"""Geodesic tests""" import unittest import math from geographiclib.geodesic import Geodesic class GeodesicTest(unittest.TestCase): """Geodesic test suite""" testcases = [ [35.60777, -139.44815, 111.098748429560326, -11.17491, -69.95921, 129.289270889708762, 8935244.5604818305, 80.50729714281974, 6273170.2055303837, 0.16606318447386067, 0.16479116945612937, 12841384694976.432], [55.52454, 106.05087, 22.020059880982801, 77.03196, 197.18234, 109.112041110671519, 4105086.1713924406, 36.892740690445894, 3828869.3344387607, 0.80076349608092607, 0.80101006984201008, 61674961290615.615], [-21.97856, 142.59065, -32.44456876433189, 41.84138, 98.56635, -41.84359951440466, 8394328.894657671, 75.62930491011522, 6161154.5773110616, 0.24816339233950381, 0.24930251203627892, -6637997720646.717], [-66.99028, 112.2363, 173.73491240878403, -12.70631, 285.90344, 2.512956620913668, 11150344.2312080241, 100.278634181155759, 6289939.5670446687, -0.17199490274700385, -0.17722569526345708, -121287239862139.744], [-17.42761, 173.34268, -159.033557661192928, -15.84784, 5.93557, -20.787484651536988, 16076603.1631180673, 144.640108810286253, 3732902.1583877189, -0.81273638700070476, -0.81299800519154474, 97825992354058.708], [32.84994, 48.28919, 150.492927788121982, -56.28556, 202.29132, 48.113449399816759, 16727068.9438164461, 150.565799985466607, 3147838.1910180939, -0.87334918086923126, -0.86505036767110637, -72445258525585.010], [6.96833, 52.74123, 92.581585386317712, -7.39675, 206.17291, 90.721692165923907, 17102477.2496958388, 154.147366239113561, 2772035.6169917581, -0.89991282520302447, -0.89986892177110739, -1311796973197.995], [-50.56724, -16.30485, -105.439679907590164, -33.56571, -94.97412, -47.348547835650331, 6455670.5118668696, 58.083719495371259, 5409150.7979815838, 0.53053508035997263, 0.52988722644436602, 41071447902810.047], [-58.93002, -8.90775, 140.965397902500679, -8.91104, 133.13503, 19.255429433416599, 11756066.0219864627, 105.755691241406877, 6151101.2270708536, -0.26548622269867183, -0.27068483874510741, -86143460552774.735], [-68.82867, -74.28391, 93.774347763114881, -50.63005, -8.36685, 34.65564085411343, 3956936.926063544, 35.572254987389284, 3708890.9544062657, 0.81443963736383502, 0.81420859815358342, -41845309450093.787], [-10.62672, -32.0898, -86.426713286747751, 5.883, -134.31681, -80.473780971034875, 11470869.3864563009, 103.387395634504061, 6184411.6622659713, -0.23138683500430237, -0.23155097622286792, 4198803992123.548], [-21.76221, 166.90563, 29.319421206936428, 48.72884, 213.97627, 43.508671946410168, 9098627.3986554915, 81.963476716121964, 6299240.9166992283, 0.13965943368590333, 0.14152969707656796, 10024709850277.476], [-19.79938, -174.47484, 71.167275780171533, -11.99349, -154.35109, 65.589099775199228, 2319004.8601169389, 20.896611684802389, 2267960.8703918325, 0.93427001867125849, 0.93424887135032789, -3935477535005.785], [-11.95887, -116.94513, 92.712619830452549, 4.57352, 7.16501, 78.64960934409585, 13834722.5801401374, 124.688684161089762, 5228093.177931598, -0.56879356755666463, -0.56918731952397221, -9919582785894.853], [-87.85331, 85.66836, -65.120313040242748, 66.48646, 16.09921, -4.888658719272296, 17286615.3147144645, 155.58592449699137, 2635887.4729110181, -0.90697975771398578, -0.91095608883042767, 42667211366919.534], [1.74708, 128.32011, -101.584843631173858, -11.16617, 11.87109, -86.325793296437476, 12942901.1241347408, 116.650512484301857, 5682744.8413270572, -0.44857868222697644, -0.44824490340007729, 10763055294345.653], [-25.72959, -144.90758, -153.647468693117198, -57.70581, -269.17879, -48.343983158876487, 9413446.7452453107, 84.664533838404295, 6356176.6898881281, 0.09492245755254703, 0.09737058264766572, 74515122850712.444], [-41.22777, 122.32875, 14.285113402275739, -7.57291, 130.37946, 10.805303085187369, 3812686.035106021, 34.34330804743883, 3588703.8812128856, 0.82605222593217889, 0.82572158200920196, -2456961531057.857], [11.01307, 138.25278, 79.43682622782374, 6.62726, 247.05981, 103.708090215522657, 11911190.819018408, 107.341669954114577, 6070904.722786735, -0.29767608923657404, -0.29785143390252321, 17121631423099.696], [-29.47124, 95.14681, -163.779130441688382, -27.46601, -69.15955, -15.909335945554969, 13487015.8381145492, 121.294026715742277, 5481428.9945736388, -0.51527225545373252, -0.51556587964721788, 104679964020340.318]] def test_inverse(self): """Helper function for testing inverse calculation""" for l in GeodesicTest.testcases: (lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12) = l inv = Geodesic.WGS84.Inverse(lat1, lon1, lat2, lon2, Geodesic.ALL | Geodesic.LONG_UNROLL) self.assertAlmostEqual(lon2, inv["lon2"], delta = 1e-13) self.assertAlmostEqual(azi1, inv["azi1"], delta = 1e-13) self.assertAlmostEqual(azi2, inv["azi2"], delta = 1e-13) self.assertAlmostEqual(s12, inv["s12"], delta = 1e-8) self.assertAlmostEqual(a12, inv["a12"], delta = 1e-13) self.assertAlmostEqual(m12, inv["m12"], delta = 1e-8) self.assertAlmostEqual(M12, inv["M12"], delta = 1e-15) self.assertAlmostEqual(M21, inv["M21"], delta = 1e-15) self.assertAlmostEqual(S12, inv["S12"], delta = 0.1) def test_direct(self): """Helper function for testing direct calculation""" for l in GeodesicTest.testcases: (lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12) = l direct = Geodesic.WGS84.Direct(lat1, lon1, azi1, s12, Geodesic.ALL | Geodesic.LONG_UNROLL) self.assertAlmostEqual(lat2, direct["lat2"], delta = 1e-13) self.assertAlmostEqual(lon2, direct["lon2"], delta = 1e-13) self.assertAlmostEqual(azi2, direct["azi2"], delta = 1e-13) self.assertAlmostEqual(a12, direct["a12"], delta = 1e-13) self.assertAlmostEqual(m12, direct["m12"], delta = 1e-8) self.assertAlmostEqual(M12, direct["M12"], delta = 1e-15) self.assertAlmostEqual(M21, direct["M21"], delta = 1e-15) self.assertAlmostEqual(S12, direct["S12"], delta = 0.1) def test_arcdirect(self): """Helper function for testing direct calculation with arc length""" for l in GeodesicTest.testcases: (lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12) = l direct = Geodesic.WGS84.ArcDirect(lat1, lon1, azi1, a12, Geodesic.ALL | Geodesic.LONG_UNROLL) self.assertAlmostEqual(lat2, direct["lat2"], delta = 1e-13) self.assertAlmostEqual(lon2, direct["lon2"], delta = 1e-13) self.assertAlmostEqual(azi2, direct["azi2"], delta = 1e-13) self.assertAlmostEqual(s12, direct["s12"], delta = 1e-8) self.assertAlmostEqual(m12, direct["m12"], delta = 1e-8) self.assertAlmostEqual(M12, direct["M12"], delta = 1e-15) self.assertAlmostEqual(M21, direct["M21"], delta = 1e-15) self.assertAlmostEqual(S12, direct["S12"], delta = 0.1) class GeodSolveTest(unittest.TestCase): """GeodSolve tests""" def test_GeodSolve0(self): """GeodSolve0""" inv = Geodesic.WGS84.Inverse(40.6, -73.8, 49.01666667, 2.55) self.assertAlmostEqual(inv["azi1"], 53.47022, delta = 0.5e-5) self.assertAlmostEqual(inv["azi2"], 111.59367, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 5853226, delta = 0.5) def test_GeodSolve1(self): """GeodSolve1""" direct = Geodesic.WGS84.Direct(40.63972222, -73.77888889, 53.5, 5850e3) self.assertAlmostEqual(direct["lat2"], 49.01467, delta = 0.5e-5) self.assertAlmostEqual(direct["lon2"], 2.56106, delta = 0.5e-5) self.assertAlmostEqual(direct["azi2"], 111.62947, delta = 0.5e-5) def test_GeodSolve2(self): """Check fix for antipodal prolate bug found 2010-09-04""" geod = Geodesic(6.4e6, -1/150.0) inv = geod.Inverse(0.07476, 0, -0.07476, 180) self.assertAlmostEqual(inv["azi1"], 90.00078, delta = 0.5e-5) self.assertAlmostEqual(inv["azi2"], 90.00078, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 20106193, delta = 0.5) inv = geod.Inverse(0.1, 0, -0.1, 180) self.assertAlmostEqual(inv["azi1"], 90.00105, delta = 0.5e-5) self.assertAlmostEqual(inv["azi2"], 90.00105, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 20106193, delta = 0.5) def test_GeodSolve4(self): """Check fix for short line bug found 2010-05-21""" inv = Geodesic.WGS84.Inverse(36.493349428792, 0, 36.49334942879201, 0.0000008) self.assertAlmostEqual(inv["s12"], 0.072, delta = 0.5e-3) def test_GeodSolve5(self): """Check fix for point2=pole bug found 2010-05-03""" direct = Geodesic.WGS84.Direct(0.01777745589997, 30, 0, 10e6) self.assertAlmostEqual(direct["lat2"], 90, delta = 0.5e-5) if direct["lon2"] < 0: self.assertAlmostEqual(direct["lon2"], -150, delta = 0.5e-5) self.assertAlmostEqual(abs(direct["azi2"]), 180, delta = 0.5e-5) else: self.assertAlmostEqual(direct["lon2"], 30, delta = 0.5e-5) self.assertAlmostEqual(direct["azi2"], 0, delta = 0.5e-5) def test_GeodSolve6(self): """Check fix for volatile sbet12a bug found 2011-06-25 (gcc 4.4.4 x86 -O3). Found again on 2012-03-27 with tdm-mingw32 (g++ 4.6.1).""" inv = Geodesic.WGS84.Inverse(88.202499451857, 0, -88.202499451857, 179.981022032992859592) self.assertAlmostEqual(inv["s12"], 20003898.214, delta = 0.5e-3) inv = Geodesic.WGS84.Inverse(89.262080389218, 0, -89.262080389218, 179.992207982775375662) self.assertAlmostEqual(inv["s12"], 20003925.854, delta = 0.5e-3) inv = Geodesic.WGS84.Inverse(89.333123580033, 0, -89.333123580032997687, 179.99295812360148422) self.assertAlmostEqual(inv["s12"], 20003926.881, delta = 0.5e-3) def test_GeodSolve9(self): """Check fix for volatile x bug found 2011-06-25 (gcc 4.4.4 x86 -O3)""" inv = Geodesic.WGS84.Inverse(56.320923501171, 0, -56.320923501171, 179.664747671772880215) self.assertAlmostEqual(inv["s12"], 19993558.287, delta = 0.5e-3) def test_GeodSolve10(self): """Check fix for adjust tol1_ bug found 2011-06-25 (Visual Studio 10 rel + debug)""" inv = Geodesic.WGS84.Inverse(52.784459512564, 0, -52.784459512563990912, 179.634407464943777557) self.assertAlmostEqual(inv["s12"], 19991596.095, delta = 0.5e-3) def test_GeodSolve11(self): """Check fix for bet2 = -bet1 bug found 2011-06-25 (Visual Studio 10 rel + debug)""" inv = Geodesic.WGS84.Inverse(48.522876735459, 0, -48.52287673545898293, 179.599720456223079643) self.assertAlmostEqual(inv["s12"], 19989144.774, delta = 0.5e-3) def test_GeodSolve12(self): """Check fix for inverse geodesics on extreme prolate/oblate ellipsoids Reported 2012-08-29 Stefan Guenther ; fixed 2012-10-07""" geod = Geodesic(89.8, -1.83) inv = geod.Inverse(0, 0, -10, 160) self.assertAlmostEqual(inv["azi1"], 120.27, delta = 1e-2) self.assertAlmostEqual(inv["azi2"], 105.15, delta = 1e-2) self.assertAlmostEqual(inv["s12"], 266.7, delta = 1e-1) def test_GeodSolve14(self): """Check fix for inverse ignoring lon12 = nan""" inv = Geodesic.WGS84.Inverse(0, 0, 1, math.nan) self.assertTrue(math.isnan(inv["azi1"])) self.assertTrue(math.isnan(inv["azi2"])) self.assertTrue(math.isnan(inv["s12"])) def test_GeodSolve15(self): """Initial implementation of Math::eatanhe was wrong for e^2 < 0. This checks that this is fixed.""" geod = Geodesic(6.4e6, -1/150.0) direct = geod.Direct(1, 2, 3, 4, Geodesic.AREA) self.assertAlmostEqual(direct["S12"], 23700, delta = 0.5) def test_GeodSolve17(self): """Check fix for LONG_UNROLL bug found on 2015-05-07""" direct = Geodesic.WGS84.Direct(40, -75, -10, 2e7, Geodesic.STANDARD | Geodesic.LONG_UNROLL) self.assertAlmostEqual(direct["lat2"], -39, delta = 1) self.assertAlmostEqual(direct["lon2"], -254, delta = 1) self.assertAlmostEqual(direct["azi2"], -170, delta = 1) line = Geodesic.WGS84.Line(40, -75, -10) direct = line.Position(2e7, Geodesic.STANDARD | Geodesic.LONG_UNROLL) self.assertAlmostEqual(direct["lat2"], -39, delta = 1) self.assertAlmostEqual(direct["lon2"], -254, delta = 1) self.assertAlmostEqual(direct["azi2"], -170, delta = 1) direct = Geodesic.WGS84.Direct(40, -75, -10, 2e7) self.assertAlmostEqual(direct["lat2"], -39, delta = 1) self.assertAlmostEqual(direct["lon2"], 105, delta = 1) self.assertAlmostEqual(direct["azi2"], -170, delta = 1) direct = line.Position(2e7) self.assertAlmostEqual(direct["lat2"], -39, delta = 1) self.assertAlmostEqual(direct["lon2"], 105, delta = 1) self.assertAlmostEqual(direct["azi2"], -170, delta = 1) def test_GeodSolve26(self): """Check 0/0 problem with area calculation on sphere 2015-09-08""" geod = Geodesic(6.4e6, 0) inv = geod.Inverse(1, 2, 3, 4, Geodesic.AREA) self.assertAlmostEqual(inv["S12"], 49911046115.0, delta = 0.5) def test_GeodSolve28(self): """Check for bad placement of assignment of r.a12 with |f| > 0.01 (bug in Java implementation fixed on 2015-05-19).""" geod = Geodesic(6.4e6, 0.1) direct = geod.Direct(1, 2, 10, 5e6) self.assertAlmostEqual(direct["a12"], 48.55570690, delta = 0.5e-8) def test_GeodSolve29(self): """Check longitude unrolling with inverse calculation 2015-09-16""" direct = Geodesic.WGS84.Inverse(0, 539, 0, 181) self.assertAlmostEqual(direct["lon1"], 179, delta = 1e-10) self.assertAlmostEqual(direct["lon2"], -179, delta = 1e-10) self.assertAlmostEqual(direct["s12"], 222639, delta = 0.5) direct = Geodesic.WGS84.Inverse(0, 539, 0, 181, Geodesic.STANDARD | Geodesic.LONG_UNROLL) self.assertAlmostEqual(direct["lon1"], 539, delta = 1e-10) self.assertAlmostEqual(direct["lon2"], 541, delta = 1e-10) self.assertAlmostEqual(direct["s12"], 222639, delta = 0.5) def test_GeodSolve33(self): """Check max(-0.0,+0.0) issues 2015-08-22 (triggered by bugs in Octave -- sind(-0.0) = +0.0 -- and in some version of Visual Studio -- fmod(-0.0, 360.0) = +0.0.""" inv = Geodesic.WGS84.Inverse(0, 0, 0, 179) self.assertAlmostEqual(inv["azi1"], 90.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["azi2"], 90.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 19926189, delta = 0.5) inv = Geodesic.WGS84.Inverse(0, 0, 0, 179.5) self.assertAlmostEqual(inv["azi1"], 55.96650, delta = 0.5e-5) self.assertAlmostEqual(inv["azi2"], 124.03350, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 19980862, delta = 0.5) inv = Geodesic.WGS84.Inverse(0, 0, 0, 180) self.assertAlmostEqual(inv["azi1"], 0.00000, delta = 0.5e-5) self.assertAlmostEqual(abs(inv["azi2"]), 180.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 20003931, delta = 0.5) inv = Geodesic.WGS84.Inverse(0, 0, 1, 180) self.assertAlmostEqual(inv["azi1"], 0.00000, delta = 0.5e-5) self.assertAlmostEqual(abs(inv["azi2"]), 180.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 19893357, delta = 0.5) geod = Geodesic(6.4e6, 0) inv = geod.Inverse(0, 0, 0, 179) self.assertAlmostEqual(inv["azi1"], 90.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["azi2"], 90.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 19994492, delta = 0.5) inv = geod.Inverse(0, 0, 0, 180) self.assertAlmostEqual(inv["azi1"], 0.00000, delta = 0.5e-5) self.assertAlmostEqual(abs(inv["azi2"]), 180.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 20106193, delta = 0.5) inv = geod.Inverse(0, 0, 1, 180) self.assertAlmostEqual(inv["azi1"], 0.00000, delta = 0.5e-5) self.assertAlmostEqual(abs(inv["azi2"]), 180.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 19994492, delta = 0.5) geod = Geodesic(6.4e6, -1/300.0) inv = geod.Inverse(0, 0, 0, 179) self.assertAlmostEqual(inv["azi1"], 90.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["azi2"], 90.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 19994492, delta = 0.5) inv = geod.Inverse(0, 0, 0, 180) self.assertAlmostEqual(inv["azi1"], 90.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["azi2"], 90.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 20106193, delta = 0.5) inv = geod.Inverse(0, 0, 0.5, 180) self.assertAlmostEqual(inv["azi1"], 33.02493, delta = 0.5e-5) self.assertAlmostEqual(inv["azi2"], 146.97364, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 20082617, delta = 0.5) inv = geod.Inverse(0, 0, 1, 180) self.assertAlmostEqual(inv["azi1"], 0.00000, delta = 0.5e-5) self.assertAlmostEqual(abs(inv["azi2"]), 180.00000, delta = 0.5e-5) self.assertAlmostEqual(inv["s12"], 20027270, delta = 0.5) def test_GeodSolve55(self): """Check fix for nan + point on equator or pole not returning all nans in Geodesic::Inverse, found 2015-09-23.""" inv = Geodesic.WGS84.Inverse(math.nan, 0, 0, 90) self.assertTrue(math.isnan(inv["azi1"])) self.assertTrue(math.isnan(inv["azi2"])) self.assertTrue(math.isnan(inv["s12"])) inv = Geodesic.WGS84.Inverse(math.nan, 0, 90, 9) self.assertTrue(math.isnan(inv["azi1"])) self.assertTrue(math.isnan(inv["azi2"])) self.assertTrue(math.isnan(inv["s12"])) def test_GeodSolve59(self): """Check for points close with longitudes close to 180 deg apart.""" inv = Geodesic.WGS84.Inverse(5, 0.00000000000001, 10, 180) self.assertAlmostEqual(inv["azi1"], 0.000000000000035, delta = 1.5e-14) self.assertAlmostEqual(inv["azi2"], 179.99999999999996, delta = 1.5e-14) self.assertAlmostEqual(inv["s12"], 18345191.174332713, delta = 5e-9) def test_GeodSolve61(self): """Make sure small negative azimuths are west-going""" direct = Geodesic.WGS84.Direct(45, 0, -0.000000000000000003, 1e7, Geodesic.STANDARD | Geodesic.LONG_UNROLL) self.assertAlmostEqual(direct["lat2"], 45.30632, delta = 0.5e-5) self.assertAlmostEqual(direct["lon2"], -180, delta = 0.5e-5) self.assertAlmostEqual(abs(direct["azi2"]), 180, delta = 0.5e-5) line = Geodesic.WGS84.InverseLine(45, 0, 80, -0.000000000000000003) direct = line.Position(1e7, Geodesic.STANDARD | Geodesic.LONG_UNROLL) self.assertAlmostEqual(direct["lat2"], 45.30632, delta = 0.5e-5) self.assertAlmostEqual(direct["lon2"], -180, delta = 0.5e-5) self.assertAlmostEqual(abs(direct["azi2"]), 180, delta = 0.5e-5) def test_GeodSolve65(self): """Check for bug in east-going check in GeodesicLine (needed to check for sign of 0) and sign error in area calculation due to a bogus override of the code for alp12. Found/fixed on 2015-12-19.""" line = Geodesic.WGS84.InverseLine(30, -0.000000000000000001, -31, 180, Geodesic.ALL) direct = line.Position(1e7, Geodesic.ALL | Geodesic.LONG_UNROLL) self.assertAlmostEqual(direct["lat1"], 30.00000 , delta = 0.5e-5) self.assertAlmostEqual(direct["lon1"], -0.00000 , delta = 0.5e-5) self.assertAlmostEqual(abs(direct["azi1"]), 180.00000, delta = 0.5e-5) self.assertAlmostEqual(direct["lat2"], -60.23169 , delta = 0.5e-5) self.assertAlmostEqual(direct["lon2"], -0.00000 , delta = 0.5e-5) self.assertAlmostEqual(abs(direct["azi2"]), 180.00000, delta = 0.5e-5) self.assertAlmostEqual(direct["s12"] , 10000000 , delta = 0.5) self.assertAlmostEqual(direct["a12"] , 90.06544 , delta = 0.5e-5) self.assertAlmostEqual(direct["m12"] , 6363636 , delta = 0.5) self.assertAlmostEqual(direct["M12"] , -0.0012834, delta = 0.5e7) self.assertAlmostEqual(direct["M21"] , 0.0013749 , delta = 0.5e-7) self.assertAlmostEqual(direct["S12"] , 0 , delta = 0.5) direct = line.Position(2e7, Geodesic.ALL | Geodesic.LONG_UNROLL) self.assertAlmostEqual(direct["lat1"], 30.00000 , delta = 0.5e-5) self.assertAlmostEqual(direct["lon1"], -0.00000 , delta = 0.5e-5) self.assertAlmostEqual(abs(direct["azi1"]), 180.00000, delta = 0.5e-5) self.assertAlmostEqual(direct["lat2"], -30.03547 , delta = 0.5e-5) self.assertAlmostEqual(direct["lon2"], -180.00000, delta = 0.5e-5) self.assertAlmostEqual(direct["azi2"], -0.00000 , delta = 0.5e-5) self.assertAlmostEqual(direct["s12"] , 20000000 , delta = 0.5) self.assertAlmostEqual(direct["a12"] , 179.96459 , delta = 0.5e-5) self.assertAlmostEqual(direct["m12"] , 54342 , delta = 0.5) self.assertAlmostEqual(direct["M12"] , -1.0045592, delta = 0.5e7) self.assertAlmostEqual(direct["M21"] , -0.9954339, delta = 0.5e-7) self.assertAlmostEqual(direct["S12"] , 127516405431022.0, delta = 0.5) def test_GeodSolve66(self): """Check for InverseLine if line is slightly west of S and that s13 is correctly set.""" line = Geodesic.WGS84.InverseLine(-5, -0.000000000000002, -10, 180) direct = line.Position(2e7, Geodesic.STANDARD | Geodesic.LONG_UNROLL) self.assertAlmostEqual(direct["lat2"], 4.96445 , delta = 0.5e-5) self.assertAlmostEqual(direct["lon2"], -180.00000, delta = 0.5e-5) self.assertAlmostEqual(direct["azi2"], -0.00000 , delta = 0.5e-5) direct = line.Position(0.5 * line.s13, Geodesic.STANDARD | Geodesic.LONG_UNROLL) self.assertAlmostEqual(direct["lat2"], -87.52461 , delta = 0.5e-5) self.assertAlmostEqual(direct["lon2"], -0.00000 , delta = 0.5e-5) self.assertAlmostEqual(direct["azi2"], -180.00000, delta = 0.5e-5) def test_GeodSolve71(self): """Check that DirectLine sets s13.""" line = Geodesic.WGS84.DirectLine(1, 2, 45, 1e7) direct = line.Position(0.5 * line.s13, Geodesic.STANDARD | Geodesic.LONG_UNROLL) self.assertAlmostEqual(direct["lat2"], 30.92625, delta = 0.5e-5) self.assertAlmostEqual(direct["lon2"], 37.54640, delta = 0.5e-5) self.assertAlmostEqual(direct["azi2"], 55.43104, delta = 0.5e-5) def test_GeodSolve73(self): """Check for backwards from the pole bug reported by Anon on 2016-02-13. This only affected the Java implementation. It was introduced in Java version 1.44 and fixed in 1.46-SNAPSHOT on 2016-01-17. Also the + sign on azi2 is a check on the normalizing of azimuths (converting -0.0 to +0.0).""" direct = Geodesic.WGS84.Direct(90, 10, 180, -1e6) self.assertAlmostEqual(direct["lat2"], 81.04623, delta = 0.5e-5) self.assertAlmostEqual(direct["lon2"], -170, delta = 0.5e-5) self.assertAlmostEqual(direct["azi2"], 0, delta = 0.5e-5) self.assertTrue(math.copysign(1, direct["azi2"]) > 0) def test_GeodSolve74(self): """Check fix for inaccurate areas, bug introduced in v1.46, fixed 2015-10-16.""" inv = Geodesic.WGS84.Inverse(54.1589, 15.3872, 54.1591, 15.3877, Geodesic.ALL) self.assertAlmostEqual(inv["azi1"], 55.723110355, delta = 5e-9) self.assertAlmostEqual(inv["azi2"], 55.723515675, delta = 5e-9) self.assertAlmostEqual(inv["s12"], 39.527686385, delta = 5e-9) self.assertAlmostEqual(inv["a12"], 0.000355495, delta = 5e-9) self.assertAlmostEqual(inv["m12"], 39.527686385, delta = 5e-9) self.assertAlmostEqual(inv["M12"], 0.999999995, delta = 5e-9) self.assertAlmostEqual(inv["M21"], 0.999999995, delta = 5e-9) self.assertAlmostEqual(inv["S12"], 286698586.30197, delta = 5e-4) def test_GeodSolve76(self): """The distance from Wellington and Salamanca (a classic failure of Vincenty)""" inv = Geodesic.WGS84.Inverse(-(41+19/60.0), 174+49/60.0, 40+58/60.0, -(5+30/60.0)) self.assertAlmostEqual(inv["azi1"], 160.39137649664, delta = 0.5e-11) self.assertAlmostEqual(inv["azi2"], 19.50042925176, delta = 0.5e-11) self.assertAlmostEqual(inv["s12"], 19960543.857179, delta = 0.5e-6) def test_GeodSolve78(self): """An example where the NGS calculator fails to converge""" inv = Geodesic.WGS84.Inverse(27.2, 0.0, -27.1, 179.5) self.assertAlmostEqual(inv["azi1"], 45.82468716758, delta = 0.5e-11) self.assertAlmostEqual(inv["azi2"], 134.22776532670, delta = 0.5e-11) self.assertAlmostEqual(inv["s12"], 19974354.765767, delta = 0.5e-6) def test_GeodSolve80(self): """Some tests to add code coverage: computing scale in special cases + zero length geodesic (includes GeodSolve80 - GeodSolve83) + using an incapable line.""" inv = Geodesic.WGS84.Inverse(0, 0, 0, 90, Geodesic.GEODESICSCALE) self.assertAlmostEqual(inv["M12"], -0.00528427534, delta = 0.5e-10) self.assertAlmostEqual(inv["M21"], -0.00528427534, delta = 0.5e-10) inv = Geodesic.WGS84.Inverse(0, 0, 1e-6, 1e-6, Geodesic.GEODESICSCALE) self.assertAlmostEqual(inv["M12"], 1, delta = 0.5e-10) self.assertAlmostEqual(inv["M21"], 1, delta = 0.5e-10) inv = Geodesic.WGS84.Inverse(20.001, 0, 20.001, 0, Geodesic.ALL) self.assertAlmostEqual(inv["a12"], 0, delta = 1e-13) self.assertAlmostEqual(inv["s12"], 0, delta = 1e-8) self.assertAlmostEqual(inv["azi1"], 180, delta = 1e-13) self.assertAlmostEqual(inv["azi2"], 180, delta = 1e-13) self.assertAlmostEqual(inv["m12"], 0, delta = 1e-8) self.assertAlmostEqual(inv["M12"], 1, delta = 1e-15) self.assertAlmostEqual(inv["M21"], 1, delta = 1e-15) self.assertAlmostEqual(inv["S12"], 0, delta = 1e-10) self.assertTrue(math.copysign(1, inv["a12"]) > 0) self.assertTrue(math.copysign(1, inv["s12"]) > 0) self.assertTrue(math.copysign(1, inv["m12"]) > 0) inv = Geodesic.WGS84.Inverse(90, 0, 90, 180, Geodesic.ALL) self.assertAlmostEqual(inv["a12"], 0, delta = 1e-13) self.assertAlmostEqual(inv["s12"], 0, delta = 1e-8) self.assertAlmostEqual(inv["azi1"], 0, delta = 1e-13) self.assertAlmostEqual(inv["azi2"], 180, delta = 1e-13) self.assertAlmostEqual(inv["m12"], 0, delta = 1e-8) self.assertAlmostEqual(inv["M12"], 1, delta = 1e-15) self.assertAlmostEqual(inv["M21"], 1, delta = 1e-15) self.assertAlmostEqual(inv["S12"], 127516405431022.0, delta = 0.5) # An incapable line which can't take distance as input line = Geodesic.WGS84.Line(1, 2, 90, Geodesic.LATITUDE) direct = line.Position(1000, Geodesic.EMPTY) self.assertTrue(math.isnan(direct["a12"])) def test_GeodSolve84(self): """Tests for python implementation to check fix for range errors with {fmod,sin,cos}(inf) (includes GeodSolve84 - GeodSolve91).""" direct = Geodesic.WGS84.Direct(0, 0, 90, math.inf) self.assertTrue(math.isnan(direct["lat2"])) self.assertTrue(math.isnan(direct["lon2"])) self.assertTrue(math.isnan(direct["azi2"])) direct = Geodesic.WGS84.Direct(0, 0, 90, math.nan) self.assertTrue(math.isnan(direct["lat2"])) self.assertTrue(math.isnan(direct["lon2"])) self.assertTrue(math.isnan(direct["azi2"])) direct = Geodesic.WGS84.Direct(0, 0, math.inf, 1000) self.assertTrue(math.isnan(direct["lat2"])) self.assertTrue(math.isnan(direct["lon2"])) self.assertTrue(math.isnan(direct["azi2"])) direct = Geodesic.WGS84.Direct(0, 0, math.nan, 1000) self.assertTrue(math.isnan(direct["lat2"])) self.assertTrue(math.isnan(direct["lon2"])) self.assertTrue(math.isnan(direct["azi2"])) direct = Geodesic.WGS84.Direct(0, math.inf, 90, 1000) self.assertTrue(direct["lat1"] == 0) self.assertTrue(math.isnan(direct["lon2"])) self.assertTrue(direct["azi2"] == 90) direct = Geodesic.WGS84.Direct(0, math.nan, 90, 1000) self.assertTrue(direct["lat1"] == 0) self.assertTrue(math.isnan(direct["lon2"])) self.assertTrue(direct["azi2"] == 90) direct = Geodesic.WGS84.Direct(math.inf, 0, 90, 1000) self.assertTrue(math.isnan(direct["lat2"])) self.assertTrue(math.isnan(direct["lon2"])) self.assertTrue(math.isnan(direct["azi2"])) direct = Geodesic.WGS84.Direct(math.nan, 0, 90, 1000) self.assertTrue(math.isnan(direct["lat2"])) self.assertTrue(math.isnan(direct["lon2"])) self.assertTrue(math.isnan(direct["azi2"])) def test_GeodSolve92(self): """Check fix for inaccurate hypot with python 3.[89]. Problem reported by agdhruv https://github.com/geopy/geopy/issues/466 ; see https://bugs.python.org/issue43088""" inv = Geodesic.WGS84.Inverse(37.757540000000006, -122.47018, 37.75754, -122.470177) self.assertAlmostEqual(inv["azi1"], 89.99999923, delta = 1e-7 ) self.assertAlmostEqual(inv["azi2"], 90.00000106, delta = 1e-7 ) self.assertAlmostEqual(inv["s12"], 0.264, delta = 0.5e-3) def test_GeodSolve94(self): """Check fix for lat2 = nan being treated as lat2 = 0 (bug found 2021-07-26)""" inv = Geodesic.WGS84.Inverse(0, 0, math.nan, 90) self.assertTrue(math.isnan(inv["azi1"])) self.assertTrue(math.isnan(inv["azi2"])) self.assertTrue(math.isnan(inv["s12"])) def test_GeodSolve96(self): """Failure with long doubles found with test case from Nowak + Nowak Da Costa (2022). Problem was using somg12 > 1 as a test that it needed to be set when roundoff could result in somg12 slightly bigger that 1. Found + fixed 2022-03-30.""" geod = Geodesic(6378137, 1/298.257222101) inv = geod.Inverse(0, 0, 60.0832522871723, 89.8492185074635, Geodesic.AREA) self.assertAlmostEqual(inv["S12"], 42426932221845, delta = 0.5) class PlanimeterTest(unittest.TestCase): """Planimeter tests""" polygon = Geodesic.WGS84.Polygon(False) polyline = Geodesic.WGS84.Polygon(True) @staticmethod def Planimeter(points): """Helper function for polygons""" PlanimeterTest.polygon.Clear() for p in points: PlanimeterTest.polygon.AddPoint(p[0], p[1]) return PlanimeterTest.polygon.Compute(False, True) @staticmethod def PolyLength(points): """Helper function for polylines""" PlanimeterTest.polyline.Clear() for p in points: PlanimeterTest.polyline.AddPoint(p[0], p[1]) return PlanimeterTest.polyline.Compute(False, True) def test_Planimeter0(self): """Check fix for pole-encircling bug found 2011-03-16""" points = [[89, 0], [89, 90], [89, 180], [89, 270]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 631819.8745, delta = 1e-4) self.assertAlmostEqual(area, 24952305678.0, delta = 1) points = [[-89, 0], [-89, 90], [-89, 180], [-89, 270]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 631819.8745, delta = 1e-4) self.assertAlmostEqual(area, -24952305678.0, delta = 1) points = [[0, -1], [-1, 0], [0, 1], [1, 0]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 627598.2731, delta = 1e-4) self.assertAlmostEqual(area, 24619419146.0, delta = 1) points = [[90, 0], [0, 0], [0, 90]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 30022685, delta = 1) self.assertAlmostEqual(area, 63758202715511.0, delta = 1) _, perimeter, area = PlanimeterTest.PolyLength(points) self.assertAlmostEqual(perimeter, 20020719, delta = 1) self.assertTrue(math.isnan(area)) def test_Planimeter5(self): """Check fix for Planimeter pole crossing bug found 2011-06-24""" points = [[89, 0.1], [89, 90.1], [89, -179.9]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 539297, delta = 1) self.assertAlmostEqual(area, 12476152838.5, delta = 1) def test_Planimeter6(self): """Check fix for Planimeter lon12 rounding bug found 2012-12-03""" points = [[9, -0.00000000000001], [9, 180], [9, 0]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 36026861, delta = 1) self.assertAlmostEqual(area, 0, delta = 1) points = [[9, 0.00000000000001], [9, 0], [9, 180]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 36026861, delta = 1) self.assertAlmostEqual(area, 0, delta = 1) points = [[9, 0.00000000000001], [9, 180], [9, 0]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 36026861, delta = 1) self.assertAlmostEqual(area, 0, delta = 1) points = [[9, -0.00000000000001], [9, 0], [9, 180]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 36026861, delta = 1) self.assertAlmostEqual(area, 0, delta = 1) def test_Planimeter12(self): """Area of arctic circle (not really -- adjunct to rhumb-area test)""" points = [[66.562222222, 0], [66.562222222, 180], [66.562222222, 360]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 10465729, delta = 1) self.assertAlmostEqual(area, 0, delta = 1) def test_Planimeter12r(self): """Reverse area of arctic circle""" points = [[66.562222222, -0], [66.562222222, -180], [66.562222222, -360]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 10465729, delta = 1) self.assertAlmostEqual(area, 0, delta = 1) def test_Planimeter13(self): """Check encircling pole twice""" points = [[89,-360], [89,-240], [89,-120], [89,0], [89,120], [89,240]] _, perimeter, area = PlanimeterTest.Planimeter(points) self.assertAlmostEqual(perimeter, 1160741, delta = 1) self.assertAlmostEqual(area, 32415230256.0, delta = 1) def test_Planimeter15(self): """Coverage tests, includes Planimeter15 - Planimeter18 (combinations of reverse and sign) + calls to testpoint, testedge.""" lat = [2, 1, 3] lon = [1, 2, 3] r = 18454562325.45119 a0 = 510065621724088.5093 # ellipsoid area PlanimeterTest.polygon.Clear() PlanimeterTest.polygon.AddPoint(lat[0], lon[0]) PlanimeterTest.polygon.AddPoint(lat[1], lon[1]) _, _, area = PlanimeterTest.polygon.TestPoint(lat[2], lon[2], False, True) self.assertAlmostEqual(area, r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestPoint(lat[2], lon[2], False, False) self.assertAlmostEqual(area, r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestPoint(lat[2], lon[2], True, True) self.assertAlmostEqual(area, -r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestPoint(lat[2], lon[2], True, False) self.assertAlmostEqual(area, a0-r, delta = 0.5) inv = Geodesic.WGS84.Inverse(lat[1], lon[1], lat[2], lon[2]) azi1 = inv["azi1"] s12 = inv["s12"] _, _, area = PlanimeterTest.polygon.TestEdge(azi1, s12, False, True) self.assertAlmostEqual(area, r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestEdge(azi1, s12, False, False) self.assertAlmostEqual(area, r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestEdge(azi1, s12, True, True) self.assertAlmostEqual(area, -r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestEdge(azi1, s12, True, False) self.assertAlmostEqual(area, a0-r, delta = 0.5) PlanimeterTest.polygon.AddPoint(lat[2], lon[2]) _, _, area = PlanimeterTest.polygon.Compute(False, True) self.assertAlmostEqual(area, r, delta = 0.5) _, _, area = PlanimeterTest.polygon.Compute(False, False) self.assertAlmostEqual(area, r, delta = 0.5) _, _, area = PlanimeterTest.polygon.Compute(True, True) self.assertAlmostEqual(area, -r, delta = 0.5) _, _, area = PlanimeterTest.polygon.Compute(True, False) self.assertAlmostEqual(area, a0-r, delta = 0.5) def test_Planimeter19(self): """Coverage tests, includes Planimeter19 - Planimeter20 (degenerate polygons) + extra cases.""" PlanimeterTest.polygon.Clear() _, perimeter, area = PlanimeterTest.polygon.Compute(False, True) self.assertTrue(area == 0) self.assertTrue(perimeter == 0) _, perimeter, area = PlanimeterTest.polygon.TestPoint(1, 1, False, True) self.assertTrue(area == 0) self.assertTrue(perimeter == 0) _, perimeter, area = PlanimeterTest.polygon.TestEdge(90, 1000, False, True) self.assertTrue(math.isnan(area)) self.assertTrue(math.isnan(perimeter)) PlanimeterTest.polygon.AddPoint(1, 1) _, perimeter, area = PlanimeterTest.polygon.Compute(False, True) self.assertTrue(area == 0) self.assertTrue(perimeter == 0) PlanimeterTest.polyline.Clear() _, perimeter, area = PlanimeterTest.polyline.Compute(False, True) self.assertTrue(perimeter == 0) _, perimeter, area = PlanimeterTest.polyline.TestPoint(1, 1, False, True) self.assertTrue(perimeter == 0) _, perimeter, area = PlanimeterTest.polyline.TestEdge(90, 1000, False, True) self.assertTrue(math.isnan(perimeter)) PlanimeterTest.polyline.AddPoint(1, 1) _, perimeter, area = PlanimeterTest.polyline.Compute(False, True) self.assertTrue(perimeter == 0) PlanimeterTest.polygon.AddPoint(1, 1) _, perimeter, area = PlanimeterTest.polyline.TestEdge(90, 1000, False, True) self.assertAlmostEqual(perimeter, 1000, delta = 1e-10) _, perimeter, area = PlanimeterTest.polyline.TestPoint(2, 2, False, True) self.assertAlmostEqual(perimeter, 156876.149, delta = 0.5e-3) def test_Planimeter21(self): """Some tests to add code coverage: multiple circlings of pole (includes Planimeter21 - Planimeter28) + invocations via testpoint and testedge.""" lat = 45 azi = 39.2144607176828184218 s = 8420705.40957178156285 r = 39433884866571.4277 # Area for one circuit a0 = 510065621724088.5093 # Ellipsoid area PlanimeterTest.polygon.Clear() PlanimeterTest.polygon.AddPoint(lat, 60) PlanimeterTest.polygon.AddPoint(lat, 180) PlanimeterTest.polygon.AddPoint(lat, -60) PlanimeterTest.polygon.AddPoint(lat, 60) PlanimeterTest.polygon.AddPoint(lat, 180) PlanimeterTest.polygon.AddPoint(lat, -60) for i in [3, 4]: PlanimeterTest.polygon.AddPoint(lat, 60) PlanimeterTest.polygon.AddPoint(lat, 180) _, _, area = PlanimeterTest.polygon.TestPoint(lat, -60, False, True) self.assertAlmostEqual(area, i*r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestPoint(lat, -60, False, False) self.assertAlmostEqual(area, i*r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestPoint(lat, -60, True, True) self.assertAlmostEqual(area, -i*r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestPoint(lat, -60, True, False) self.assertAlmostEqual(area, -i*r + a0, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestEdge(azi, s, False, True) self.assertAlmostEqual(area, i*r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestEdge(azi, s, False, False) self.assertAlmostEqual(area, i*r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestEdge(azi, s, True, True) self.assertAlmostEqual(area, -i*r, delta = 0.5) _, _, area = PlanimeterTest.polygon.TestEdge(azi, s, True, False) self.assertAlmostEqual(area, -i*r + a0, delta = 0.5) PlanimeterTest.polygon.AddPoint(lat, -60) _, _, area = PlanimeterTest.polygon.Compute(False, True) self.assertAlmostEqual(area, i*r, delta = 0.5) _, _, area = PlanimeterTest.polygon.Compute(False, False) self.assertAlmostEqual(area, i*r, delta = 0.5) _, _, area = PlanimeterTest.polygon.Compute(True, True) self.assertAlmostEqual(area, -i*r, delta = 0.5) _, _, area = PlanimeterTest.polygon.Compute(True, False) self.assertAlmostEqual(area, -i*r + a0, delta = 0.5) def test_Planimeter29(self): """Check fix to transitdirect vs transit zero handling inconsistency""" PlanimeterTest.polygon.Clear() PlanimeterTest.polygon.AddPoint(0, 0) PlanimeterTest.polygon.AddEdge( 90, 1000) PlanimeterTest.polygon.AddEdge( 0, 1000) PlanimeterTest.polygon.AddEdge(-90, 1000) _, _, area = PlanimeterTest.polygon.Compute(False, True) # The area should be 1e6. Prior to the fix it was 1e6 - A/2, where # A = ellipsoid area. self.assertAlmostEqual(area, 1000000.0, delta = 0.01)