projected
Microsoft.
2009-02-09
true
false
http://www.opengis.net/def/crs/EPSG/0/3857
WGS 84 / Pseudo-Mercator
Uses spherical development of ellipsoidal coordinates. Relative to an ellipsoidal development errors of up to 800 metres in position and 0.7 percent in scale may arise. It is not a recognised geodetic system: see WGS 84 / World Mercator (CRS code 3395).
World between 85.06°S and 85.06°N.
-180
180
-85.06
85.06
OGP
2014-05-01
false
false
http://www.opengis.net/def/area/EPSG/0/3544
World - 85°S to 85°N
Web map tile service latitude limit is +/- 85.05112878°.
Certain Web mapping and visualisation applications.
conversion
Microsoft
2009-02-09
true
false
http://www.opengis.net/def/coordinateOperation/EPSG/0/3856
Popular Visualisation Pseudo-Mercator
World.
-180
180
-90
90
OGP
2001-06-05
false
false
http://www.opengis.net/def/area/EPSG/0/1262
World
Web mapping and visualisation.
OGP Guidance Note 7-2
2009-06-07
true
false
true
For Projected Coordinate Reference System: WGS 84 / Pseudo-Mercator
Parameters:
Ellipsoid: WGS 84 a = 6378137.0 metres 1/f = 298.2572236
Latitude of natural origin (latO) = 0°00'00.000"N = 0.0 rad
Longitude of natural origin (lonO) = 0°00'00.000"E = 0.0 rad
False easting (FE) = 0.00 metres
False northing (FN) = 0.00 metres
Forward calculation for the same coordinate values as used for the Mercator (1SP) (Spherical) example (method code 9841):
Latitude (lat) = 24°22'54.433"N = 0.425542460 rad
Longitude (lon) = 100°20'00.000"W = -1.751147016 rad
R = 6378137.0
whence
E = -11 169 055.58 m
N = 2 800 000.00 m
and
h = 1.1034264
k = 1.0972914
omega = 0°19'10.01"
Reverse calculation for a point 10km north on the grid (-11 169 055.58 m E, 2 810 000.00m N) first gives:
D = -0.44056752
Then Latitude (lat) = 0.426970023 rad = 24°27'48.889"N
Longitude (lon) = -1.751147016 rad = 100°20'00.000"W
http://www.opengis.net/def/method/EPSG/0/1024
Popular Visualisation Pseudo Mercator
Applies spherical formulas to the ellipsoid. As such does not have the properties of a true Mercator 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.
This method is utilised by some popular web mapping and visualisation applications. It applies standard Mercator (Spherical) formulas (method code 1026) to ellipsoidal coordinates and the sphere radius is taken to be the semi-major axis of the ellipsoid. This approach only approximates to the more rigorous application of ellipsoidal formulas to ellipsoidal coordinates (as given in EPSG dataset coordinate operation method codes 9804 and 9805). Unlike either the spherical or ellipsoidal Mercator projection methods, this method is not conformal: scale factor varies as a function of azimuth, which creates angular distortion. Despite angular distortion there is no convergence in the meridian.
The formulas to derive projected Easting and Northing coordinates from ellipsoidal latitude (lat) and longitude (lon) first derive the radius of the sphere (R) from:
R = a
Then applying spherical Mercator formulae:
E = FE + R(lon - lonO)
N = FN + R ln[tan(pi/4 + lat/2)]
where FE and FN are false easting and false nothing at the projection origin, other symbols are as listed above and logarithms are natural.
If latitude lat = 90º, N is infinite. The above formula for N will fail near to the pole, and should not be used poleward of 88º.
The reverse formulas to derive latitude and longitude on the sphere from E and N values are:
D = -(N-FN)/R = (FN-N)/R
lat = pi/2 - 2 atan(e^D) where e=base of natural logarithms, 2.7182818...
lon = [(E - FE)/R] + lonO
If q_alpha is the scale factor at a given azimuth alpha, it is a function of R', the radius of curvature at that azimuth derived from:
R' = rho nu / (nu cos^2alpha + rho sin^2alpha)
q_alpha = R / (R' cos lat)
where rho and nu are the radii of curvature of the ellipsoid at latitude lat in the plane of the meridian and perpendicular to the meridian respectively;
rho = a(1 - e^2)/(1 - e^2 sin^2(lat))^3/2
nu = a /(1 - e^2 sin^2(lat))^1/2
Then when the azimuth is 0º, 180º, 90º or 270º the scale factors in the meridian (h) and on the parallel (k) are:
q_0 = q_180 = h = R / (rho cos(lat))
q_90 = q_270 = k = R / (nu cos(lat))
which demonstrates the non-conformallity of the Pseudo Mercator method.
Maximum angular distortion omega is a function of latitude and is found from:
omega = 2 asin{[ABS(h - k)] / (h + k)}
0
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
0
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
0
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
0
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
geographic 2D
EPSG. See 3D CRS for original information source.
2007-08-27
true
false
http://www.opengis.net/def/crs/EPSG/0/4326
WGS 84
World.
-180
180
-90
90
OGP
2001-06-05
false
false
http://www.opengis.net/def/area/EPSG/0/1262
World
Horizontal component of 3D system. Used by the GPS satellite navigation system and for NATO military geodetic surveying.
ellipsoidal
OGP
2008-06-23
false
http://www.opengis.net/def/cs/EPSG/0/6422
Ellipsoidal 2D CS. Axes: latitude, longitude. Orientations: north, east. UoM: degree
Coordinates referenced to this CS are in degrees. Any degree representation (e.g. DMSH, decimal, etc.) may be used but that used must be declared for the user by the supplier of data. Used in geographic 2D coordinate reference systems.
http://www.opengis.net/def/axis/EPSG/0/106
Lat
north
http://www.opengis.net/def/axis/EPSG/0/107
Long
east
geodetic
NIMA TR8350.2 June 2004 revision. http://earth-info.nga.mil/GandG/publications/tr8350.2/tr8350_2.html and
http://gis-lab.info/docs/nima-tr8350.2-addendum.pdf
2013-06-15
true
false
http://www.opengis.net/def/datum/EPSG/0/6326
World Geodetic System 1984
EPSG::6326 has been the then current realisation. No distinction is made between the original and subsequent (G730, G873, G1150 and G1674) WGS 84 frames. Since 1997, WGS 84 has been maintained within 10cm of the then current ITRF.
Satellite navigation.
Defined through a consistent set of station coordinates. These have changed with time: by 0.7m on 29/06/1994 (G730), a further 0.2m on 29/01/1997 (G873) and a further 0.06m on 20/01/2002 (G1150) and on 8/02/2012 (G1674).
1984-01-01
Cartesian
OGP
2001-04-29
false
http://www.opengis.net/def/cs/EPSG/0/4499
Cartesian 2D CS. Axes: easting, northing (X,Y). Orientations: east, north. UoM: m.
Used in projected and engineering coordinate reference systems.
http://www.opengis.net/def/axis/EPSG/0/41
X
east
http://www.opengis.net/def/axis/EPSG/0/42
Y
north