]^2}^0.5
and D, Rq, and ßO are as in the forward equations.
Polar aspect
For the polar aspect of the Lambert Azimuthal Equal Area projection, some of the above equations are indeterminate. Instead, for the forward case from latitude and longitude (lat, lon) to Easting (E) and Northing (N):
For the north polar case:
Easting, E = FE + [rho sin(lon ? lonO)]
Northing, N = FN ? [rho cos(lon ? lonO)]
where
rho = a (qP ? q)^0.5
and qP and q are found as for the general case above.
For the south polar case:
Easting, E = FE + [rho . sin(lon ? lonO)]
Northing, N = FN + [rho . cos(lon ? lonO)]
where
rho = a (qP + q)^0.5
and qP and q are found as for the general case above.
For the reverse formulas to derive the geodetic latitude and longitude of a point from its Easting and Northing:
lat = ß' + [(e^2/3 + 31e^4/180 + 517e^6/5040) sin 2ß'] + [(23e^4/360 + 251e^6/3780) sin 4ß'] + [(761e^6/45360) sin 6ß']
as for the oblique case, but where
ß' = ±asin [1? rho^2 / (a^2{1? [(1? e^2)/2e)) ln[(1-e)/(1+ e)]})], taking the sign of latO
and rho = {[(E ?FE)]^2 + [(N ? FN)]^2}^0.5
Then
lon = lonO + atan [(E ?FE)] / (N ?FN)] for the south pole case
and
lon = lonO + atan [(E ?FE)] / ? (N ?FN)] for the north pole case.
2
2
52
EPSG guidance note number 7.
1999-09-09
false
The latitude of the point from which the values of both the geographical coordinates on the ellipsoid and the grid coordinates on the projection are deemed to increment or decrement for computational purposes. Alternatively it may be considered as the latitude of the point which in the absence of application of false coordinates has grid coordinates of (0,0).
http://www.opengis.net/def/parameter/EPSG/0/8801
Latitude of natural origin
10
Abbeviated as "CM".
Abbreviation for "Central Meridian".
EPSG guidance note number 7.
2002-06-22
false
The longitude of the point from which the values of both the geographical coordinates on the ellipsoid and the grid coordinates on the projection are deemed to increment or decrement for computational purposes. Alternatively it may be considered as the longitude of the point which in the absence of application of false coordinates has grid coordinates of (0,0). Sometimes known as "central meridian (CM)".
http://www.opengis.net/def/parameter/EPSG/0/8802
Longitude of natural origin
4321000
This alias applies only in the case of projection methods which have an axis positive west, e.g. Transverse Mercator (South Orientated).
EPSG guidance note number 7.
2002-07-31
false
Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Easting, FE, is the value assigned to the abscissa (east or west) axis of the projection grid at the natural origin.
http://www.opengis.net/def/parameter/EPSG/0/8806
False easting
3210000
This alias applies only in the case of projection methods which have an axis positive south, e.g. Transverse Mercator (South Orientated).
EPSG guidance note number 7.
2002-07-31
false
Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Northing, FN, is the value assigned to the ordinate (north or south) axis of the projection grid at the natural origin.
http://www.opengis.net/def/parameter/EPSG/0/8807
False northing
Cartesian
OGP
2001-04-29
false
http://www.opengis.net/def/cs/EPSG/0/4532
Cartesian 2D CS. Axes: northing, easting (Y,X). Orientations: north, east. UoM: m.
Used in projected and engineering coordinate reference systems.
http://www.opengis.net/def/axis/EPSG/0/52
Y
north
http://www.opengis.net/def/axis/EPSG/0/51
X
east