GeodesicTest.java

Go to the documentation of this file.

package net.sf.geographiclib.test;
 
import static org.junit.Assert.assertEquals;
import static org.junit.Assert.assertTrue;
import org.junit.Test;
import net.sf.geographiclib.*;
 
public class GeodesicTest {
 
  private static boolean isNaN(double x) { return x != x; }
  private static final PolygonArea polygon =
    new PolygonArea(Geodesic.WGS84, false);
  private static final PolygonArea polyline =
    new PolygonArea(Geodesic.WGS84, true);
 
  private static PolygonResult Planimeter(double points[][]) {
    polygon.Clear();
    for (int i = 0; i < points.length; ++i) {
      polygon.AddPoint(points[i][0], points[i][1]);
    }
    return polygon.Compute(false, true);
  }
 
  private static PolygonResult PolyLength(double points[][]) {
    polyline.Clear();
    for (int i = 0; i < points.length; ++i) {
      polyline.AddPoint(points[i][0], points[i][1]);
    }
    return polyline.Compute(false, true);
  }
 
  private static final double 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}};
 
  @Test
  public void InverseCheck() {
    for (int i = 0; i < testcases.length; ++i) {
      double
        lat1 = testcases[i][0], lon1 = testcases[i][1], azi1 = testcases[i][2],
        lat2 = testcases[i][3], lon2 = testcases[i][4], azi2 = testcases[i][5],
        s12 = testcases[i][6], a12 = testcases[i][7], m12 = testcases[i][8],
        M12 = testcases[i][9], M21 = testcases[i][10], S12 = testcases[i][11];
      GeodesicData inv = Geodesic.WGS84.Inverse(lat1, lon1, lat2, lon2,
                                                GeodesicMask.ALL |
                                                GeodesicMask.LONG_UNROLL);
      assertEquals(lon2, inv.lon2, 1e-13);
      assertEquals(azi1, inv.azi1, 1e-13);
      assertEquals(azi2, inv.azi2, 1e-13);
      assertEquals(s12, inv.s12, 1e-8);
      assertEquals(a12, inv.a12, 1e-13);
      assertEquals(m12, inv.m12, 1e-8);
      assertEquals(M12, inv.M12, 1e-15);
      assertEquals(M21, inv.M21, 1e-15);
      assertEquals(S12, inv.S12, 0.1);
    }
  }
 
  @Test
  public void DirectCheck() {
    for (int i = 0; i < testcases.length; ++i) {
      double
        lat1 = testcases[i][0], lon1 = testcases[i][1], azi1 = testcases[i][2],
        lat2 = testcases[i][3], lon2 = testcases[i][4], azi2 = testcases[i][5],
        s12 = testcases[i][6], a12 = testcases[i][7], m12 = testcases[i][8],
        M12 = testcases[i][9], M21 = testcases[i][10], S12 = testcases[i][11];
      GeodesicData dir = Geodesic.WGS84.Direct(lat1, lon1, azi1, s12,
                                               GeodesicMask.ALL |
                                               GeodesicMask.LONG_UNROLL);
      assertEquals(lat2, dir.lat2, 1e-13);
      assertEquals(lon2, dir.lon2, 1e-13);
      assertEquals(azi2, dir.azi2, 1e-13);
      assertEquals(a12, dir.a12, 1e-13);
      assertEquals(m12, dir.m12, 1e-8);
      assertEquals(M12, dir.M12, 1e-15);
      assertEquals(M21, dir.M21, 1e-15);
      assertEquals(S12, dir.S12, 0.1);
    }
  }
 
  @Test
  public void ArcDirectCheck() {
    for (int i = 0; i < testcases.length; ++i) {
      double
        lat1 = testcases[i][0], lon1 = testcases[i][1], azi1 = testcases[i][2],
        lat2 = testcases[i][3], lon2 = testcases[i][4], azi2 = testcases[i][5],
        s12 = testcases[i][6], a12 = testcases[i][7], m12 = testcases[i][8],
        M12 = testcases[i][9], M21 = testcases[i][10], S12 = testcases[i][11];
      GeodesicData dir = Geodesic.WGS84.ArcDirect(lat1, lon1, azi1, a12,
                                               GeodesicMask.ALL |
                                               GeodesicMask.LONG_UNROLL);
      assertEquals(lat2, dir.lat2, 1e-13);
      assertEquals(lon2, dir.lon2, 1e-13);
      assertEquals(azi2, dir.azi2, 1e-13);
      assertEquals(s12, dir.s12, 1e-8);
      assertEquals(m12, dir.m12, 1e-8);
      assertEquals(M12, dir.M12, 1e-15);
      assertEquals(M21, dir.M21, 1e-15);
      assertEquals(S12, dir.S12, 0.1);
    }
  }
 
  @Test
  public void GeodSolve0() {
    GeodesicData inv = Geodesic.WGS84.Inverse(40.6, -73.8,
                                              49.01666667, 2.55);
    assertEquals(inv.azi1, 53.47022, 0.5e-5);
    assertEquals(inv.azi2, 111.59367, 0.5e-5);
    assertEquals(inv.s12, 5853226, 0.5);
  }
 
  @Test
  public void GeodSolve1() {
    GeodesicData dir = Geodesic.WGS84.Direct(40.63972222, -73.77888889,
                                             53.5, 5850e3);
    assertEquals(dir.lat2, 49.01467, 0.5e-5);
    assertEquals(dir.lon2, 2.56106, 0.5e-5);
    assertEquals(dir.azi2, 111.62947, 0.5e-5);
  }
 
  @Test
  public void GeodSolve2() {
    // Check fix for antipodal prolate bug found 2010-09-04
    Geodesic geod = new Geodesic(6.4e6, -1/150.0);
    GeodesicData inv = geod.Inverse(0.07476, 0, -0.07476, 180);
    assertEquals(inv.azi1, 90.00078, 0.5e-5);
    assertEquals(inv.azi2, 90.00078, 0.5e-5);
    assertEquals(inv.s12, 20106193, 0.5);
    inv = geod.Inverse(0.1, 0, -0.1, 180);
    assertEquals(inv.azi1, 90.00105, 0.5e-5);
    assertEquals(inv.azi2, 90.00105, 0.5e-5);
    assertEquals(inv.s12, 20106193, 0.5);
  }
 
  @Test
  public void GeodSolve4() {
    // Check fix for short line bug found 2010-05-21
    GeodesicData inv = Geodesic.WGS84.Inverse(36.493349428792, 0,
                                              36.49334942879201, .0000008);
    assertEquals(inv.s12, 0.072, 0.5e-3);
  }
 
  @Test
  public void GeodSolve5() {
    // Check fix for point2=pole bug found 2010-05-03
    GeodesicData dir = Geodesic.WGS84.Direct(0.01777745589997, 30, 0, 10e6);
    assertEquals(dir.lat2, 90, 0.5e-5);
    if (dir.lon2 < 0) {
      assertEquals(dir.lon2, -150, 0.5e-5);
      assertEquals(Math.abs(dir.azi2), 180, 0.5e-5);
    } else {
      assertEquals(dir.lon2, 30, 0.5e-5);
      assertEquals(dir.azi2, 0, 0.5e-5);
    }
  }
 
  @Test
  public void GeodSolve6() {
    // 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).
    GeodesicData inv =
      Geodesic.WGS84.Inverse(88.202499451857, 0,
                             -88.202499451857, 179.981022032992859592);
    assertEquals(inv.s12, 20003898.214, 0.5e-3);
    inv = Geodesic.WGS84.Inverse(89.262080389218, 0,
                                 -89.262080389218, 179.992207982775375662);
    assertEquals(inv.s12, 20003925.854, 0.5e-3);
    inv = Geodesic.WGS84.Inverse(89.333123580033, 0, -89.333123580032997687,
                                 179.99295812360148422);
    assertEquals(inv.s12, 20003926.881, 0.5e-3);
  }
 
  @Test
  public void GeodSolve9() {
    // Check fix for volatile x bug found 2011-06-25 (gcc 4.4.4 x86 -O3)
    GeodesicData inv =
      Geodesic.WGS84.Inverse(56.320923501171, 0,
                             -56.320923501171, 179.664747671772880215);
    assertEquals(inv.s12, 19993558.287, 0.5e-3);
  }
 
  @Test
  public void GeodSolve10() {
    // Check fix for adjust tol1_ bug found 2011-06-25 (Visual Studio
    // 10 rel + debug)
    GeodesicData inv =
      Geodesic.WGS84.Inverse(52.784459512564, 0,
                             -52.784459512563990912, 179.634407464943777557);
    assertEquals(inv.s12, 19991596.095, 0.5e-3);
  }
 
  @Test
  public void GeodSolve11() {
    // Check fix for bet2 = -bet1 bug found 2011-06-25 (Visual Studio
    // 10 rel + debug)
    GeodesicData inv =
      Geodesic.WGS84.Inverse(48.522876735459, 0,
                             -48.52287673545898293, 179.599720456223079643);
    assertEquals(inv.s12, 19989144.774, 0.5e-3);
  }
 
  @Test
  public void GeodSolve12() {
    // Check fix for inverse geodesics on extreme prolate/oblate
    // ellipsoids Reported 2012-08-29 Stefan Guenther
    // <stefan.gunther@embl.de>; fixed 2012-10-07
    Geodesic geod = new Geodesic(89.8, -1.83);
    GeodesicData inv = geod.Inverse(0, 0, -10, 160);
    assertEquals(inv.azi1, 120.27, 1e-2);
    assertEquals(inv.azi2, 105.15, 1e-2);
    assertEquals(inv.s12, 266.7, 1e-1);
  }
 
  @Test
  public void GeodSolve14() {
    // Check fix for inverse ignoring lon12 = nan
    GeodesicData inv = Geodesic.WGS84.Inverse(0, 0, 1, Double.NaN);
    assertTrue(isNaN(inv.azi1));
    assertTrue(isNaN(inv.azi2));
    assertTrue(isNaN(inv.s12));
  }
 
  @Test
  public void GeodSolve15() {
    // Initial implementation of Math::eatanhe was wrong for e^2 < 0.  This
    // checks that this is fixed.
    Geodesic geod = new Geodesic(6.4e6, -1/150.0);
    GeodesicData dir = geod.Direct(1, 2, 3, 4, GeodesicMask.AREA);
    assertEquals(dir.S12, 23700, 0.5);
  }
 
  @Test
  public void GeodSolve17() {
    // Check fix for LONG_UNROLL bug found on 2015-05-07
    GeodesicData dir =
      Geodesic.WGS84.Direct(40, -75, -10, 2e7,
                            GeodesicMask.STANDARD | GeodesicMask.LONG_UNROLL);
    assertEquals(dir.lat2, -39, 1);
    assertEquals(dir.lon2, -254, 1);
    assertEquals(dir.azi2, -170, 1);
    GeodesicLine line = Geodesic.WGS84.Line(40, -75, -10);
    dir = line.Position(2e7, GeodesicMask.STANDARD | GeodesicMask.LONG_UNROLL);
    assertEquals(dir.lat2, -39, 1);
    assertEquals(dir.lon2, -254, 1);
    assertEquals(dir.azi2, -170, 1);
    dir = Geodesic.WGS84.Direct(40, -75, -10, 2e7);
    assertEquals(dir.lat2, -39, 1);
    assertEquals(dir.lon2, 105, 1);
    assertEquals(dir.azi2, -170, 1);
    dir = line.Position(2e7);
    assertEquals(dir.lat2, -39, 1);
    assertEquals(dir.lon2, 105, 1);
    assertEquals(dir.azi2, -170, 1);
  }
 
  @Test
  public void GeodSolve26() {
    // Check 0/0 problem with area calculation on sphere 2015-09-08
    Geodesic geod = new Geodesic(6.4e6, 0);
    GeodesicData inv = geod.Inverse(1, 2, 3, 4, GeodesicMask.AREA);
    assertEquals(inv.S12, 49911046115.0, 0.5);
  }
 
  @Test
  public void GeodSolve28() {
    // Check for bad placement of assignment of r.a12 with |f| > 0.01 (bug in
    // Java implementation fixed on 2015-05-19).
    Geodesic geod = new Geodesic(6.4e6, 0.1);
    GeodesicData dir = geod.Direct(1, 2, 10, 5e6);
    assertEquals(dir.a12, 48.55570690, 0.5e-8);
  }
 
  @Test
  public void GeodSolve29() {
    // Check longitude unrolling with inverse calculation 2015-09-16
    GeodesicData dir = Geodesic.WGS84.Inverse(0, 539, 0, 181);
    assertEquals(dir.lon1, 179, 1e-10);
    assertEquals(dir.lon2, -179, 1e-10);
    assertEquals(dir.s12, 222639, 0.5);
    dir = Geodesic.WGS84.Inverse(0, 539, 0, 181,
                                 GeodesicMask.STANDARD |
                                 GeodesicMask.LONG_UNROLL);
    assertEquals(dir.lon1, 539, 1e-10);
    assertEquals(dir.lon2, 541, 1e-10);
    assertEquals(dir.s12, 222639, 0.5);
  }
 
  @Test
  public void GeodSolve33() {
    // 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.
    GeodesicData inv = Geodesic.WGS84.Inverse(0, 0, 0, 179);
    assertEquals(inv.azi1, 90.00000, 0.5e-5);
    assertEquals(inv.azi2, 90.00000, 0.5e-5);
    assertEquals(inv.s12, 19926189, 0.5);
    inv = Geodesic.WGS84.Inverse(0, 0, 0, 179.5);
    assertEquals(inv.azi1, 55.96650, 0.5e-5);
    assertEquals(inv.azi2, 124.03350, 0.5e-5);
    assertEquals(inv.s12, 19980862, 0.5);
    inv = Geodesic.WGS84.Inverse(0, 0, 0, 180);
    assertEquals(inv.azi1, 0.00000, 0.5e-5);
    assertEquals(Math.abs(inv.azi2), 180.00000, 0.5e-5);
    assertEquals(inv.s12, 20003931, 0.5);
    inv = Geodesic.WGS84.Inverse(0, 0, 1, 180);
    assertEquals(inv.azi1, 0.00000, 0.5e-5);
    assertEquals(Math.abs(inv.azi2), 180.00000, 0.5e-5);
    assertEquals(inv.s12, 19893357, 0.5);
    Geodesic geod = new Geodesic(6.4e6, 0);
    inv = geod.Inverse(0, 0, 0, 179);
    assertEquals(inv.azi1, 90.00000, 0.5e-5);
    assertEquals(inv.azi2, 90.00000, 0.5e-5);
    assertEquals(inv.s12, 19994492, 0.5);
    inv = geod.Inverse(0, 0, 0, 180);
    assertEquals(inv.azi1, 0.00000, 0.5e-5);
    assertEquals(Math.abs(inv.azi2), 180.00000, 0.5e-5);
    assertEquals(inv.s12, 20106193, 0.5);
    inv = geod.Inverse(0, 0, 1, 180);
    assertEquals(inv.azi1, 0.00000, 0.5e-5);
    assertEquals(Math.abs(inv.azi2), 180.00000, 0.5e-5);
    assertEquals(inv.s12, 19994492, 0.5);
    geod = new Geodesic(6.4e6, -1/300.0);
    inv = geod.Inverse(0, 0, 0, 179);
    assertEquals(inv.azi1, 90.00000, 0.5e-5);
    assertEquals(inv.azi2, 90.00000, 0.5e-5);
    assertEquals(inv.s12, 19994492, 0.5);
    inv = geod.Inverse(0, 0, 0, 180);
    assertEquals(inv.azi1, 90.00000, 0.5e-5);
    assertEquals(inv.azi2, 90.00000, 0.5e-5);
    assertEquals(inv.s12, 20106193, 0.5);
    inv = geod.Inverse(0, 0, 0.5, 180);
    assertEquals(inv.azi1, 33.02493, 0.5e-5);
    assertEquals(inv.azi2, 146.97364, 0.5e-5);
    assertEquals(inv.s12, 20082617, 0.5);
    inv = geod.Inverse(0, 0, 1, 180);
    assertEquals(inv.azi1, 0.00000, 0.5e-5);
    assertEquals(Math.abs(inv.azi2), 180.00000, 0.5e-5);
    assertEquals(inv.s12, 20027270, 0.5);
  }
 
  @Test
  public void GeodSolve55() {
    // Check fix for nan + point on equator or pole not returning all nans in
    // Geodesic::Inverse, found 2015-09-23.
    GeodesicData inv = Geodesic.WGS84.Inverse(Double.NaN, 0, 0, 90);
    assertTrue(isNaN(inv.azi1));
    assertTrue(isNaN(inv.azi2));
    assertTrue(isNaN(inv.s12));
    inv = Geodesic.WGS84.Inverse(Double.NaN, 0, 90, 3);
    assertTrue(isNaN(inv.azi1));
    assertTrue(isNaN(inv.azi2));
    assertTrue(isNaN(inv.s12));
  }
 
  @Test
  public void GeodSolve59() {
    // Check for points close with longitudes close to 180 deg apart.
    GeodesicData inv = Geodesic.WGS84.Inverse(5, 0.00000000000001, 10, 180);
    assertEquals(inv.azi1, 0.000000000000035, 1.5e-14);
    assertEquals(inv.azi2, 179.99999999999996, 1.5e-14);
    assertEquals(inv.s12, 18345191.174332713, 4e-9);
  }
 
  @Test
  public void GeodSolve61() {
    // Make sure small negative azimuths are west-going
    GeodesicData dir =
      Geodesic.WGS84.Direct(45, 0, -0.000000000000000003, 1e7,
                            GeodesicMask.STANDARD | GeodesicMask.LONG_UNROLL);
    assertEquals(dir.lat2, 45.30632, 0.5e-5);
    assertEquals(dir.lon2, -180, 0.5e-5);
    assertEquals(Math.abs(dir.azi2), 180, 0.5e-5);
    GeodesicLine line = Geodesic.WGS84.InverseLine(45, 0, 80,
                                                   -0.000000000000000003);
    dir = line.Position(1e7, GeodesicMask.STANDARD | GeodesicMask.LONG_UNROLL);
    assertEquals(dir.lat2, 45.30632, 0.5e-5);
    assertEquals(dir.lon2, -180, 0.5e-5);
    assertEquals(Math.abs(dir.azi2), 180, 0.5e-5);
  }
 
  @Test
  public void GeodSolve65() {
    // 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.
    GeodesicLine line = Geodesic.WGS84.InverseLine(30, -0.000000000000000001,
                                                   -31, 180);
    GeodesicData dir =
      line.Position(1e7, GeodesicMask.ALL | GeodesicMask.LONG_UNROLL);
    assertEquals(dir.lat1, 30.00000  , 0.5e-5);
    assertEquals(dir.lon1, -0.00000  , 0.5e-5);
    assertEquals(Math.abs(dir.azi1), 180.00000, 0.5e-5);
    assertEquals(dir.lat2, -60.23169 , 0.5e-5);
    assertEquals(dir.lon2, -0.00000  , 0.5e-5);
    assertEquals(Math.abs(dir.azi2), 180.00000, 0.5e-5);
    assertEquals(dir.s12 , 10000000  , 0.5);
    assertEquals(dir.a12 , 90.06544  , 0.5e-5);
    assertEquals(dir.m12 , 6363636   , 0.5);
    assertEquals(dir.M12 , -0.0012834, 0.5e7);
    assertEquals(dir.M21 , 0.0013749 , 0.5e-7);
    assertEquals(dir.S12 , 0         , 0.5);
    dir = line.Position(2e7, GeodesicMask.ALL | GeodesicMask.LONG_UNROLL);
    assertEquals(dir.lat1, 30.00000  , 0.5e-5);
    assertEquals(dir.lon1, -0.00000  , 0.5e-5);
    assertEquals(Math.abs(dir.azi1), 180.00000, 0.5e-5);
    assertEquals(dir.lat2, -30.03547 , 0.5e-5);
    assertEquals(dir.lon2, -180.00000, 0.5e-5);
    assertEquals(dir.azi2, -0.00000  , 0.5e-5);
    assertEquals(dir.s12 , 20000000  , 0.5);
    assertEquals(dir.a12 , 179.96459 , 0.5e-5);
    assertEquals(dir.m12 , 54342     , 0.5);
    assertEquals(dir.M12 , -1.0045592, 0.5e7);
    assertEquals(dir.M21 , -0.9954339, 0.5e-7);
    assertEquals(dir.S12 , 127516405431022.0, 0.5);
  }
 
  @Test
  public void GeodSolve69() {
    // Check for InverseLine if line is slightly west of S and that s13 is
    // correctly set.
    GeodesicLine line =
      Geodesic.WGS84.InverseLine(-5, -0.000000000000002, -10, 180);
    GeodesicData dir =
      line.Position(2e7, GeodesicMask.STANDARD | GeodesicMask.LONG_UNROLL);
    assertEquals(dir.lat2, 4.96445   , 0.5e-5);
    assertEquals(dir.lon2, -180.00000, 0.5e-5);
    assertEquals(dir.azi2, -0.00000  , 0.5e-5);
    dir = line.Position(0.5 * line.Distance(),
                        GeodesicMask.STANDARD | GeodesicMask.LONG_UNROLL);
    assertEquals(dir.lat2, -87.52461 , 0.5e-5);
    assertEquals(dir.lon2, -0.00000  , 0.5e-5);
    assertEquals(dir.azi2, -180.00000, 0.5e-5);
  }
 
  @Test
  public void GeodSolve71() {
    // Check that DirectLine sets s13.
    GeodesicLine line = Geodesic.WGS84.DirectLine(1, 2, 45, 1e7);
    GeodesicData dir =
      line.Position(0.5 * line.Distance(),
                    GeodesicMask.STANDARD | GeodesicMask.LONG_UNROLL);
    assertEquals(dir.lat2, 30.92625, 0.5e-5);
    assertEquals(dir.lon2, 37.54640, 0.5e-5);
    assertEquals(dir.azi2, 55.43104, 0.5e-5);
  }
 
  @Test
  public void GeodSolve73() {
    // 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.
    GeodesicData dir = Geodesic.WGS84.Direct(90, 10, 180, -1e6);
    assertEquals(dir.lat2, 81.04623, 0.5e-5);
    assertEquals(dir.lon2, -170, 0.5e-5);
    assertEquals(dir.azi2, 0, 0.5e-5);
  }
 
  @Test
  public void GeodSolve74() {
    // Check fix for inaccurate areas, bug introduced in v1.46, fixed
    // 2015-10-16.
    GeodesicData inv = Geodesic.WGS84.Inverse(54.1589, 15.3872,
                                              54.1591, 15.3877,
                                              GeodesicMask.ALL);
    assertEquals(inv.azi1, 55.723110355, 5e-9);
    assertEquals(inv.azi2, 55.723515675, 5e-9);
    assertEquals(inv.s12,  39.527686385, 5e-9);
    assertEquals(inv.a12,   0.000355495, 5e-9);
    assertEquals(inv.m12,  39.527686385, 5e-9);
    assertEquals(inv.M12,   0.999999995, 5e-9);
    assertEquals(inv.M21,   0.999999995, 5e-9);
    assertEquals(inv.S12, 286698586.30197, 5e-4);
  }
 
  @Test
  public void GeodSolve76() {
    // The distance from Wellington and Salamanca (a classic failure of
    // Vincenty)
    GeodesicData inv = Geodesic.WGS84.Inverse(-(41+19/60.0), 174+49/60.0,
                                              40+58/60.0, -(5+30/60.0));
    assertEquals(inv.azi1, 160.39137649664, 0.5e-11);
    assertEquals(inv.azi2,  19.50042925176, 0.5e-11);
    assertEquals(inv.s12,  19960543.857179, 0.5e-6);
  }
 
  @Test
  public void GeodSolve78() {
    // An example where the NGS calculator fails to converge */
    GeodesicData inv = Geodesic.WGS84.Inverse(27.2, 0.0, -27.1, 179.5);
    assertEquals(inv.azi1,  45.82468716758, 0.5e-11);
    assertEquals(inv.azi2, 134.22776532670, 0.5e-11);
    assertEquals(inv.s12,  19974354.765767, 0.5e-6);
  }
 
  @Test
  public void Planimeter0() {
    // Check fix for pole-encircling bug found 2011-03-16
    double pa[][] = {{89, 0}, {89, 90}, {89, 180}, {89, 270}};
    PolygonResult a = Planimeter(pa);
    assertEquals(a.perimeter, 631819.8745, 1e-4);
    assertEquals(a.area, 24952305678.0, 1);
 
    double pb[][] = {{-89, 0}, {-89, 90}, {-89, 180}, {-89, 270}};
    a = Planimeter(pb);
    assertEquals(a.perimeter, 631819.8745, 1e-4);
    assertEquals(a.area, -24952305678.0, 1);
 
    double pc[][] = {{0, -1}, {-1, 0}, {0, 1}, {1, 0}};
    a = Planimeter(pc);
    assertEquals(a.perimeter, 627598.2731, 1e-4);
    assertEquals(a.area, 24619419146.0, 1);
 
    double pd[][] = {{90, 0}, {0, 0}, {0, 90}};
    a = Planimeter(pd);
    assertEquals(a.perimeter, 30022685, 1);
    assertEquals(a.area, 63758202715511.0, 1);
    a = PolyLength(pd);
    assertEquals(a.perimeter, 20020719, 1);
    assertTrue(isNaN(a.area));
  }
 
  @Test
  public void Planimeter5() {
    // Check fix for Planimeter pole crossing bug found 2011-06-24
    double points[][] = {{89, 0.1}, {89, 90.1}, {89, -179.9}};
    PolygonResult a = Planimeter(points);
    assertEquals(a.perimeter, 539297, 1);
    assertEquals(a.area, 12476152838.5, 1);
  }
 
  @Test
  public void Planimeter6() {
    // Check fix for Planimeter lon12 rounding bug found 2012-12-03
    double pa[][] = {{9, -0.00000000000001}, {9, 180}, {9, 0}};
    PolygonResult a = Planimeter(pa);
    assertEquals(a.perimeter, 36026861, 1);
    assertEquals(a.area, 0, 1);
    double pb[][] = {{9, 0.00000000000001}, {9, 0}, {9, 180}};
    a = Planimeter(pb);
    assertEquals(a.perimeter, 36026861, 1);
    assertEquals(a.area, 0, 1);
    double pc[][] = {{9, 0.00000000000001}, {9, 180}, {9, 0}};
    a = Planimeter(pc);
    assertEquals(a.perimeter, 36026861, 1);
    assertEquals(a.area, 0, 1);
    double pd[][] = {{9, -0.00000000000001}, {9, 0}, {9, 180}};
    a = Planimeter(pd);
    assertEquals(a.perimeter, 36026861, 1);
    assertEquals(a.area, 0, 1);
  }
 
  @Test
  public void Planimeter12() {
    // Area of arctic circle (not really -- adjunct to rhumb-area test)
    double points[][] = {{66.562222222, 0}, {66.562222222, 180}};
    PolygonResult a = Planimeter(points);
    assertEquals(a.perimeter, 10465729, 1);
    assertEquals(a.area, 0, 1);
  }
 
  @Test
  public void Planimeter13() {
    // Check encircling pole twice
    double points[][] = {{89,-360}, {89,-240}, {89,-120},
                         {89,0}, {89,120}, {89,240}};
    PolygonResult a =  Planimeter(points);
    assertEquals(a.perimeter, 1160741, 1);
    assertEquals(a.area, 32415230256.0, 1);
  }
 
}