text: import unittest
  
  from geographiclib.geodesic import Geodesic
  from geographiclib.geomath import Math
  
  class GeodesicTest(unittest.TestCase):
  
    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):
      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):
      for l in GeodesicTest.testcases:
        (lat1, lon1, azi1, lat2, lon2, azi2,
         s12, a12, m12, M12, M21, S12) = l
        dir = Geodesic.WGS84.Direct(lat1, lon1, azi1, s12,
                      Geodesic.ALL | Geodesic.LONG_UNROLL)
        self.assertAlmostEqual(lat2, dir["lat2"], delta = 1e-13)
        self.assertAlmostEqual(lon2, dir["lon2"], delta = 1e-13)
        self.assertAlmostEqual(azi2, dir["azi2"], delta = 1e-13)
        self.assertAlmostEqual(a12, dir["a12"], delta = 1e-13)
        self.assertAlmostEqual(m12, dir["m12"], delta = 1e-8)
        self.assertAlmostEqual(M12, dir["M12"], delta = 1e-15)
        self.assertAlmostEqual(M21, dir["M21"], delta = 1e-15)
        self.assertAlmostEqual(S12, dir["S12"], delta = 0.1)
  
    def test_arcdirect(self):
      for l in GeodesicTest.testcases:
        (lat1, lon1, azi1, lat2, lon2, azi2,
         s12, a12, m12, M12, M21, S12) = l
        dir = Geodesic.WGS84.ArcDirect(lat1, lon1, azi1, a12,
                         Geodesic.ALL | Geodesic.LONG_UNROLL)
        self.assertAlmostEqual(lat2, dir["lat2"], delta = 1e-13)
        self.assertAlmostEqual(lon2, dir["lon2"], delta = 1e-13)
        self.assertAlmostEqual(azi2, dir["azi2"], delta = 1e-13)
        self.assertAlmostEqual(s12, dir["s12"], delta = 1e-8)
        self.assertAlmostEqual(m12, dir["m12"], delta = 1e-8)
        self.assertAlmostEqual(M12, dir["M12"], delta = 1e-15)
        self.assertAlmostEqual(M21, dir["M21"], delta = 1e-15)
        self.assertAlmostEqual(S12, dir["S12"], delta = 0.1)
  
  class GeodSolveTest(unittest.TestCase):
  
    def test_GeodSolve0(self):
      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):
      dir = Geodesic.WGS84.Direct(40.63972222, -73.77888889, 53.5, 5850e3)
      self.assertAlmostEqual(dir["lat2"], 49.01467, delta = 0.5e-5)
      self.assertAlmostEqual(dir["lon2"], 2.56106, delta = 0.5e-5)
      self.assertAlmostEqual(dir["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
      dir = Geodesic.WGS84.Direct(0.01777745589997, 30, 0, 10e6)
      self.assertAlmostEqual(dir["lat2"], 90, delta = 0.5e-5)
      if dir["lon2"] < 0:
        self.assertAlmostEqual(dir["lon2"], -150, delta = 0.5e-5)
        self.assertAlmostEqual(dir["azi2"], -180, delta = 0.5e-5)
      else:
        self.assertAlmostEqual(dir["lon2"], 30, delta = 0.5e-5)
        self.assertAlmostEqual(dir["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
      # <stefan.gunther@embl.de>; 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)
      dir = geod.Direct(1, 2, 3, 4, Geodesic.AREA)
      self.assertAlmostEqual(dir["S12"], 23700, delta = 0.5)
  
    def test_GeodSolve17(self):
      # Check fix for LONG_UNROLL bug found on 2015-05-07
      dir = Geodesic.WGS84.Direct(40, -75, -10, 2e7,
                    Geodesic.STANDARD | Geodesic.LONG_UNROLL)
      self.assertAlmostEqual(dir["lat2"], -39, delta = 1)
      self.assertAlmostEqual(dir["lon2"], -254, delta = 1)
      self.assertAlmostEqual(dir["azi2"], -170, delta = 1)
      line = Geodesic.WGS84.Line(40, -75, -10)
      dir = line.Position(2e7, Geodesic.STANDARD | Geodesic.LONG_UNROLL)
      self.assertAlmostEqual(dir["lat2"], -39, delta = 1)
      self.assertAlmostEqual(dir["lon2"], -254, delta = 1)
      self.assertAlmostEqual(dir["azi2"], -170, delta = 1)
      dir = Geodesic.WGS84.Direct(40, -75, -10, 2e7)
      self.assertAlmostEqual(dir["lat2"], -39, delta = 1)
      self.assertAlmostEqual(dir["lon2"], 105, delta = 1)
      self.assertAlmostEqual(dir["azi2"], -170, delta = 1)
      dir = line.Position(2e7)
      self.assertAlmostEqual(dir["lat2"], -39, delta = 1)
      self.assertAlmostEqual(dir["lon2"], 105, delta = 1)
      self.assertAlmostEqual(dir["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)
      dir = geod.Direct(1, 2, 10, 5e6)
      self.assertAlmostEqual(dir["a12"], 48.55570690, delta = 0.5e-8)
  
    def test_GeodSolve29(self):
      # Check longitude unrolling with inverse calculation 2015-09-16
      dir = Geodesic.WGS84.Inverse(0, 539, 0, 181)
      self.assertAlmostEqual(dir["lon1"], 179, delta = 1e-10)
      self.assertAlmostEqual(dir["lon2"], -179, delta = 1e-10)
      self.assertAlmostEqual(dir["s12"], 222639, delta = 0.5)
      dir = Geodesic.WGS84.Inverse(0, 539, 0, 181,
                     Geodesic.STANDARD | Geodesic.LONG_UNROLL)
      self.assertAlmostEqual(dir["lon1"], 539, delta = 1e-10)
      self.assertAlmostEqual(dir["lon2"], 541, delta = 1e-10)
      self.assertAlmostEqual(dir["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(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(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(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(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(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 = 4e-9)
  
    def test_GeodSolve61(self):
      # Make sure small negative azimuths are west-going
      dir = Geodesic.WGS84.Direct(45, 0, -0.000000000000000003, 1e7,
                    Geodesic.STANDARD | Geodesic.LONG_UNROLL)
      self.assertAlmostEqual(dir["lat2"], 45.30632, delta = 0.5e-5)
      self.assertAlmostEqual(dir["lon2"], -180, delta = 0.5e-5)
      self.assertAlmostEqual(dir["azi2"], -180, delta = 0.5e-5)
      line = Geodesic.WGS84.InverseLine(45, 0, 80, -0.000000000000000003)
      dir = line.Position(1e7)
      self.assertAlmostEqual(dir["lat2"], 45.30632, delta = 0.5e-5)
      self.assertAlmostEqual(dir["lon2"], -180, delta = 0.5e-5)
      self.assertAlmostEqual(dir["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)
      dir = line.Position(1e7, Geodesic.ALL | Geodesic.LONG_UNROLL)
      self.assertAlmostEqual(dir["lat1"], 30.00000  , delta = 0.5e-5)
      self.assertAlmostEqual(dir["lon1"], -0.00000  , delta = 0.5e-5)
      self.assertAlmostEqual(dir["azi1"], -180.00000, delta = 0.5e-5)
      self.assertAlmostEqual(dir["lat2"], -60.23169 , delta = 0.5e-5)
      self.assertAlmostEqual(dir["lon2"], -0.00000  , delta = 0.5e-5)
      self.assertAlmostEqual(dir["azi2"], -180.00000, delta = 0.5e-5)
      self.assertAlmostEqual(dir["s12"] , 10000000  , delta = 0.5)
      self.assertAlmostEqual(dir["a12"] , 90.06544  , delta = 0.5e-5)
      self.assertAlmostEqual(dir["m12"] , 6363636   , delta = 0.5)
      self.assertAlmostEqual(dir["M12"] , -0.0012834, delta = 0.5e7)
      self.assertAlmostEqual(dir["M21"] , 0.0013749 , delta = 0.5e-7)
      self.assertAlmostEqual(dir["S12"] , 0         , delta = 0.5)
      dir = line.Position(2e7, Geodesic.ALL | Geodesic.LONG_UNROLL)
      self.assertAlmostEqual(dir["lat1"], 30.00000  , delta = 0.5e-5)
      self.assertAlmostEqual(dir["lon1"], -0.00000  , delta = 0.5e-5)
      self.assertAlmostEqual(dir["azi1"], -180.00000, delta = 0.5e-5)
      self.assertAlmostEqual(dir["lat2"], -30.03547 , delta = 0.5e-5)
      self.assertAlmostEqual(dir["lon2"], -180.00000, delta = 0.5e-5)
      self.assertAlmostEqual(dir["azi2"], -0.00000  , delta = 0.5e-5)
      self.assertAlmostEqual(dir["s12"] , 20000000  , delta = 0.5)
      self.assertAlmostEqual(dir["a12"] , 179.96459 , delta = 0.5e-5)
      self.assertAlmostEqual(dir["m12"] , 54342     , delta = 0.5)
      self.assertAlmostEqual(dir["M12"] , -1.0045592, delta = 0.5e7)
      self.assertAlmostEqual(dir["M21"] , -0.9954339, delta = 0.5e-7)
      self.assertAlmostEqual(dir["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)
      dir = line.Position(2e7, Geodesic.STANDARD | Geodesic.LONG_UNROLL)
      self.assertAlmostEqual(dir["lat2"], 4.96445   , delta = 0.5e-5)
      self.assertAlmostEqual(dir["lon2"], -180.00000, delta = 0.5e-5)
      self.assertAlmostEqual(dir["azi2"], -0.00000  , delta = 0.5e-5)
      dir = line.Position(0.5 * line.s13,
                          Geodesic.STANDARD | Geodesic.LONG_UNROLL)
      self.assertAlmostEqual(dir["lat2"], -87.52461 , delta = 0.5e-5)
      self.assertAlmostEqual(dir["lon2"], -0.00000  , delta = 0.5e-5)
      self.assertAlmostEqual(dir["azi2"], -180.00000, delta = 0.5e-5)
  
    def test_GeodSolve71(self):
      # Check that DirectLine sets s13.
      line = Geodesic.WGS84.DirectLine(1, 2, 45, 1e7)
      dir = line.Position(0.5 * line.s13,
                          Geodesic.STANDARD | Geodesic.LONG_UNROLL)
      self.assertAlmostEqual(dir["lat2"], 30.92625, delta = 0.5e-5)
      self.assertAlmostEqual(dir["lon2"], 37.54640, delta = 0.5e-5)
      self.assertAlmostEqual(dir["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.
      dir = Geodesic.WGS84.Direct(90, 10, 180, -1e6)
      self.assertAlmostEqual(dir["lat2"], 81.04623, delta = 0.5e-5)
      self.assertAlmostEqual(dir["lon2"], -170, delta = 0.5e-5)
      self.assertAlmostEqual(dir["azi2"], 0, delta = 0.5e-5)
  
  class PlanimeterTest(unittest.TestCase):
  
    polygon = Geodesic.WGS84.Polygon(False)
    polyline = Geodesic.WGS84.Polygon(True)
  
    def Planimeter(points):
      PlanimeterTest.polygon.Clear()
      for p in points:
        PlanimeterTest.polygon.AddPoint(p[0], p[1])
      return PlanimeterTest.polygon.Compute(False, True)
    Planimeter = staticmethod(Planimeter)
  
    def PolyLength(points):
      PlanimeterTest.polyline.Clear()
      for p in points:
        PlanimeterTest.polyline.AddPoint(p[0], p[1])
      return PlanimeterTest.polyline.Compute(False, True)
    PolyLength = staticmethod(PolyLength)
  
    def test_Planimeter0(self):
      # Check fix for pole-encircling bug found 2011-03-16
      points = [[89, 0], [89, 90], [89, 180], [89, 270]]
      num, 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]]
      num, 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]]
      num, 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]]
      num, perimeter, area = PlanimeterTest.Planimeter(points)
      self.assertAlmostEqual(perimeter, 30022685, delta = 1)
      self.assertAlmostEqual(area, 63758202715511.0, delta = 1)
      num, 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]]
      num, 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]]
      num, 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]]
      num, 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]]
      num, 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]]
      num, 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]]
      num, 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]]
      num, perimeter, area = PlanimeterTest.Planimeter(points)
      self.assertAlmostEqual(perimeter, 1160741, delta = 1)
      self.assertAlmostEqual(area, 32415230256.0, delta = 1)
  