# Coverage for pygeodesy/datum.py : 98%

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1422 | # -*- coding: utf-8 -*- u'''Classes L{Datum}, L{Ellipsoid} and L{Transform} and registries thereof L{Datums}, L{Ellipsoids} and L{Transforms}, respectively. Pure Python implementation of geodesy tools for ellipsoidal earth models, including datums and ellipsoid parameters for different geographic coordinate systems and methods for converting between them and to cartesian coordinates. Transcribed from JavaScript originals by I{(C) Chris Veness 2005-2016} and published under the same MIT Licence**, see U{latlon-ellipsoidal.js <https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}. Historical geodetic datums: a latitude/longitude point defines a geographic location on or above/below the earth’s surface, measured in degrees from the equator and the International Reference Meridian and meters above the ellipsoid, and based on a given datum. The datum is based on a reference ellipsoid and tied to geodetic survey reference points. Modern geodesy is generally based on the WGS84 datum (as used for instance by GPS systems), but previously various reference ellipsoids and datum references were used. The UK Ordnance Survey National Grid References are still based on the otherwise historical OSGB36 datum, q.v. U{Ordnance Survey 'A guide to coordinate systems in Great Britain', Section 6<https://www.OrdnanceSurvey.co.UK/docs/support/ guide-coordinate-systems-great-britain.pdf>}. @newfield example: Example, Examples @var Datums.BD72: Datum(name='BD72', ellipsoid=Ellipsoids.Intl1924, transform=Transforms.BD72) @var Datums.DHDN: Datum(name='DHDN', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.DHDN) @var Datums.ED50: Datum(name='ED50', ellipsoid=Ellipsoids.Intl1924, transform=Transforms.ED50) @var Datums.GDA2020: Datum(name='GDA2020', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84) @var Datums.GRS80: Datum(name='GRS80', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84) @var Datums.Irl1975: Datum(name='Irl1975', ellipsoid=Ellipsoids.AiryModified, transform=Transforms.Irl1975) @var Datums.Krassovski1940: Datum(name='Krassovski1940', ellipsoid=Ellipsoids.Krassovski1940, transform=Transforms.Krassovski1940) @var Datums.Krassowsky1940: Datum(name='Krassowsky1940', ellipsoid=Ellipsoids.Krassowsky1940, transform=Transforms.Krassowsky1940) @var Datums.MGI: Datum(name='MGI', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.MGI) @var Datums.NAD27: Datum(name='NAD27', ellipsoid=Ellipsoids.Clarke1866, transform=Transforms.NAD27) @var Datums.NAD83: Datum(name='NAD83', ellipsoid=Ellipsoids.GRS80, transform=Transforms.NAD83) @var Datums.NTF: Datum(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF) @var Datums.OSGB36: Datum(name='OSGB36', ellipsoid=Ellipsoids.Airy1830, transform=Transforms.OSGB36) @var Datums.Potsdam: Datum(name='Potsdam', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.Bessel1841) @var Datums.Sphere: Datum(name='Sphere', ellipsoid=Ellipsoids.Sphere, transform=Transforms.WGS84) @var Datums.TokyoJapan: Datum(name='TokyoJapan', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.TokyoJapan) @var Datums.WGS72: Datum(name='WGS72', ellipsoid=Ellipsoids.WGS72, transform=Transforms.WGS72) @var Datums.WGS84: Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84) @var Ellipsoids.Airy1830: Ellipsoid(name='Airy1830', a=6377563.396, b=6356256.909, f_=299.3249646, f=0.003340851, e=0.081673374, e2=0.00667054, e12=0.99332946, e22=0.006715335, n=0.00167322, R1=6370461.233666666, R2=6370459.654589442, R3=6370453.309866445, Rr=6366914.608805893, Rs=6366901.239881964) @var Ellipsoids.AiryModified: Ellipsoid(name='AiryModified', a=6377340.189, b=6356034.448, f_=299.3249646, f=0.003340851, e=0.081673374, e2=0.00667054, e12=0.99332946, e22=0.006715335, n=0.00167322, R1=6370238.275333334, R2=6370236.696361165, R3=6370230.351810658, Rr=6366691.774649803, Rs=6366678.406194146) @var Ellipsoids.Australia1966: Ellipsoid(name='Australia1966', a=6378160, b=6356774.719, f_=298.25, f=0.003352892, e=0.08182018, e2=0.006694542, e12=0.993305458, e22=0.006739661, n=0.001679261, R1=6371031.573, R2=6371029.982388151, R3=6371023.591178183, Rr=6367471.848433915, Rs=6367458.38162583) @var Ellipsoids.Bessel1841: Ellipsoid(name='Bessel1841', a=6377397.155, b=6356078.962818, f_=299.1528128, f=0.003342773, e=0.081696831, e2=0.006674372, e12=0.993325628, e22=0.006719219, n=0.001674185, R1=6370291.090939333, R2=6370289.510126558, R3=6370283.158215224, Rr=6366742.520233163, Rs=6366729.136254413) @var Ellipsoids.CPM1799: Ellipsoid(name='CPM1799', a=6375738.7, b=6356671.92557493, f_=334.39, f=0.00299052, e=0.077279343, e2=0.005972097, e12=0.994027903, e22=0.006007977, n=0.001497499, R1=6369383.108524977, R2=6369381.843415799, R3=6369376.762470212, Rr=6366208.881847335, Rs=6366198.174663714) @var Ellipsoids.Clarke1866: Ellipsoid(name='Clarke1866', a=6378206.4, b=6356583.8, f_=294.978698214, f=0.003390075, e=0.082271854, e2=0.006768658, e12=0.993231342, e22=0.006814785, n=0.001697916, R1=6370998.866666667, R2=6370997.240632997, R3=6370990.706598808, Rr=6367399.689168951, Rs=6367385.921655473) @var Ellipsoids.Clarke1880: Ellipsoid(name='Clarke1880', a=6378249.145, b=6356514.86954978, f_=293.465, f=0.003407561, e=0.0824834, e2=0.006803511, e12=0.993196489, e22=0.006850116, n=0.001706689, R1=6371004.386516593, R2=6371002.743669633, R3=6370996.141916499, Rr=6367386.643979664, Rs=6367372.733858579) @var Ellipsoids.Clarke1880IGN: Ellipsoid(name='Clarke1880IGN', a=6378249.2, b=6356515, f_=293.466021294, f=0.00340755, e=0.082483257, e2=0.006803488, e12=0.993196512, e22=0.006850092, n=0.001706683, R1=6371004.466666666, R2=6371002.823831111, R3=6370996.22212394, Rr=6367386.736672513, Rs=6367372.826648208) @var Ellipsoids.Clarke1880Mod: Ellipsoid(name='Clarke1880Mod', a=6378249.145, b=6356514.96582849, f_=293.4663, f=0.003407546, e=0.082483218, e2=0.006803481, e12=0.993196519, e22=0.006850086, n=0.001706681, R1=6371004.418609496, R2=6371002.775777077, R3=6370996.174082516, Rr=6367386.692077904, Rs=6367372.782080163) @var Ellipsoids.Delambre1810: Ellipsoid(name='Delambre1810', a=6376428, b=6355957.92616372, f_=311.5, f=0.003210273, e=0.080063974, e2=0.00641024, e12=0.99358976, e22=0.006451596, n=0.001607717, R1=6369604.642054573, R2=6369603.184197493, R3=6369597.327390675, Rr=6366197.076842674, Rs=6366184.735554905) @var Ellipsoids.Engelis1985: Ellipsoid(name='Engelis1985', a=6378136.05, b=6356751.32272154, f_=298.2566, f=0.003352818, e=0.081819276, e2=0.006694394, e12=0.993305606, e22=0.006739511, n=0.001679224, R1=6371007.807573847, R2=6371006.217070852, R3=6370999.826135725, Rr=6367448.175078915, Rs=6367434.70891814) @var Ellipsoids.Everest1969: Ellipsoid(name='Everest1969', a=6377295.664, b=6356094.667915, f_=300.8017, f=0.003324449, e=0.081472981, e2=0.006637847, e12=0.993362153, e22=0.006682202, n=0.001664992, R1=6370228.665305, R2=6370227.101785341, R3=6370220.819516171, Rr=6366699.578394239, Rs=6366686.341077896) @var Ellipsoids.Fisher1968: Ellipsoid(name='Fisher1968', a=6378150, b=6356768.33724438, f_=298.3, f=0.00335233, e=0.081813334, e2=0.006693422, e12=0.993306578, e22=0.006738525, n=0.001678979, R1=6371022.77908146, R2=6371021.189037352, R3=6371014.799950343, Rr=6367463.656043012, Rs=6367450.193774211) @var Ellipsoids.GEM10C: Ellipsoid(name='GEM10C', a=6378137, b=6356752.31424783, f_=298.2572236, f=0.003352811, e=0.081819191, e2=0.00669438, e12=0.99330562, e22=0.006739497, n=0.00167922, R1=6371008.771415944, R2=6371007.180919358, R3=6371000.790010039, Rr=6367449.145823942, Rs=6367435.679717519) @var Ellipsoids.GRS67: Ellipsoid(name='GRS67', a=6378160, b=6356774.516, f_=298.247167427, f=0.003352924, e=0.081820568, e2=0.006694605, e12=0.993305395, e22=0.006739725, n=0.001679277, R1=6371031.505333333, R2=6371029.914708731, R3=6371023.523359839, Rr=6367471.747019209, Rs=6367458.279955242) @var Ellipsoids.GRS80: Ellipsoid(name='GRS80', a=6378137, b=6356752.314140347, f_=298.257222101, f=0.003352811, e=0.081819191, e2=0.00669438, e12=0.99330562, e22=0.006739497, n=0.00167922, R1=6371008.771380115, R2=6371007.180883513, R3=6371000.789974131, Rr=6367449.145770246, Rs=6367435.679663688) @var Ellipsoids.Helmert1906: Ellipsoid(name='Helmert1906', a=6378200, b=6356818.16962789, f_=298.3, f=0.00335233, e=0.081813334, e2=0.006693422, e12=0.993306578, e22=0.006738525, n=0.001678979, R1=6371072.723209296, R2=6371071.133152724, R3=6371064.744015628, Rr=6367513.572269944, Rs=6367500.10989561) @var Ellipsoids.IERS1989: Ellipsoid(name='IERS1989', a=6378136, b=6356751.302, f_=298.257, f=0.003352813, e=0.081819221, e2=0.006694385, e12=0.993305615, e22=0.006739502, n=0.001679222, R1=6371007.767333333, R2=6371006.176906484, R3=6370999.785917024, Rr=6367448.139705879, Rs=6367434.673581903) @var Ellipsoids.IERS1992TOPEX: Ellipsoid(name='IERS1992TOPEX', a=6378136.3, b=6356751.61659215, f_=298.257223563, f=0.003352811, e=0.081819191, e2=0.00669438, e12=0.99330562, e22=0.006739497, n=0.00167922, R1=6371008.072197382, R2=6371006.481700972, R3=6371000.090792353, Rr=6367448.446995611, Rs=6367434.980890662) @var Ellipsoids.IERS2003: Ellipsoid(name='IERS2003', a=6378136.6, b=6356751.85797165, f_=298.25642, f=0.00335282, e=0.081819301, e2=0.006694398, e12=0.993305602, e22=0.006739515, n=0.001679225, R1=6371008.352657217, R2=6371006.762152168, R3=6371000.371208764, Rr=6367448.71770978, Rs=6367435.251531576) @var Ellipsoids.Intl1924: Ellipsoid(name='Intl1924', a=6378388, b=6356911.946, f_=297, f=0.003367003, e=0.08199189, e2=0.00672267, e12=0.99327733, e22=0.00676817, n=0.001686341, R1=6371229.315333334, R2=6371227.711270464, R3=6371221.265832124, Rr=6367654.499992855, Rs=6367640.919007843) @var Ellipsoids.Intl1967: Ellipsoid(name='Intl1967', a=6378157.5, b=6356772.2, f_=298.24961539, f=0.003352896, e=0.081820233, e2=0.00669455, e12=0.99330545, e22=0.00673967, n=0.001679263, R1=6371029.066666666, R2=6371027.476083895, R3=6371021.084827519, Rr=6367469.33894366, Rs=6367455.872106339) @var Ellipsoids.Krassovski1940: Ellipsoid(name='Krassovski1940', a=6378245, b=6356863.01877305, f_=298.3, f=0.00335233, e=0.081813334, e2=0.006693422, e12=0.993306578, e22=0.006738525, n=0.001678979, R1=6371117.67292435, R2=6371116.08285656, R3=6371109.693674386, Rr=6367558.496874185, Rs=6367545.034404869) @var Ellipsoids.Krassowsky1940: Ellipsoid(name='Krassowsky1940', a=6378245, b=6356863.01877305, f_=298.3, f=0.00335233, e=0.081813334, e2=0.006693422, e12=0.993306578, e22=0.006738525, n=0.001678979, R1=6371117.67292435, R2=6371116.08285656, R3=6371109.693674386, Rr=6367558.496874185, Rs=6367545.034404869) @var Ellipsoids.Maupertuis1738: Ellipsoid(name='Maupertuis1738', a=6397300, b=6363806.28272251, f_=191, f=0.005235602, e=0.102194876, e2=0.010443793, e12=0.989556207, e22=0.010554017, n=0.002624672, R1=6386135.42757417, R2=6386131.541448465, R3=6386115.886282292, Rr=6380564.130113637, Rs=6380531.163818629) @var Ellipsoids.Mercury1960: Ellipsoid(name='Mercury1960', a=6378166, b=6356784.28360711, f_=298.3, f=0.00335233, e=0.081813334, e2=0.006693422, e12=0.993306578, e22=0.006738525, n=0.001678979, R1=6371038.76120237, R2=6371037.171154276, R3=6371030.782051236, Rr=6367479.629235634, Rs=6367466.166933062) @var Ellipsoids.Mercury1968Mod: Ellipsoid(name='Mercury1968Mod', a=6378150, b=6356768.33724438, f_=298.3, f=0.00335233, e=0.081813334, e2=0.006693422, e12=0.993306578, e22=0.006738525, n=0.001678979, R1=6371022.77908146, R2=6371021.189037352, R3=6371014.799950343, Rr=6367463.656043012, Rs=6367450.193774211) @var Ellipsoids.NWL1965: Ellipsoid(name='NWL1965', a=6378145, b=6356759.76948868, f_=298.25, f=0.003352892, e=0.08182018, e2=0.006694542, e12=0.993305458, e22=0.006739661, n=0.001679261, R1=6371016.58982956, R2=6371014.999254003, R3=6371008.60802666, Rr=6367456.873667615, Rs=6367443.406891448) @var Ellipsoids.OSU86F: Ellipsoid(name='OSU86F', a=6378136.2, b=6356751.51693008, f_=298.2572236, f=0.003352811, e=0.081819191, e2=0.00669438, e12=0.99330562, e22=0.006739497, n=0.00167922, R1=6371007.972310026, R2=6371006.381813641, R3=6370999.990905124, Rr=6367448.347164505, Rs=6367434.88105977) @var Ellipsoids.OSU91A: Ellipsoid(name='OSU91A', a=6378136.3, b=6356751.6165948, f_=298.2572236, f=0.003352811, e=0.081819191, e2=0.00669438, e12=0.99330562, e22=0.006739497, n=0.00167922, R1=6371008.072198267, R2=6371006.481701856, R3=6371000.090793238, Rr=6367448.446996935, Rs=6367434.98089199) @var Ellipsoids.Plessis1817: Ellipsoid(name='Plessis1817', a=6376523, b=6355862.93325557, f_=308.64, f=0.003240021, e=0.080433474, e2=0.006469544, e12=0.993530456, e22=0.006511671, n=0.001622639, R1=6369636.31108519, R2=6369634.826085826, R3=6369628.859996674, Rr=6366197.15710669, Rs=6366184.585664447) @var Ellipsoids.SGS85: Ellipsoid(name='SGS85', a=6378136, b=6356751.30156878, f_=298.257, f=0.003352813, e=0.081819221, e2=0.006694385, e12=0.993305615, e22=0.006739502, n=0.001679222, R1=6371007.767189593, R2=6371006.176690875, R3=6370999.785772962, Rr=6367448.13949045, Rs=6367434.673365931) @var Ellipsoids.SoAmerican1969: Ellipsoid(name='SoAmerican1969', a=6378160, b=6356774.71919531, f_=298.25, f=0.003352892, e=0.08182018, e2=0.006694542, e12=0.993305458, e22=0.006739661, n=0.001679261, R1=6371031.573065103, R2=6371029.982485807, R3=6371023.591243432, Rr=6367471.848531487, Rs=6367458.38172365) @var Ellipsoids.Sphere: Ellipsoid(name='Sphere', a=6371008.771415, b=6371008.771415, f_=0, f=0, e=0, e2=0, e12=1, e22=0, n=0, R1=6371008.771415, R2=6371008.771415, R3=6371008.771415, Rr=6371008.771415, Rs=6371008.771415) @var Ellipsoids.SphereAuthalic: Ellipsoid(name='SphereAuthalic', a=6371000, b=6371000, f_=0, f=0, e=0, e2=0, e12=1, e22=0, n=0, R1=6371000, R2=6371000, R3=6371000, Rr=6371000, Rs=6371000) @var Ellipsoids.SpherePopular: Ellipsoid(name='SpherePopular', a=6378137, b=6378137, f_=0, f=0, e=0, e2=0, e12=1, e22=0, n=0, R1=6378137, R2=6378137, R3=6378137, Rr=6378137, Rs=6378137) @var Ellipsoids.Struve1860: Ellipsoid(name='Struve1860', a=6378298.3, b=6356657.14266956, f_=294.73, f=0.003392936, e=0.082306499, e2=0.00677436, e12=0.99322564, e22=0.006820565, n=0.001699351, R1=6371084.580889854, R2=6371082.952089875, R3=6371076.406914177, Rr=6367482.318324657, Rs=6367468.527348378) @var Ellipsoids.WGS60: Ellipsoid(name='WGS60', a=6378165, b=6356783.28695944, f_=298.3, f=0.00335233, e=0.081813334, e2=0.006693422, e12=0.993306578, e22=0.006738525, n=0.001678979, R1=6371037.762319813, R2=6371036.172271968, R3=6371029.783169931, Rr=6367478.630911095, Rs=6367465.168610634) @var Ellipsoids.WGS66: Ellipsoid(name='WGS66', a=6378145, b=6356759.76948868, f_=298.25, f=0.003352892, e=0.08182018, e2=0.006694542, e12=0.993305458, e22=0.006739661, n=0.001679261, R1=6371016.58982956, R2=6371014.999254003, R3=6371008.60802666, Rr=6367456.873667615, Rs=6367443.406891448) @var Ellipsoids.WGS72: Ellipsoid(name='WGS72', a=6378135, b=6356750.52, f_=298.26, f=0.003352779, e=0.081818811, e2=0.006694318, e12=0.993305682, e22=0.006739434, n=0.001679205, R1=6371006.84, R2=6371005.249530816, R3=6370998.858745317, Rr=6367447.24861499, Rs=6367433.78276368) @var Ellipsoids.WGS84: Ellipsoid(name='WGS84', a=6378137, b=6356752.31425, f_=298.257223563, f=0.003352811, e=0.081819191, e2=0.00669438, e12=0.99330562, e22=0.006739497, n=0.00167922, R1=6371008.771416667, R2=6371007.180920884, R3=6371000.790010764, Rr=6367449.145825027, Rs=6367435.679718607) @var Transforms.BD72: Transform(name='BD72', tx=106.86863, ty=-52.29778, tz=103.72389, rx=-0, ry=-0, rz=-0.00001, s=1.2727, s1=1, sx=-0.33657, sy=-0.45696, sz=-1.84218) @var Transforms.Bessel1841: Transform(name='Bessel1841', tx=-582, ty=-105, tz=-414, rx=-0.00001, ry=-0, rz=0.00001, s=-8.3, s1=0.99999, sx=-1.04, sy=-0.35, sz=3.08) @var Transforms.Clarke1866: Transform(name='Clarke1866', tx=8, ty=-160, tz=-176, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) @var Transforms.DHDN: Transform(name='DHDN', tx=-591.28, ty=-81.35, tz=-396.39, rx=0.00001, ry=-0, rz=-0.00001, s=-9.82, s1=0.99999, sx=1.477, sy=-0.0736, sz=-1.458) @var Transforms.ED50: Transform(name='ED50', tx=89.5, ty=93.8, tz=123.1, rx=0, ry=0, rz=0, s=-1.2, s1=1, sx=0, sy=0, sz=0.156) @var Transforms.Irl1965: Transform(name='Irl1965', tx=-482.53, ty=130.596, tz=-564.557, rx=0.00001, ry=0, rz=0, s=-8.15, s1=0.99999, sx=1.042, sy=0.214, sz=0.631) @var Transforms.Irl1975: Transform(name='Irl1975', tx=-482.53, ty=130.596, tz=-564.557, rx=-0.00001, ry=-0, rz=-0, s=-1.1, s1=1, sx=-1.042, sy=-0.214, sz=-0.631) @var Transforms.Krassovski1940: Transform(name='Krassovski1940', tx=-24, ty=123, tz=94, rx=-0, ry=0, rz=0, s=-2.423, s1=1, sx=-0.02, sy=0.26, sz=0.13) @var Transforms.Krassowsky1940: Transform(name='Krassowsky1940', tx=-24, ty=123, tz=94, rx=-0, ry=0, rz=0, s=-2.423, s1=1, sx=-0.02, sy=0.26, sz=0.13) @var Transforms.MGI: Transform(name='MGI', tx=-577.326, ty=-90.129, tz=-463.92, rx=0.00002, ry=0.00001, rz=0.00003, s=-2.423, s1=1, sx=5.137, sy=1.474, sz=5.297) @var Transforms.NAD27: Transform(name='NAD27', tx=8, ty=-160, tz=-176, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) @var Transforms.NAD83: Transform(name='NAD83', tx=1.004, ty=-1.91, tz=-0.515, rx=0, ry=0, rz=0, s=-0.0015, s1=1, sx=0.0267, sy=0.00034, sz=0.011) @var Transforms.NTF: Transform(name='NTF', tx=-168, ty=-60, tz=320, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) @var Transforms.OSGB36: Transform(name='OSGB36', tx=-446.448, ty=125.157, tz=-542.06, rx=-0, ry=-0, rz=-0, s=20.4894, s1=1.00002, sx=-0.1502, sy=-0.247, sz=-0.8421) @var Transforms.TokyoJapan: Transform(name='TokyoJapan', tx=148, ty=-507, tz=-685, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) @var Transforms.WGS72: Transform(name='WGS72', tx=0, ty=0, tz=-4.5, rx=0, ry=0, rz=0, s=-0.22, s1=1, sx=0, sy=0, sz=0.554) @var Transforms.WGS84: Transform(name='WGS84', tx=0, ty=0, tz=0, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0) ''' # make sure int/int division yields float quotient from __future__ import division division = 1 / 2 # double check int division, see .fmath.py, .utily.py if not division: raise ImportError('%s 1/2 == %d' % ('division', division)) del division from pygeodesy.basics import EPS, EPS1, R_M, property_doc_, \ property_RO, _TypeError from pygeodesy.fmath import _2_3rd, cbrt, cbrt2, fdot, fpowers, \ Fsum, fsum_, hypot1, hypot2, sqrt3 from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import Curvature2Tuple, Distance2Tuple, \ _NamedEnum, _NamedEnumItem, Vector3Tuple from pygeodesy.streprs import instr, fstr from pygeodesy.utily import PI2, PI_2, degrees360, \ m2degrees, m2km, m2NM, m2SM from math import atan, atan2, atanh, copysign, cos, exp, hypot, \ radians, sin, sinh, sqrt R_M = R_M #: Mean (spherical) earth radius (C{meter}). R_MA = 6378137.0 #: Major (equatorial) earth radius (C{meter}) WGS84, EPSG:3785. R_MB = 6356752.0 #: Minor (polar) earth radius (C{meter}) WGS84, EPSG:3785. R_KM = m2km(R_M) #: Mean (spherical) earth radius (C{KM}, kilo meter). R_NM = m2NM(R_M) #: Mean (spherical) earth radius (C{NM}, nautical miles). R_SM = m2SM(R_M) #: Mean (spherical) earth radius (C{SM}, statute miles). # See <https://www.EdWilliams.org/avform.htm>, # <https://www.DTIC.mil/dtic/tr/fulltext/u2/a216843.pdf> and # <https://GitHub.com/NASA/MultiDop/blob/master/src/share/man/man3/geog_lib.3> # based on International Standard Nautical Mile of 1,852 meter (1' latitude) R_FM = 6371000.0 #: Former FAI Sphere earth radius (C{meter}). R_VM = 6366707.0194937 #: Aviation/Navigation earth radius (C{meter}). # R_ = 6372797.560856 #: XXX some other earth radius??? # all public contants, classes and functions __all__ = _ALL_LAZY.datum __version__ = '20.04.04' _floats = {} # cache, deleted below _TOL = sqrt(EPS * 0.1) # for Ellipsoid.estauf, imported by .ups def _4Ecef(this, Ecef): '''Return an ECEF converter. ''' from pygeodesy.ecef import EcefKarney, EcefVeness, EcefYou if Ecef is None: Ecef = EcefKarney else: _TypeError(EcefKarney, EcefVeness, EcefYou, Ecef=Ecef) return Ecef(this, name=this.name) # datum or ellipsoid def _float(f): '''(INTERNAL) cache initial C{float}s. ''' f = float(f) return _floats.setdefault(f, f) # PYCHOK del _floats class Ellipsoid(_NamedEnumItem): '''Ellipsoid with major and minor radius, semi-axis, (inverse) flattening and other pre-computed, frequently used attributes. ''' _a = 0 #: Major (equatorial) radius, semi-axis (C{meter}). _b = 0 #: Minor (polar) radius, semi-axis (C{meter}): a * (f - 1) / f. _f = 0 #: Flattening: (a - b) / a _f_ = 0 #: Inverse flattening: a / (a - b) = 1 / f _f2 = None #: 2nd Flattening: (a - b) / b # un-/rarely used _n = None #: 3rd Flattening: f / (2 - f) = (a - b) / (a + b) # for .A and utm _a2 = None #: a**2 _a2_ = None #: (1 / a**2) # for ellipsiodalNvector.Cartesian.toNvector _a_b = None #: (a / b) = 1 / (1 - f) # for ellipsoidalNvector.Nvector.toCartesian _b2 = None #: b**2 # curvatures <https://WikiPedia.org/wiki/Earth_radius#Radii_of_curvature> _a2_b = None #: (INTERNAL) Meridional radius of curvature at poles: a**2 / b (C{meter}) _b2_a = None #: (INTERNAL) Meridional radius of curvature at equator: b**2 / a (C{meter}) # eccentricities _e = None #: 1st Eccentricity: sqrt(1 - (b / a)**2)) # for utm _es_c = None #: M{(1 - f) * exp(es_atanh(1))} _e2 = None #: 1st Eccentricity squared: f * (2 - f) = 1 - (b / a)**2 _e4 = None #: e2**2 = e**4 for ellipsoidalNvector.Cartesian.toNvector, ecef _e12 = None #: 1 - e2 = (1 - f)**2 for ellipsoidalNvector.Cartesian.toNvector, ecef utm _e22 = None #: 2nd Eccentricity squared: e2 / (1 - e2) = (a / b)**2 - 1 # fixed earth radii from <https://WikiPedia.org/wiki/Earth_radius> _R1 = None #: (INTERNAL) Mean earth radius: (2 * a + b) / 3 per IUGG definition (C{meter}) _R2 = None #: (INTERNAL) Authalic radius: sqrt((a**2 + b**2 * atanh(e) / e) / 2) (C{meter}) # _c = None #: (INTERNAL) Authalic radius: equ (60) in Karney's "Algorithms for Geodesics" _R3 = None #: (INTERNAL) Volumetric radius: (a * a * b)**1/3 (C{meter}) _Rr = None #: (INTERNAL) Rectifying radius: ((a**3/2 + b**3/2) / 2)**2/3 (C{meter}) _Rs = None #: (INTERNAL) Mean earth radius: sqrt(a * b) (C{meter}) _ab_90 = None #: (a - b) / 90 # for .Rlat below _area = None #: (INTERNAL) Surface area: 4 * PI * R2**2 _volume = None #: (INTERNAL) Volume: 4 / 3 * PI * a**2 * b _A = None #: (INTERNAL) Meridional radius _AlphaKs = None #: (INTERNAL) Up to 8th-order Krüger Alpha series _BetaKs = None #: (INTERNAL) Up to 8th-order Krüger Beta series _KsOrder = 8 #: (INTERNAL) Krüger series order (4, 6 or 8) _Mabcd = None #: (INTERNAL) OSGB meridional coefficients _geodesic = None #: (INTERNAL) Cached C{karney._wrapped_.Geodesic} instance _Math = None #: (INTERNAL) Cached C{geographiclib.geomath.Math} module def __init__(self, a, b, f_, name=''): '''New L{Ellipsoid}. @arg a: Semi-major, equatorial axis (C{meter}). @arg b: Semi-minor, polar axis (C{meter}). @arg f_: Inverse flattening: a / (a - b) (C{float} >>> 1.0). @kwarg name: Optional, unique name (C{str}). @raise NameError: Ellipsoid with that B{C{name}} already exists. ''' self._a = a = _float(a) # major half-axis in meter if not b: # get b from a and f_, minor half-axis in meter self._b = b = _float(a * (f_ - 1) / _float(f_)) else: # get f_ from a and b if not spherical self._b = b = _float(b) if not f_ and a > b: f_ = a / (a - b) if f_ > 0 and a > b > 0: self._f_ = f_ = _float(f_) # inverse flattening self._f = f = _float(1 / f_) # flattening elif a > 0: # sphere self._b = b = self._a2b = self._b2a = a self._f2 = self._n = f_ = f = 0 self._a_b = 1 self._R1 = self._R2 = self._R3 = self._Rr = self._Rs = a else: raise ValueError('%s invalid: %s' % ('ellipsoid', instr(self, a, b, f_, name=name))) d = a - b # some sanity checks to catch mistakes if d < 0 or min(a, b) < 1: raise AssertionError('%s: %s=%0.9g vs %s=%0.9g' % (name, 'a', a, 'b', b)) t = d / a if abs(f - t) > 1e-8: raise AssertionError('%s: %s=%.9g vs %s=%.9g' % (name, 'f', f, '(a-b)/a', t)) t = (1 - self.f)**2 if abs(self.e12 - t) > EPS: raise AssertionError('%s: %s=%.9g vs %s=%.9g' % (name, 'e12', self.e12, '(1-f)**2', t)) self._register(Ellipsoids, name) def __eq__(self, other): '''Compare this and an other ellipsoid. @arg other: The other ellipsoid (L{Ellipsoid}). @return: C{True} if equal, C{False} otherwise. ''' return self is other or (isinstance(other, Ellipsoid) and self.a == other.a and (self.b == other.b or self.f == other.f)) def _Kseries(self, *AB8Ks): '''(INTERNAL) Compute the 4-, 6- or 8-th order Krüger Alpha or Beta series coefficients per Karney 2011, 'Transverse Mercator with an accuracy of a few nanometers', U{page 7, equations 35 and 36<https://Arxiv.org/pdf/1002.1417v3.pdf>}. @arg AB8Ks: 8-Tuple of 8-th order Krüger Alpha or Beta series coefficient tuples. @return: Krüger series coefficients (C{.KsOrder}-tuple). @see: The 30-th order U{TMseries30 <https://GeographicLib.SourceForge.io/html/tmseries30.html>}. ''' k = self.KsOrder ns = fpowers(self.n, k) return tuple(fdot(AB8Ks[i][:k-i], *ns[i:]) for i in range(k)) @property_RO def a(self): '''Get the major (equatorial) radius, semi-axis (C{meter}). ''' return self._a @property_RO def a2(self): '''Get the major radius I{squared} (C{float}), M{a**2}. ''' if self._a2 is None: self._a2 = self.a**2 return self._a2 @property_RO def a2_(self): '''Get the inverse of the major radius I{squared} (C{float}), M{1 / a**2}. ''' if self._a2_ is None: self._a2_ = 1 / self.a2 return self._a2_ # (1 / a**2) @property_RO def a_b(self): '''Get ratio M{a / b} (C{float}). ''' if self._a_b is None: self._a_b = self.a / self.b return self._a_b @property_RO def a2_b(self): '''Get the polar meridional radius of curvature (C{meter}), M{a**2 / b}. @see: U{Radii of Curvature <https://WikiPedia.org/wiki/Earth_radius#Radii_of_curvature>}. ''' if self._a2_b is None: self._a2_b = self.a2 / self.b return self._a2_b @property_RO def area(self): '''Get the ellipsoid's surface area (C{meter**2}), M{4 * PI * R2**2}. ''' if self._area is None: self._area = 2 * PI2 * self.R2**2 return self._area @property_RO def A(self): '''Get the UTM meridional radius (C{meter}). ''' if self._A is None: n = self.n # <https://GeographicLib.SourceForge.io/html/transversemercator.html> self._A = self.a / (1 + n) * (fsum_(65536, 16384 * n**2, 1024 * n**4, 256 * n**6, 100 * n**8, 49 * n**10) / 65536) # <https://www.MyGeodesy.id.AU/documents/Karney-Krueger%20equations.pdf> # self._A = self.a / (1 + n) * (fhorner(n**2, 16384, 4096, 256, 64, 25) / 16384) return self._A @property_RO def AlphaKs(self): '''Get the U{Krüger Alpha series coefficients<https://GeographicLib.SourceForge.io/html/tmseries30.html>} (C{KsOrder}-tuple). ''' if self._AlphaKs is None: self._AlphaKs = self._Kseries( # XXX int/int quotients may require from __future__ import division # n n**2 n**3 n**4 n**5 n**6 n**7 n**8 (1/2, -2/3, 5/16, 41/180, -127/288, 7891/37800, 72161/387072, -18975107/50803200), (13/48, -3/5, 557/1440, 281/630, -1983433/1935360, 13769/28800, 148003883/174182400), # PYCHOK unaligned (61/240, -103/140, 15061/26880, 167603/181440, -67102379/29030400, 79682431/79833600), # PYCHOK unaligned (49561/161280, -179/168, 6601661/7257600, 97445/49896, -40176129013/7664025600), # PYCHOK unaligned (34729/80640, -3418889/1995840, 14644087/9123840, 2605413599/622702080), # PYCHOK unaligned (212378941/319334400, -30705481/10378368, 175214326799/58118860800), # PYCHOK unaligned (1522256789/1383782400, -16759934899/3113510400), # PYCHOK unaligned (1424729850961/743921418240,)) # PYCHOK unaligned return self._AlphaKs @property_RO def b(self): '''Get the minor (polar) radius, semi-axis (C{meter}). ''' return self._b @property_RO def b2(self): '''Get the minor radius I{squared} (C{float}), M{b**2}. ''' if self._b2 is None: self._b2 = self.b**2 return self._b2 @property_RO def b2_a(self): '''Get the equatorial meridional radius of curvature (C{meter}), M{b**2 / a}. @see: U{Radii of Curvature <https://WikiPedia.org/wiki/Earth_radius#Radii_of_curvature>}. ''' if self._b2_a is None: self._b2_a = self.b2 / self.a return self._b2_a @property_RO def BetaKs(self): '''Get the U{Krüger Beta series coefficients<https://GeographicLib.SourceForge.io/html/tmseries30.html>} (C{KsOrder}-tuple). ''' if self._BetaKs is None: self._BetaKs = self._Kseries( # XXX int/int quotients may require from __future__ import division # n n**2 n**3 n**4 n**5 n**6 n**7 n**8 (1/2, -2/3, 37/96, -1/360, -81/512, 96199/604800, -5406467/38707200, 7944359/67737600), (1/48, 1/15, -437/1440, 46/105, -1118711/3870720, 51841/1209600, 24749483/348364800), # PYCHOK unaligned (17/480, -37/840, -209/4480, 5569/90720, 9261899/58060800, -6457463/17740800), # PYCHOK unaligned (4397/161280, -11/504, -830251/7257600, 466511/2494800, 324154477/7664025600), # PYCHOK unaligned (4583/161280, -108847/3991680, -8005831/63866880, 22894433/124540416), # PYCHOK unaligned (20648693/638668800, -16363163/518918400, -2204645983/12915302400), # PYCHOK unaligned (219941297/5535129600, -497323811/12454041600), # PYCHOK unaligned (191773887257/3719607091200,)) # PYCHOK unaligned return self._BetaKs @property_RO def c(self): '''Get the authalic earth radius (C{meter}), see C{R2}. @see: Symbol C{c} in U{equation 60 <https://Link.Springer.com/article/10.1007%2Fs00190-012-0578-z>}. ''' return self.R2 def distance2(self, lat0, lon0, lat1, lon1): '''Approximate the distance and (initial) bearing between two points based on the radii of curvature at the initial point. Suitable only for distances of several hundred Km or Miles and only between points not near-polar. @arg lat0: From latitude (C{degrees}). @arg lon0: From longitude (C{degrees}). @arg lat1: To latitude (C{degrees}). @arg lon1: To longitude (C{degrees}). @return: A L{Distance2Tuple}C{(distance, initial)} with C{distance} in same units as this ellipsoid's axes. @see: Function L{flatLocal}, U{local, flat earth approximation <https://www.EdWilliams.org/avform.htm#flat>} and meridional and prime vertical U{Radii of Curvature <https://WikiPedia.org/wiki/Earth_radius#Radii_of_curvature>}. ''' m, n = self.roc2(lat0, scaled=True) m *= radians(lat1 - lat0) n *= radians(lon1 - lon0) return Distance2Tuple(hypot(m, n), degrees360(atan2(n, m))) @property_RO def e(self): '''Get the (1st) Eccentricity (C{float}), M{sqrt(1 - (b / a)**2))}. ''' if self._e is None: self._e = sqrt(abs(self.e2)) return self._e @property_RO def e12(self): '''Get M{1 - e**2} (C{float}). ''' if self._e12 is None: self._e12 = 1 - self.e2 return self._e12 # 1 - e2 @property_RO def e2(self): '''Get the (1st) Eccentricity I{squared} (C{float}), M{f * (2 - f) == 1 - (b / a)**2}. ''' if self._e2 is None: self._e2 = e2 = self.f * (2 - self.f) t = 1 - (self.b / self.a)**2 if abs(e2 - t) > 1e-9: raise AssertionError('%s: %s=%.9g vs %s=%.9g' % (self.name, 'e2', e2, '1-(b/a)**2', t)) return self._e2 @property_RO def e22(self): '''Get the 2nd Eccentricity I{squared} (C{float}), M{e2 / (1 - e2) == (a / b)**2 - 1}. ''' if self._e22 is None: self._e22 = e22 = self.e2 / (1 - self.e2) t = self.a_b**2 - 1 if abs(e22 - t) > 1e-9: raise AssertionError('%s: %s=%.9g vs %s=%.9g' % (self.name, 'e22', e22, '(a/b)**2-1', t)) return self._e22 @property_RO def e4(self): '''Get the (1st) Eccentricity to 4th power (C{float}), M{e**4 == e2**2}. ''' if self._e4 is None: self._e4 = self.e2**2 return self._e4 def ecef(self, Ecef=None): '''Return U{ECEF<https://WikiPedia.org/wiki/ECEF>} converter. @kwarg Ecef: ECEF class to use (L{EcefKarney}, L{EcefVeness} or L{EcefYou}). @return: An ECEF converter for this C{ellipsoid} (L{EcefKarney}, L{EcefVeness} or L{EcefYou}). @raise TypeError: Invalid B{C{Ecef}}. ''' return _4Ecef(self, Ecef) def e2s(self, s): '''Compute norm M{sqrt(1 - e2 * s**2)}. @arg s: S value (C{scalar}). @return: Norm (C{float}). @raise ValueError: Invalid B{C{s}}. ''' try: return sqrt(self.e2s2(s)) except (TypeError, ValueError): raise ValueError('%s invalid: %r' % (self._dot_('e2s'), s)) def e2s2(self, s): '''Compute M{1 - e2 * s**2}. @arg s: S value (C{scalar}). @return: Result (C{float}). @raise ValueError: Invalid B{C{s}}. ''' try: r = 1 - self.e2 * s**2 if r >= 0: return r except (TypeError, ValueError): pass raise ValueError('%s invalid: %r' % (self._dot_('e2s2'), s)) @property_RO def es(self): '''Get the (1st) Eccentricity I{signed} (C{float}). ''' # note, self.e is always non-negative return copysign(self.e, self.f) # see .ups.py def es_atanh(self, x): '''Compute M{es * atanh(es * x)} where I{es} is the I{signed} 1st Eccentricity. @see: Function U{Math::eatanhe<https://GeographicLib.SourceForge.io/ html/classGeographicLib_1_1Math.html>}. ''' # note, self.e is always non-negative if self.f > 0: r = self.e * atanh(self.e * x) elif self.f < 0: # PYCHOK no cover r = self.e * atan(-self.e * x) else: r = 0 return r @property_RO def es_c(self): '''Get M{(1 - f) * exp(es_atanh(1))} C{float}. ''' if self._es_c is None: self._es_c = (1 - self.f) * exp(self.es_atanh(1.0)) return self._es_c def es_tauf(self, taup): '''Compute U{Karney's<https://ArXiv.org/abs/1002.1417>} equations (19), (20) and (21). @see: Function U{Math::tauf<https://GeographicLib.SourceForge.io/ html/classGeographicLib_1_1Math.html>}. ''' tol = max(abs(taup), 1) * _TOL e2m = 1 - abs(self.e2) # == self.e**2 t = taup / e2m T = Fsum(t) for _ in range(5): a = self.es_taupf(t) d = (taup - a) * (1 + e2m * t**2) / (e2m * hypot1(t) * hypot1(a)) t, d = T.fsum2_(d) if abs(d) < tol: break return t def es_taupf(self, tau): '''Compute U{Karney's<https://ArXiv.org/abs/1002.1417>} equations (7), (8) and (9). @see: Function U{Math::taupf<https://GeographicLib.SourceForge.io/ html/classGeographicLib_1_1Math.html>}. ''' t = hypot1(tau) s = sinh(self.es_atanh(tau / t)) return hypot1(s) * tau - s * t @property_RO def f(self): '''Get the Flattening (C{float}), M{(a - b) / a}. ''' return self._f @property_RO def f_(self): '''Get the Inverse flattening (C{float}), M{1 / f == a / (a - b)}. ''' return self._f_ @property_RO def f2(self): '''Get the 2nd Flattening (C{float}), M{(a - b) / b}. ''' if self._f2 is None: self._f2 = (self.a - self.b) / self.b return self._f2 def _flatRad2_(self, phi2, phi1, lam21): '''(INTERNAL) like function L{flatLocal_} but returning the I{angular} distance in C{radians squared}. ''' m, n = self.roc2_((phi2 + phi1) * 0.5, scaled=True) return hypot2(m * (phi2 - phi1), n * lam21) * self.a2_ @property_RO def geodesic(self): '''Get this ellipsoid's I{wrapped} U{Karney Geodesic <https://GeographicLib.SourceForge.io/html/python/code.html>}, provided the U{GeographicLib <https://PyPI.org/project/geographiclib>} package is installed. ''' if self._geodesic is None: # if not self.isEllipsoidal: # raise _isnotError('ellipsoidal', ellipsoid=self) from pygeodesy.karney import _wrapped self._geodesic = _wrapped.Geodesic(self.a, self.f) return self._geodesic @property_RO def _geodesic_Math2(self): '''(INTERNAL) Get this ellipsoid's C{Geodesic} and Karney's C{Math} class. ''' if Ellipsoid._Math is None: from pygeodesy.karney import _wrapped Ellipsoid._Math = _wrapped.Math return self.geodesic, Ellipsoid._Math @property_RO def isEllipsoidal(self): '''Check whether this model is ellipsoidal (C{bool}). ''' return self.a > self.R1 > self.b @property_RO def isSpherical(self): '''Check whether this model is spherical (C{bool}). ''' return self.a == self.R1 == self.b @property_doc_(''' the Krüger series' order (C{int}).''') def KsOrder(self): '''Get the Krüger series order (C{int} 4, 6 or 8). ''' return self._KsOrder @KsOrder.setter # PYCHOK setter! def KsOrder(self, order): '''Set the Krüger series' order. @arg order: New Krüger series' order (C{int} 4, 6 or 8). @raise ValueError: Invalid B{C{order}}. ''' if order not in (4, 6, 8): raise ValueError('%s invalid: %r' % ('order', order)) if order != self._KsOrder: if self._AlphaKs: self._AlphaKs = None if self._BetaKs: self._BetaKs = None self._KsOrder = order def m2degrees(self, meter): '''Convert distance to angle along equator. @arg meter: Distance (C{meter}). @return: Angle (C{degrees}). ''' return m2degrees(meter, self.a) @property_RO def Mabcd(self): '''Get the OSGR meridional coefficients (4-tuple), Airy130 only. ''' if self._Mabcd is None: n, n2, n3 = fpowers(self.n, 3) # PYCHOK false! self._Mabcd = (fdot((1, n, n2, n3), 4, 4, 5, 5) / 4, fdot( (n, n2, n3), 24, 24, 21) / 8, fdot( (n2, n3), 15, 15) / 8, 35 * n3 / 24) return self._Mabcd @property_RO def n(self): '''Get the 3rd Flattening (C{float}), M{f / (2 - f) == (a - b) / (a + b)}. ''' if self._n is None: self._n = n = self.f / (2 - self.f) t = (self.a - self.b) / (self.a + self.b) if abs(n - t) > 1e-9: raise AssertionError('%s: %s=%.9g vs %s=%.9g' % (self.name, 'n', n, '(a-b)/(a+b)', t)) return self._n @property_RO def R1(self): '''Get the mean earth radius per IUGG (C{meter}), M{(2 * a + b) / 3}. @see: U{Earth radius<https://WikiPedia.org/wiki/Earth_radius>}. ''' if self._R1 is None: self._R1 = (self.a * 2 + self.b) / 3 return self._R1 @property_RO def R2(self): '''Get the authalic earth radius (C{meter}), M{sqrt((a**2 + b**2 * atanh(e) / e) / 2)}. @see: U{Earth radius<https://WikiPedia.org/wiki/Earth_radius>} and U{c<https://Link.Springer.com/article/10.1007%2Fs00190-012-0578-z>}. ''' if self._R2 is None: if self.e2 > 0: r = atanh(self.e) / self.e elif self.e2 < 0: # GeographicLib Ellipsoid Area r = atan(self.e) / self.e else: r = 1 self._R2 = sqrt((self.a2 + self.b2 * r) * 0.5) return self._R2 @property_RO def R3(self): '''Get the volumetric earth radius (C{meter}), M{(a * a * b)**(1/3)}. @see: U{Earth radius<https://WikiPedia.org/wiki/Earth_radius>}. ''' if self._R3 is None: self._R3 = cbrt(self.a2 * self.b) return self._R3 def Rgeocentric(self, lat): '''Compute the geocentric earth radius at the given latitude. @arg lat: Latitude (C{degrees90}). @return: Geocentric earth radius (C{meter}). @see: U{Geocentric Radius <https://WikiPedia.org/wiki/Earth_radius#Geocentric_radius>} ''' a2 = self.a2 b2 = self.b2 c2 = cos(radians(lat))**2 s2 = 1 - c2 return sqrt((a2**2 * c2 + b2**2 * s2) / (a2 * c2 + b2 * s2)) @property_RO def Rr(self): '''Get the rectifying earth radius (C{meter}), M{((a**(3/2) + b**(3/2)) / 2)**(2/3)}. @see: U{Earth radius<https://WikiPedia.org/wiki/Earth_radius>}. ''' if self._Rr is None: self._Rr = cbrt2((sqrt3(self.a) + sqrt3(self.b)) * 0.5) return self._Rr @property_RO def Rs(self): '''Get another mean earth radius (C{meter}), M{sqrt(a * b)}. ''' if self._Rs is None: self._Rs = sqrt(self.a * self.b) return self._Rs def Rlat(self, lat): '''Approximate the earth radius at the given latitude. @arg lat: Latitude (C{degrees90}). @return: Approximate earth radius (C{meter}). ''' if self._ab_90 is None: self._ab_90 = (self.a - self.b) / 90.0 # r = major - (major - minor) * |lat| / 90 return self.a - self._ab_90 * min(abs(lat), 90) def roc2(self, lat, scaled=False): '''Compute the meridional and prime-vertical, I{normal} radii of curvature at the given latitude. @arg lat: Latitude (C{degrees90}). @kwarg scaled: Scale prime_vertical by B{C{cos(phi)}} (C{bool}). @return: An L{Curvature2Tuple}C{(meridional, prime_vertical)} with the radii of curvature. @see: Method C{.roc2_}, U{Local, flat earth approximation <https://www.EdWilliams.org/avform.htm#flat>} and U{Radii of Curvature <https://WikiPedia.org/wiki/Earth_radius#Radii_of_curvature>}. ''' return self.roc2_(radians(lat), scaled=scaled) def roc2_(self, phi, scaled=False): '''Compute the meridional and prime-vertical, I{normal} radii of curvature at the given latitude. @arg phi: Latitude (C{radians}). @kwarg scaled: Scale prime_vertical by B{C{cos(phi)}} (C{bool}). @return: An L{Curvature2Tuple}C{(meridional, prime_vertical)} with the radii of curvature. @see: Method C{.roc2}, U{Local, flat earth approximation <https://www.EdWilliams.org/avform.htm#flat>} and meridional and prime vertical U{Radii of Curvature <https://WikiPedia.org/wiki/Earth_radius#Radii_of_curvature>}. ''' a = abs(phi) r = self.e2s2(sin(a) if a < PI_2 else 1) if r < EPS: m = n = 0 # PYCHOK e2s2 attr? elif r < EPS1: n = self.a / sqrt(r) m = n * self.e12 / r # PYCHOK e2s2 attr? else: n = self.a m = n * self.e12 if scaled: n *= cos(a) if a < PI_2 else 0 return Curvature2Tuple(m, n) def rocBearing(self, lat, bearing): '''Compute the directional radius of curvature at the given latitude and compass direction. @arg lat: Latitude (C{degrees90}). @arg bearing: Direction (compass C{degrees360}). @return: Directional radius of curvature (C{meter}). @see: U{Radii of Curvature <https://WikiPedia.org/wiki/Earth_radius#Radii_of_curvature>} ''' c2 = cos(radians(bearing))**2 s2 = 1 - c2 m, n = self.roc2(lat) if n < m: # == n / (c2 * n / m + s2) c2 *= n / m elif m < n: # == m / (c2 + s2 * m / n) s2 *= m / n n = m return n / (c2 + s2) # == 1 / (c2 / m + s2 / n) def rocGauss(self, lat): '''Compute the Gaussian radius of curvature at the given latitude. @arg lat: Latitude (C{degrees90}). @return: Gaussian radius of curvature (C{meter}). @see: U{Radii of Curvature <https://WikiPedia.org/wiki/Earth_radius#Radii_of_curvature>} ''' # using ... # m, n = self.roc2(lat) # return sqrt(m * n) # ... requires 1 or 2 sqrt a2, c2 = self.a2, cos(radians(lat))**2 return a2 * self.b / (a2 * c2 + self.b2 * (1 - c2)) def rocMean(self, lat): '''Compute the mean radius of curvature at the given latitude. @arg lat: Latitude (C{degrees90}). @return: Mean radius of curvature (C{meter}). @see: U{Radii of Curvature <https://WikiPedia.org/wiki/Earth_radius#Radii_of_curvature>} ''' m, n = self.roc2(lat) return 2 * m * n / (m + n) # == 2 / (1 / m + 1 / n) def rocMeridional(self, lat): '''Compute the meridional radius of curvature at the given latitude. @arg lat: Latitude (C{degrees90}). @return: Meridional radius of curvature (C{meter}). @see: U{Local, flat earth approximation <https://www.EdWilliams.org/avform.htm#flat>} and U{Radii of Curvature <https://WikiPedia.org/wiki/Earth_radius#Radii_of_curvature>}. ''' return self.roc2(lat).meridional def rocPrimeVertical(self, lat): '''Compute the prime-vertical, I{normal} radius of curvature at the given latitude. @arg lat: Latitude (C{degrees90}). @return: Prime-vertical radius of curvature (C{meter}). @see: U{Local, flat earth approximation <https://www.EdWilliams.org/avform.htm#flat>} and U{Radii of Curvature <https://WikiPedia.org/wiki/Earth_radius#Radii_of_curvature>}. ''' return self.roc2(lat).prime_vertical def toStr(self, prec=9): # PYCHOK expected '''Return this ellipsoid as a text string. @kwarg prec: Optional number of decimals, unstripped (C{int}). @return: Ellipsoid attributes (C{str}). ''' return self._instr(prec, 'a', 'b', 'f_', 'f', 'e', 'e2', 'e12', 'e22', 'n', 'R1', 'R2', 'R3', 'Rr', 'Rs') @property_RO def volume(self): '''Get the ellipsoid's volume (C{meter**3}), M{4 / 3 * PI * a**2 * b}. ''' if self._volume is None: self._volume = PI2 * _2_3rd * self.a2 * self.b return self._volume Ellipsoids = _NamedEnum('Ellipsoids', Ellipsoid) #: Registered ellipsoids. # <https://www.GNU.org/software/gama/manual/html_node/Supported-ellipsoids.html> # <https://w3.Energistics.org/archive/Epicentre/Epicentre_v3.0/DataModel/ # LogicalDictionary/StandardValues/ellipsoid.html> # <https://kb.OSU.edu/dspace/handle/1811/77986> Ellipsoids._assert( # <https://WikiPedia.org/wiki/Earth_ellipsoid> Airy1830 = Ellipsoid(6377563.396, 6356256.909, 299.3249646, 'Airy1830'), AiryModified = Ellipsoid(6377340.189, 6356034.448, 299.3249646, 'AiryModified'), # ANS = Ellipsoid(6378160.0, 6356774.719, 298.25, 'ANS'), Australia1966 = Ellipsoid(6378160.0, 6356774.719, 298.25, 'Australia1966'), # Bessel1841 = Ellipsoid(6377397.155, 6356078.963, 299.152815351, 'Bessel1841'), Bessel1841 = Ellipsoid(6377397.155, 6356078.962818, 299.1528128, 'Bessel1841'), Clarke1866 = Ellipsoid(6378206.4, 6356583.8, 294.978698214, 'Clarke1866'), Clarke1880 = Ellipsoid(6378249.145, 6356514.86954978, 293.465, 'Clarke1880'), Clarke1880IGN = Ellipsoid(6378249.2, 6356515.0, 293.466021294, 'Clarke1880IGN'), Clarke1880Mod = Ellipsoid(6378249.145, 6356514.96582849, 293.4663, 'Clarke1880Mod'), CPM1799 = Ellipsoid(6375738.7, 6356671.92557493, 334.39, 'CPM1799'), # Comm. des Poids et Mesures Delambre1810 = Ellipsoid(6376428.0, 6355957.92616372, 311.5, 'Delambre1810'), # Belgium Engelis1985 = Ellipsoid(6378136.05, 6356751.32272154, 298.2566, 'Engelis1985'), Everest1969 = Ellipsoid(6377295.664, 6356094.667915, 300.8017, 'Everest1969'), Fisher1968 = Ellipsoid(6378150.0, 6356768.33724438, 298.3, 'Fisher1968'), GEM10C = Ellipsoid(6378137.0, 6356752.31424783, 298.2572236, 'GEM10C'), GRS67 = Ellipsoid(6378160.0, 6356774.516, 298.247167427, 'GRS67'), # Lucerne GRS80 = Ellipsoid(6378137.0, 6356752.314140347, 298.257222101, 'GRS80'), # ITRS, ETRS89 Helmert1906 = Ellipsoid(6378200.0, 6356818.16962789, 298.3, 'Helmert1906'), IERS1989 = Ellipsoid(6378136.0, 6356751.302, 298.257, 'IERS1989'), IERS1992TOPEX = Ellipsoid(6378136.3, 6356751.61659215, 298.257223563, 'IERS1992TOPEX'), # IERS/TOPEX/Poseidon/McCarthy IERS2003 = Ellipsoid(6378136.6, 6356751.85797165, 298.25642, 'IERS2003'), Intl1924 = Ellipsoid(6378388.0, 6356911.946, 297.0, 'Intl1924'), # aka Hayford Intl1967 = Ellipsoid(6378157.5, 6356772.2, 298.24961539, 'Intl1967'), # New Int'l Krassovski1940 = Ellipsoid(6378245.0, 6356863.01877305, 298.3, 'Krassovski1940'), # spelling Krassowsky1940 = Ellipsoid(6378245.0, 6356863.01877305, 298.3, 'Krassowsky1940'), # spelling Maupertuis1738 = Ellipsoid(6397300.0, 6363806.28272251, 191.0, 'Maupertuis1738'), # France Mercury1960 = Ellipsoid(6378166.0, 6356784.28360711, 298.3, 'Mercury1960'), Mercury1968Mod = Ellipsoid(6378150.0, 6356768.33724438, 298.3, 'Mercury1968Mod'), NWL1965 = Ellipsoid(6378145.0, 6356759.76948868, 298.25, 'NWL1965'), # Naval Weapons Lab. OSU86F = Ellipsoid(6378136.2, 6356751.51693008, 298.2572236, 'OSU86F'), OSU91A = Ellipsoid(6378136.3, 6356751.6165948, 298.2572236, 'OSU91A'), # Plessis1817 = Ellipsoid(6397523.0, 6355863.0, 153.56512242, 'Plessis1817'), # XXX incorrect? Plessis1817 = Ellipsoid(6376523.0, 6355862.93325557, 308.64, 'Plessis1817'), # XXX IGN France 1972 SGS85 = Ellipsoid(6378136.0, 6356751.30156878, 298.257, 'SGS85'), # Soviet Geodetic System SoAmerican1969 = Ellipsoid(6378160.0, 6356774.71919531, 298.25, 'SoAmerican1969'), # South American Struve1860 = Ellipsoid(6378298.3, 6356657.14266956, 294.73, 'Struve1860'), WGS60 = Ellipsoid(6378165.0, 6356783.28695944, 298.3, 'WGS60'), WGS66 = Ellipsoid(6378145.0, 6356759.76948868, 298.25, 'WGS66'), WGS72 = Ellipsoid(6378135.0, 6356750.52, 298.26, 'WGS72'), WGS84 = Ellipsoid(6378137.0, 6356752.31425, 298.257223563, 'WGS84'), # GPS Sphere = Ellipsoid(R_M, R_M, 0.0, 'Sphere'), # pseudo SphereAuthalic = Ellipsoid(R_FM, R_FM, 0.0, 'SphereAuthalic'), # pseudo SpherePopular = Ellipsoid(R_MA, R_MA, 0.0, 'SpherePopular'), # EPSG:3857 Spheroid ) def _r_s2(s): '''(INTERNAL) rotation in C{radians} and C{degree seconds}. ''' return _float(radians(s / 3600.0)), _float(s) class Transform(_NamedEnumItem): '''Helmert transformation. ''' tx = 0 #: X translation (C{meter}). ty = 0 #: Y translation (C{meter}). tz = 0 #: Z translation (C{meter}). rx = 0 #: X rotation (C{radians}). ry = 0 #: Y rotation (C{radians}). rz = 0 #: Z rotation (C{radians}). s = 0 #: Scale ppm (C{float}). s1 = 1 #: Scale + 1 (C{float}). sx = 0 #: X rotation (degree seconds). sy = 0 #: Y rotation (degree seconds). sz = 0 #: Z rotation (degree seconds). def __init__(self, name='', tx=0, ty=0, tz=0, sx=0, sy=0, sz=0, s=0): '''New L{Transform}. @kwarg name: Optional, unique name (C{str}). @kwarg tx: Optional X translation (C{meter}). @kwarg ty: Optional Y translation (C{meter}). @kwarg tz: Optional Z translation (C{meter}). @kwarg s: Optional scale ppm (C{float}). @kwarg sx: Optional X rotation (C{degree seconds}). @kwarg sy: Optional Y rotation (C{degree seconds}). @kwarg sz: Optional Z rotation (C{degree seconds}). @raise NameError: Transform with that B{C{name}} already exists. ''' if tx: self.tx = _float(tx) if ty: self.ty = _float(ty) if tz: self.tz = _float(tz) if sx: # secs to rads self.rx, self.sx = _r_s2(sx) if sy: self.ry, self.sy = _r_s2(sy) if sz: self.rz, self.sz = _r_s2(sz) if s: self.s = _float(s) self.s1 = _float(s * 1.e-6 + 1) # normalize ppm to (s + 1) self._register(Transforms, name) def __eq__(self, other): '''Compare this and an other transform. @arg other: The other transform (L{Transform}). @return: C{True} if equal, C{False} otherwise. ''' return self is other or (isinstance(other, Transform) and self.tx == other.tx and self.ty == other.ty and self.tz == other.tz and self.rx == other.rx and self.ry == other.ry and self.rz == other.rz and self.s == other.s) def inverse(self, name=''): '''Return the inverse of this transform. @kwarg name: Optional, unique name (C{str}). @return: Inverse (Transform). @raise NameError: Transform with that B{C{name}} already exists. ''' return Transform(name=name or (self.name + 'Inverse'), tx=-self.tx, ty=-self.ty, tz=-self.tz, sx=-self.sx, sy=-self.sy, sz=-self.sz, s=-self.s) def toStr(self, prec=5): # PYCHOK expected '''Return this transform as a string. @kwarg prec: Optional number of decimals, unstripped (C{int}). @return: Transform attributes (C{str}). ''' return self._instr(prec, 'tx', 'ty', 'tz', 'rx', 'ry', 'rz', 's', 's1', 'sx', 'sy', 'sz') def transform(self, x, y, z, inverse=False): '''Transform a (geocentric) Cartesian point, forward or inverse. @arg x: X coordinate (C{meter}). @arg y: Y coordinate (C{meter}). @arg z: Z coordinate (C{meter}). @kwarg inverse: Optional direction, forward or inverse (C{bool}). @return: A L{Vector3Tuple}C{(x, y, z)}, transformed. ''' if inverse: xyz = -1, -x, -y, -z _s1 = self.s1 - 2 # negative inverse: -(1 - s * 1.e-6) else: xyz = 1, x, y, z _s1 = self.s1 # x', y', z' = (.tx + x * .s1 - y * .rz + z * .ry, # .ty + x * .rz + y * .s1 - z * .rx, # .tz - x * .ry + y * .rx + z * .s1) r = Vector3Tuple(fdot(xyz, self.tx, _s1, -self.rz, self.ry), fdot(xyz, self.ty, self.rz, _s1, -self.rx), fdot(xyz, self.tz, -self.ry, self.rx, _s1)) return self._xnamed(r) Transforms = _NamedEnum('Transforms', Transform) #: Registered transforms. # <https://WikiPedia.org/wiki/Helmert_transformation> from WGS84 Transforms._assert( BD72 = Transform('BD72', tx=106.868628, ty=-52.297783, tz=103.723893, # <https://www.NGI.BE/FR/FR4-4.shtm> ETRS89 == WG84 # <https://GeoRepository.com/transformation_15929/BD72-to-WGS-84-3.html> sx=-0.33657, sy= -0.456955, sz= -1.84218, s= 1.2727), Bessel1841 = Transform('Bessel1841', tx=-582.0, ty=-105.0, tz=-414.0, sx= -1.04, sy= -0.35, sz= 3.08, s= -8.3), Clarke1866 = Transform('Clarke1866', tx=8, ty=-160, tz=-176), DHDN = Transform('DHDN', tx=-591.28, ty=-81.35, tz=-396.39, sx= 1.477, sy= -0.0736, sz= -1.458, s= -9.82), # Germany ED50 = Transform('ED50', tx=89.5, ty=93.8, tz=123.1, # <https://GeoNet.ESRI.com/thread/36583> sz=-0.156 # <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal.js> # <https://www.Gov.UK/guidance/oil-and-gas-petroleum-operations-notices#pon-4> sz= 0.156, s=-1.2), Irl1965 = Transform('Irl1965', tx=-482.530, ty=130.596, tz=-564.557, sx= 1.042, sy= 0.214, sz= 0.631, s= -8.15), Irl1975 = Transform('Irl1975', tx=-482.530, ty=130.596, tz=-564.557, # XXX rotation signs may be opposite, to be checked sx= -1.042, sy= -0.214, sz= -0.631, s= -1.1), Krassovski1940 = Transform('Krassovski1940', tx=-24.0, ty=123.0, tz=94.0, sx= -0.02, sy= 0.26, sz= 0.13, s= -2.423), # spelling Krassowsky1940 = Transform('Krassowsky1940', tx=-24.0, ty=123.0, tz=94.0, sx= -0.02, sy= 0.26, sz= 0.13, s= -2.423), # spelling MGI = Transform('MGI', tx=-577.326, ty=-90.129, tz=-463.920, sx= 5.137, sy= 1.474, sz= 5.297, s= -2.423), # Austria NAD27 = Transform('NAD27', tx=8, ty=-160, tz=-176), NAD83 = Transform('NAD83', tx= 1.004, ty=-1.910, tz=-0.515, sx= 0.0267, sy= 0.00034, sz= 0.011, s=-0.0015), NTF = Transform('NTF', tx=-168, ty= -60, tz=320), # XXX verify OSGB36 = Transform('OSGB36', tx=-446.448, ty=125.157, tz=-542.060, sx= -0.1502, sy= -0.2470, sz= -0.8421, s= 20.4894), TokyoJapan = Transform('TokyoJapan', tx=148, ty=-507, tz=-685), WGS72 = Transform('WGS72', tz=-4.5, sz=0.554, s=-0.22), WGS84 = Transform('WGS84'), # unity ) class Datum(_NamedEnumItem): '''Ellipsoid and transform parameters for an earth model. ''' _ellipsoid = Ellipsoids.WGS84 #: (INTERNAL) Default ellipsoid (L{Ellipsoid}). _exactTM = None #: (INTERNAL) L{ExactTransverseMercator} projection. _transform = Transforms.WGS84 #: (INTERNAL) Default transform (L{Transform}). def __init__(self, ellipsoid, transform=None, name=''): '''New L{Datum}. @arg ellipsoid: The ellipsoid (L{Ellipsoid}). @kwarg transform: Optional transform (L{Transform}). @kwarg name: Optional, unique name (C{str}). @raise NameError: Datum with that B{C{name}} already exists. @raise TypeError: If B{C{ellipsoid}} is not an L{Ellipsoid} or B{C{transform}} is not a L{Transform}. ''' self._ellipsoid = ellipsoid or Datum._ellipsoid _TypeError(Ellipsoid, ellipsoid=self.ellipsoid) self._transform = transform or Datum._transform _TypeError(Transform, transform=self.transform) self._register(Datums, name or self.transform.name or self.ellipsoid.name) def __eq__(self, other): '''Compare this and an other datum. @arg other: The other datum (L{Datum}). @return: C{True} if equal, C{False} otherwise. ''' return self is other or (isinstance(other, Datum) and self.ellipsoid == other.ellipsoid and self.transform == other.transform) def ecef(self, Ecef=None): '''Return U{ECEF<https://WikiPedia.org/wiki/ECEF>} converter. @kwarg Ecef: ECEF class to use (L{EcefKarney}, L{EcefVeness} or L{EcefYou}). @return: An ECEF converter for this C{datum} (L{EcefKarney}, L{EcefVeness} or L{EcefYou}). @raise TypeError: Invalid B{C{Ecef}}. ''' return _4Ecef(self, Ecef) @property_RO def ellipsoid(self): '''Get this datum's ellipsoid (L{Ellipsoid}). ''' return self._ellipsoid @property_RO def exactTM(self): '''Get the C{ExactTM} projection (L{ExactTransverseMercator}). ''' if self._exactTM is None: from pygeodesy.etm import ExactTransverseMercator self._exactTM = ExactTransverseMercator(datum=self) return self._exactTM @property_RO def isEllipsoidal(self): '''Check whether this datum is ellipsoidal (C{bool}). ''' return self._ellipsoid.isEllipsoidal @property_RO def isSpherical(self): '''Check whether this datum is spherical (C{bool}). ''' return self._ellipsoid.isSpherical def toStr(self, **unused): # PYCHOK expected '''Return this datum as a string. @return: Datum attributes (C{str}). ''' t = ['name=' + repr(self.named)] for a in ('ellipsoid', 'transform'): v = getattr(self, a) t.append('%s=%ss.%s' % (a, v.classname, v.name)) return ', '.join(t) @property_RO def transform(self): '''Get this datum's transform (L{Transform}). ''' return self._transform Datums = _NamedEnum('Datums', Datum) #: Registered datums. # Datums with associated ellipsoid and Helmert transform parameters # to convert from WGS84 into the given datum. More are available at # <https://Earth-Info.NGA.mil/GandG/coordsys/datums/NATO_DT.pdf> and # <XXX://www.FieldenMaps.info/cconv/web/cconv_params.js>. Datums._assert( # Belgian Datum 1972, based on Hayford ellipsoid. # <https://NL.WikiPedia.org/wiki/Belgian_Datum_1972> # <https://SpatialReference.org/ref/sr-org/7718/html/> BD72 = Datum(Ellipsoids.Intl1924, Transforms.BD72), # Germany <https://WikiPedia.org/wiki/Bessel-Ellipsoid> # <https://WikiPedia.org/wiki/Helmert_transformation> DHDN = Datum(Ellipsoids.Bessel1841, Transforms.DHDN), # <https://www.Gov.UK/guidance/oil-and-gas-petroleum-operations-notices#pon-4> ED50 = Datum(Ellipsoids.Intl1924, Transforms.ED50), # Australia <https://ICSM.Gov.AU/datum/gda2020-and-gda94-technical-manuals> # ADG66 = Datum(Ellipsoids.ANS, Transforms.WGS84, name='ADG66'), # XXX Transform? # ADG84 = Datum(Ellipsoids.ANS, Transforms.WGS84, name='ADG84'), # XXX Transform? # GDA94 = Datum(Ellipsoids.GRS80, Transforms.WGS84, name='GDA94'), GDA2020 = Datum(Ellipsoids.GRS80, Transforms.WGS84, name='GDA2020'), # XXX Transform? # <https://WikiPedia.org/wiki/GRS_80> GRS80 = Datum(Ellipsoids.GRS80, Transforms.WGS84, name='GRS80'), # <https://OSI.IE/OSI/media/OSI/Content/Publications/transformations_booklet.pdf> Irl1975 = Datum(Ellipsoids.AiryModified, Transforms.Irl1975), # Germany <https://WikiPedia.org/wiki/Helmert_transformation> Krassovski1940 = Datum(Ellipsoids.Krassovski1940, Transforms.Krassovski1940), # XXX spelling? Krassowsky1940 = Datum(Ellipsoids.Krassowsky1940, Transforms.Krassowsky1940), # XXX spelling? # Austria <https://DE.WikiPedia.org/wiki/Datum_Austria> MGI = Datum(Ellipsoids.Bessel1841, Transforms.MGI), # <https://WikiPedia.org/wiki/Helmert_transformation> NAD27 = Datum(Ellipsoids.Clarke1866, Transforms.NAD27), # NAD83 (2009) == WGS84 - <https://www.UVM.edu/giv/resources/WGS84_NAD83.pdf> # (If you *really* must convert WGS84<->NAD83, you need more than this!) NAD83 = Datum(Ellipsoids.GRS80, Transforms.NAD83), # Nouvelle Triangulation Francaise (Paris) XXX verify NTF = Datum(Ellipsoids.Clarke1880IGN, Transforms.NTF), # <https://www.OrdnanceSurvey.co.UK/docs/support/guide-coordinate-systems-great-britain.pdf> OSGB36 = Datum(Ellipsoids.Airy1830, Transforms.OSGB36), # Germany <https://WikiPedia.org/wiki/Helmert_transformation> Potsdam = Datum(Ellipsoids.Bessel1841, Transforms.Bessel1841, name='Potsdam'), # XXX psuedo-ellipsoids for spherical LatLon Sphere = Datum(Ellipsoids.Sphere, Transforms.WGS84, name='Sphere'), # <https://www.GeoCachingToolbox.com?page=datumEllipsoidDetails> TokyoJapan = Datum(Ellipsoids.Bessel1841, Transforms.TokyoJapan), # <https://www.ICAO.int/safety/pbn/documentation/eurocontrol/eurocontrol%20wgs%2084%20implementation%20manual.pdf> WGS72 = Datum(Ellipsoids.WGS72, Transforms.WGS72), WGS84 = Datum(Ellipsoids.WGS84, Transforms.WGS84), ) if __name__ == '__main__': for E in (Datums.WGS84.ellipsoid, Datums.NAD83.ellipsoid, Ellipsoids.Sphere, Ellipsoids.SpherePopular): if E.f: f_ = 'f_=1/%.10F' % (1 / E.f,) else: f_ = 'f_=N/A' e = (E.a - E.b) / (E.a + E.b) - E.n t = (E.toStr(prec=10), 'A=%r, e=%s, %s, n=%s(%s)' % (E.A, fstr(E.e, prec=13, fmt='e'), f_, fstr(E.n, prec=13, fmt='F'), fstr(e, prec=3, fmt='e'),), 'AlphaKs=(%s)' % (fstr(E.AlphaKs, prec=20),), 'BetaKs= (%s)' % (fstr(E.BetaKs, prec=20),), 'KsOrder=(%s)' % (fstr(E.KsOrder, prec=20),), 'Mabcd= (%s)' % (fstr(E.Mabcd, prec=20),)) print('\nEllipsoid.%s: %s' % (E.name, ',\n '.join(t))) # __doc__ of this file for e in (Datums, Ellipsoids, Transforms): t = [''] + repr(e).split('\n') print('\n@var '.join(i.strip(',') for i in t)) # zap floats cache _float = float # PYCHOK expected del _floats # **) MIT License # # Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE. # % python -m pygeodesy.datum # Ellipsoid.WGS84: name='WGS84', a=6378137, b=6356752.3142499998, f_=298.257223563, f=0.0033528107, e=0.0818191908, e2=0.00669438, e12=0.99330562, e22=0.0067394967, n=0.0016792204, R1=6371008.7714166669, R2=6371007.180920884, R3=6371000.7900107643, Rr=6367449.1458250266, Rs=6367435.6797186071, # A=6367449.145823414, e=8.1819190842621e-02, f_=1/298.2572235630, n=0.0016792203864(-3.791e-13), # AlphaKs=(0.00083773182062446983, 0.00000076085277735725, 0.00000000119764550324, 0.00000000000242917068, 0.00000000000000571182, 0.0000000000000000148, 0.00000000000000000004, 0.0), # BetaKs= (0.00083773216405794864, 0.0000000590587015222, 0.00000000016734826653, 0.00000000000021647981, 0.00000000000000037879, 0.00000000000000000072, 0.0, 0.0), # KsOrder=(8.0), # Mabcd= (1.00168275103155868244, 0.00504613293193328927, 0.00000529596776243447, 0.00000000690525779769) # Ellipsoid.GRS80: name='GRS80', a=6378137, b=6356752.3141403468, f_=298.257222101, f=0.0033528107, e=0.081819191, e2=0.00669438, e12=0.99330562, e22=0.0067394968, n=0.0016792204, R1=6371008.7713801153, R2=6371007.1808835128, R3=6371000.7899741307, Rr=6367449.1457702462, Rs=6367435.6796636879, # A=6367449.145771047, e=8.1819191042816e-02, f_=1/298.2572221010, n=0.0016792203946(7.091e-16), # AlphaKs=(0.00083773182472855138, 0.00000076085278481497, 0.00000000119764552086, 0.00000000000242917073, 0.00000000000000571182, 0.0000000000000000148, 0.00000000000000000004, 0.0), # BetaKs= (0.00083773216816203529, 0.00000005905870210369, 0.000000000167348269, 0.00000000000021647982, 0.00000000000000037879, 0.00000000000000000072, 0.0, 0.0), # KsOrder=(8.0), # Mabcd= (1.00168275103983850371, 0.00504613295675166405, 0.0000052959678144849, 0.0000000069052578994) # Ellipsoid.Sphere: name='Sphere', a=6371008.7714149999, b=6371008.7714149999, f_=0, f=0, e=0, e2=0, e12=1, e22=0, n=0, R1=6371008.7714149999, R2=6371008.7714149999, R3=6371008.7714149999, Rr=6371008.7714149999, Rs=6371008.7714149999, # A=6371008.771415, e=0.0e+00, f_=N/A, n=0.0(0.0e+00), # AlphaKs=(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), # BetaKs= (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), # KsOrder=(8.0), # Mabcd= (1.0, 0.0, 0.0, 0.0) # Ellipsoid.SpherePopular: name='SpherePopular', a=6378137, b=6378137, f_=0, f=0, e=0, e2=0, e12=1, e22=0, n=0, R1=6378137, R2=6378137, R3=6378137, Rr=6378137, Rs=6378137, # A=6378137.0, e=0.0e+00, f_=N/A, n=0.0(0.0e+00), # AlphaKs=(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), # BetaKs= (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), # KsOrder=(8.0), # Mabcd= (1.0, 0.0, 0.0, 0.0)