projected
2007-01-11
true
false
http://www.opengis.net/def/crs/EPSG/0/29701
Tananarive (Paris) / Laborde Grid
May be approximated by Tananarive (Paris) / Laborde Grid approximation - see CRS code 29702.
Madagascar - onshore.
43.18
50.56
-25.64
-11.89
OGP
2014-05-01
false
false
http://www.opengis.net/def/area/EPSG/0/3273
Madagascar - onshore
Large and medium scale topographic mapping and engineering survey.
conversion
IGN Technical Note 74.
2007-01-11
true
false
http://www.opengis.net/def/coordinateOperation/EPSG/0/19861
Laborde Grid
Longitude is referenced to the Paris meridian. Within a few hundred km of origin, may be approximated by Oblique Mercator method - see proj code 19911.
Madagascar - onshore and nearshore.
42.53
51.03
-26.59
-11.69
OGP
2012-04-18
false
false
http://www.opengis.net/def/area/EPSG/0/1149
Madagascar - onshore and nearshore
Large and medium scale topographic mapping and engineering survey.
ISO 1000.
1995-06-02
false
http://www.opengis.net/def/uom/EPSG/0/9001
metre
Also known as International metre. SI standard unit.
length
0
This was the method name used prior to October 2010.
"La nouvelle projection du Service Geographique de Madagascar"; J. Laborde; 1928. Also IGN Paris technical note NT/G 74.
2010-11-02
true
false
true
See information source.
http://www.opengis.net/def/method/EPSG/0/9813
Laborde Oblique Mercator
Note : these formulas have been transcribed from IGN Document NT/G 74. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.
From the defining parameters the following constants for the map projection may be calculated:
B = {1+[e^2 cos^4(phiC)]/(1? e^2)}^0.5
phiS = asin[sin(phiC) / B]
R = a kC {(1?e^2)^0.5 / [1?e^2 sin^2(phiC)]}
C = ln[tan(pi/4+phiS /2)] ? B. ln{tan(pi/4+phiC /2) ([1 ? e sin(phiC)]/[1+e sin(phiC)])^(e/2)}
Forward case: To compute (E,N) from a given (lat,lon)
L = B.(lon?lonC)
q = C + B . ln{tan(pi/4+lat/2) ([1?e sin(lat)] / [1+e sin(lat)])^(e/2)}
P = 2.atan[e ^q] ? pi/2 where e is the base of natural logarithms
U = cos(P).cos(L).cos(phiS) + sin(P).sin(phiS)
V = cos(P).cos(L).sin(phiS) - sin(P).cos(phiS)
W = cos(P).sin(L)
d = (U^2+V^2)^0.5
if d <> 0 then L' = 2.atan(V/(U+d)) and P' = atan(W/d)
if d = 0 then L' = 0 and P' = sign(W).pi/2
H = ?L' + i.ln(tan(pi/4+P'/2)) where i^2 = ?1
G = (1 ? cos(2.alphaC) + i.sin(2.alphaC))/12
E = FE + R . IMAGINARY(H + G.H^3)
N = FN + R . REAL(H + G.H^3)
Reverse case: To compute (lat, lon) from a given (E,N):
G = (1?cos(2.alphaC) + i.sin(2.alphaC))/12 where i^2 = ?1
To solve for Latitude and Longitude, a re-iterative solution is required, where the first two elements are
H0 = (N?FN)/R + i.(E?FE)/R ie k = 0
H1 = H0/(H0 + G.H0^3), i.e. k = 1,
and in subsequent reiterations, k increments by 1
Hk+1 = (H0+2.G.Hk^3)/(3.G.Hk^2+1)
Re-iterate until ABSOLUTE(REAL([H0-Hk-G.Hk^3)])) < 1E-11
L' = ?1.REAL(Hk)
P' = 2.atan{ e ^[IMAGINARY(Hk)]} ? pi/2 where e is the base of natural logarithms.
U' = cos(P').cos(L').cos(phiS) + cos(P').sin(L').sin(phiS)
V' = sin(P')
W' = cos(P').cos(L').sin(phiS) ? cos(P').sin(L').cos(phiS)
d = (U'^2+ V'^2)^0.5
if d <> 0 then L = 2 atan[V'/( U'+d)] and P = atan(W'/d)
if d = 0 then L = 0 and P = SIGN(W') . pi/2
lon = lonC + (L/B)
q' = {ln[tan(pi/4+P/2)] ? C}/B
The final solution for latitude requires a second re-iterative process, where the first element is
lat'(0) = 2.atan(e ^q') ? pi/2 where e is the base of natural logarithms.
And the subsequent elements are
lat'(k) = 2.atan{({1+e.sin[lat(k-1)]} / {1?e.sin[lat(k-1)]})^(e/2).e ^q'} ? pi/2 for K =1 ?
Iterate until ABSOLUTE(lat(k)-lat(k-1)) < 1E-11
lat = lat(k)
-21
EPSG guidance note number 7.
1999-09-09
false
For an oblique projection, this is the latitude of the point at which the azimuth of the central line is defined.
http://www.opengis.net/def/parameter/EPSG/0/8811
Latitude of projection centre
49
EPSG guidance note number 7.
1999-09-09
false
For an oblique projection, this is the longitude of the point at which the azimuth of the central line is defined.
http://www.opengis.net/def/parameter/EPSG/0/8812
Longitude of projection centre
21
EPSG guidance note number 7.
1999-09-09
false
The azimuthal direction (north zero, east of north being positive) of the great circle which is the centre line of an oblique projection. The azimuth is given at the projection centre.
http://www.opengis.net/def/parameter/EPSG/0/8813
Azimuth of initial line
0.9995
EPSG guidance note number 7.
1999-09-09
false
The factor by which the map grid is reduced or enlarged during the projection process, defined by its value at the projection center.
http://www.opengis.net/def/parameter/EPSG/0/8815
Scale factor on initial line
400000
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
800000
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
2004-01-06
true
false
http://www.opengis.net/def/crs/EPSG/0/4810
Tananarive (Paris)
Madagascar - onshore.
43.18
50.56
-25.64
-11.89
OGP
2014-05-01
false
false
http://www.opengis.net/def/area/EPSG/0/3273
Madagascar - onshore
Geodetic survey.
ellipsoidal
OGP
2002-11-18
false
http://www.opengis.net/def/cs/EPSG/0/6403
Ellipsoidal 2D CS. Axes: latitude, longitude. Orientations: north, east. UoM: grads.
Used in geographic 2D coordinate reference systems.
http://www.opengis.net/def/axis/EPSG/0/58
Lat
north
http://www.opengis.net/def/axis/EPSG/0/59
Long
east
geodetic
IGN Paris
2003-12-31
false
http://www.opengis.net/def/datum/EPSG/0/6810
Tananarive 1925 (Paris)
Topographic mapping.
Fundamental point: Tananarive observatory. Latitude: 21.0191667g S, longitude: 50.23849537g E (of Paris)
1925-01-01
Cartesian
OGP
2001-04-29
false
http://www.opengis.net/def/cs/EPSG/0/4530
Cartesian 2D CS. Axes: northing, easting (X,Y). Orientations: north, east. UoM: m.
Used in projected and engineering coordinate reference systems.
http://www.opengis.net/def/axis/EPSG/0/48
X
north
http://www.opengis.net/def/axis/EPSG/0/47
Y
east