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