GeodesicLine.java

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package net.sf.geographiclib;
 
public class GeodesicLine {
 
  private static final int nC1_ = Geodesic.nC1_;
  private static final int nC1p_ = Geodesic.nC1p_;
  private static final int nC2_ = Geodesic.nC2_;
  private static final int nC3_ = Geodesic.nC3_;
  private static final int nC4_ = Geodesic.nC4_;
 
  private double _lat1, _lon1, _azi1;
  private double _a, _f, _b, _c2, _f1, _salp0, _calp0, _k2,
    _salp1, _calp1, _ssig1, _csig1, _dn1, _stau1, _ctau1, _somg1, _comg1,
    _A1m1, _A2m1, _A3c, _B11, _B21, _B31, _A4, _B41;
  private double _a13, _s13;
  // index zero elements of _C1a, _C1pa, _C2a, _C3a are unused
  private double _C1a[], _C1pa[], _C2a[], _C3a[],
    _C4a[];    // all the elements of _C4a are used
  private int _caps;
 
  public GeodesicLine(Geodesic g,
                      double lat1, double lon1, double azi1) {
    this(g, lat1, lon1, azi1, GeodesicMask.ALL);
  }
 
  public GeodesicLine(Geodesic g,
                      double lat1, double lon1, double azi1,
                      int caps) {
    azi1 = GeoMath.AngNormalize(azi1);
    double salp1, calp1;
    // Guard against underflow in salp0
    { Pair p = GeoMath.sincosd(GeoMath.AngRound(azi1));
      salp1 = p.first; calp1 = p.second; }
    LineInit(g, lat1, lon1, azi1, salp1, calp1, caps);
  }
 
  private void LineInit(Geodesic g,
                        double lat1, double lon1,
                        double azi1, double salp1, double calp1,
                        int caps) {
    _a = g._a;
    _f = g._f;
    _b = g._b;
    _c2 = g._c2;
    _f1 = g._f1;
    // Always allow latitude and azimuth and unrolling the longitude
    _caps = caps | GeodesicMask.LATITUDE | GeodesicMask.AZIMUTH |
      GeodesicMask.LONG_UNROLL;
 
    _lat1 = GeoMath.LatFix(lat1);
    _lon1 = lon1;
    _azi1 = azi1; _salp1 = salp1; _calp1 = calp1;
    double cbet1, sbet1;
    { Pair p = GeoMath.sincosd(GeoMath.AngRound(_lat1));
      sbet1 = _f1 * p.first; cbet1 = p.second; }
    // Ensure cbet1 = +epsilon at poles
    { Pair p = GeoMath.norm(sbet1, cbet1);
      sbet1 = p.first; cbet1 = Math.max(Geodesic.tiny_, p.second); }
    _dn1 = Math.sqrt(1 + g._ep2 * GeoMath.sq(sbet1));
 
    // Evaluate alp0 from sin(alp1) * cos(bet1) = sin(alp0),
    _salp0 = _salp1 * cbet1; // alp0 in [0, pi/2 - |bet1|]
    // Alt: calp0 = hypot(sbet1, calp1 * cbet1).  The following
    // is slightly better (consider the case salp1 = 0).
    _calp0 = GeoMath.hypot(_calp1, _salp1 * sbet1);
    // Evaluate sig with tan(bet1) = tan(sig1) * cos(alp1).
    // sig = 0 is nearest northward crossing of equator.
    // With bet1 = 0, alp1 = pi/2, we have sig1 = 0 (equatorial line).
    // With bet1 =  pi/2, alp1 = -pi, sig1 =  pi/2
    // With bet1 = -pi/2, alp1 =  0 , sig1 = -pi/2
    // Evaluate omg1 with tan(omg1) = sin(alp0) * tan(sig1).
    // With alp0 in (0, pi/2], quadrants for sig and omg coincide.
    // No atan2(0,0) ambiguity at poles since cbet1 = +epsilon.
    // With alp0 = 0, omg1 = 0 for alp1 = 0, omg1 = pi for alp1 = pi.
    _ssig1 = sbet1; _somg1 = _salp0 * sbet1;
    _csig1 = _comg1 = sbet1 != 0 || _calp1 != 0 ? cbet1 * _calp1 : 1;
    { Pair p = GeoMath.norm(_ssig1, _csig1);
      _ssig1 = p.first; _csig1 = p.second; } // sig1 in (-pi, pi]
    // GeoMath.norm(_somg1, _comg1); -- don't need to normalize!
 
    _k2 = GeoMath.sq(_calp0) * g._ep2;
    double eps = _k2 / (2 * (1 + Math.sqrt(1 + _k2)) + _k2);
 
    if ((_caps & GeodesicMask.CAP_C1) != 0) {
      _A1m1 = Geodesic.A1m1f(eps);
      _C1a = new double[nC1_ + 1];
      Geodesic.C1f(eps, _C1a);
      _B11 = Geodesic.SinCosSeries(true, _ssig1, _csig1, _C1a);
      double s = Math.sin(_B11), c = Math.cos(_B11);
      // tau1 = sig1 + B11
      _stau1 = _ssig1 * c + _csig1 * s;
      _ctau1 = _csig1 * c - _ssig1 * s;
      // Not necessary because C1pa reverts C1a
      //    _B11 = -SinCosSeries(true, _stau1, _ctau1, _C1pa, nC1p_);
    }
 
    if ((_caps & GeodesicMask.CAP_C1p) != 0) {
      _C1pa = new double[nC1p_ + 1];
      Geodesic.C1pf(eps, _C1pa);
    }
 
    if ((_caps & GeodesicMask.CAP_C2) != 0) {
      _C2a = new double[nC2_ + 1];
      _A2m1 = Geodesic.A2m1f(eps);
      Geodesic.C2f(eps, _C2a);
      _B21 = Geodesic.SinCosSeries(true, _ssig1, _csig1, _C2a);
    }
 
    if ((_caps & GeodesicMask.CAP_C3) != 0) {
      _C3a = new double[nC3_];
      g.C3f(eps, _C3a);
      _A3c = -_f * _salp0 * g.A3f(eps);
      _B31 = Geodesic.SinCosSeries(true, _ssig1, _csig1, _C3a);
    }
 
    if ((_caps & GeodesicMask.CAP_C4) != 0) {
      _C4a = new double[nC4_];
      g.C4f(eps, _C4a);
      // Multiplier = a^2 * e^2 * cos(alpha0) * sin(alpha0)
      _A4 = GeoMath.sq(_a) * _calp0 * _salp0 * g._e2;
      _B41 = Geodesic.SinCosSeries(false, _ssig1, _csig1, _C4a);
    }
  }
 
  protected GeodesicLine(Geodesic g,
                         double lat1, double lon1,
                         double azi1, double salp1, double calp1,
                         int caps, boolean arcmode, double s13_a13) {
    LineInit(g, lat1, lon1, azi1, salp1, calp1, caps);
    GenSetDistance(arcmode, s13_a13);
  }
 
  private GeodesicLine() { _caps = 0; }
 
  public GeodesicData Position(double s12) {
    return Position(false, s12, GeodesicMask.STANDARD);
  }
  public GeodesicData Position(double s12, int outmask) {
    return Position(false, s12, outmask);
  }
 
  public GeodesicData ArcPosition(double a12) {
    return Position(true, a12, GeodesicMask.STANDARD);
  }
  public GeodesicData ArcPosition(double a12, int outmask) {
    return Position(true, a12, outmask);
  }
 
  public GeodesicData Position(boolean arcmode, double s12_a12,
                               int outmask) {
    outmask &= _caps & GeodesicMask.OUT_MASK;
    GeodesicData r = new GeodesicData();
    if (!( Init() &&
           (arcmode ||
            (_caps & (GeodesicMask.OUT_MASK & GeodesicMask.DISTANCE_IN)) != 0)
           ))
      // Uninitialized or impossible distance calculation requested
      return r;
    r.lat1 = _lat1; r.azi1 = _azi1;
    r.lon1 = ((outmask & GeodesicMask.LONG_UNROLL) != 0) ? _lon1 :
      GeoMath.AngNormalize(_lon1);
 
    // Avoid warning about uninitialized B12.
    double sig12, ssig12, csig12, B12 = 0, AB1 = 0;
    if (arcmode) {
      // Interpret s12_a12 as spherical arc length
      r.a12 = s12_a12;
      sig12 = Math.toRadians(s12_a12);
      { Pair p = GeoMath.sincosd(s12_a12);
        ssig12 = p.first; csig12 = p.second; }
    } else {
      // Interpret s12_a12 as distance
      r.s12 = s12_a12;
      double
        tau12 = s12_a12 / (_b * (1 + _A1m1)),
        s = Math.sin(tau12),
        c = Math.cos(tau12);
      // tau2 = tau1 + tau12
      B12 = - Geodesic.SinCosSeries(true,
                                    _stau1 * c + _ctau1 * s,
                                    _ctau1 * c - _stau1 * s,
                                    _C1pa);
      sig12 = tau12 - (B12 - _B11);
      ssig12 = Math.sin(sig12); csig12 = Math.cos(sig12);
      if (Math.abs(_f) > 0.01) {
        // Reverted distance series is inaccurate for |f| > 1/100, so correct
        // sig12 with 1 Newton iteration.  The following table shows the
        // approximate maximum error for a = WGS_a() and various f relative to
        // GeodesicExact.
        //     erri = the error in the inverse solution (nm)
        //     errd = the error in the direct solution (series only) (nm)
        //     errda = the error in the direct solution
        //             (series + 1 Newton) (nm)
        //
        //       f     erri  errd errda
        //     -1/5    12e6 1.2e9  69e6
        //     -1/10  123e3  12e6 765e3
        //     -1/20   1110 108e3  7155
        //     -1/50  18.63 200.9 27.12
        //     -1/100 18.63 23.78 23.37
        //     -1/150 18.63 21.05 20.26
        //      1/150 22.35 24.73 25.83
        //      1/100 22.35 25.03 25.31
        //      1/50  29.80 231.9 30.44
        //      1/20   5376 146e3  10e3
        //      1/10  829e3  22e6 1.5e6
        //      1/5   157e6 3.8e9 280e6
        double
          ssig2 = _ssig1 * csig12 + _csig1 * ssig12,
          csig2 = _csig1 * csig12 - _ssig1 * ssig12;
        B12 = Geodesic.SinCosSeries(true, ssig2, csig2, _C1a);
        double serr = (1 + _A1m1) * (sig12 + (B12 - _B11)) - s12_a12 / _b;
        sig12 = sig12 - serr / Math.sqrt(1 + _k2 * GeoMath.sq(ssig2));
        ssig12 = Math.sin(sig12); csig12 = Math.cos(sig12);
        // Update B12 below
      }
      r.a12 = Math.toDegrees(sig12);
    }
 
    double ssig2, csig2, sbet2, cbet2, salp2, calp2;
    // sig2 = sig1 + sig12
    ssig2 = _ssig1 * csig12 + _csig1 * ssig12;
    csig2 = _csig1 * csig12 - _ssig1 * ssig12;
    double dn2 = Math.sqrt(1 + _k2 * GeoMath.sq(ssig2));
    if ((outmask & (GeodesicMask.DISTANCE | GeodesicMask.REDUCEDLENGTH |
                    GeodesicMask.GEODESICSCALE)) != 0) {
      if (arcmode || Math.abs(_f) > 0.01)
        B12 = Geodesic.SinCosSeries(true, ssig2, csig2, _C1a);
      AB1 = (1 + _A1m1) * (B12 - _B11);
    }
    // sin(bet2) = cos(alp0) * sin(sig2)
    sbet2 = _calp0 * ssig2;
    // Alt: cbet2 = hypot(csig2, salp0 * ssig2);
    cbet2 = GeoMath.hypot(_salp0, _calp0 * csig2);
    if (cbet2 == 0)
      // I.e., salp0 = 0, csig2 = 0.  Break the degeneracy in this case
      cbet2 = csig2 = Geodesic.tiny_;
    // tan(alp0) = cos(sig2)*tan(alp2)
    salp2 = _salp0; calp2 = _calp0 * csig2; // No need to normalize
 
    if ((outmask & GeodesicMask.DISTANCE) != 0 && arcmode)
      r.s12 = _b * ((1 + _A1m1) * sig12 + AB1);
 
    if ((outmask & GeodesicMask.LONGITUDE) != 0) {
      // tan(omg2) = sin(alp0) * tan(sig2)
      double somg2 = _salp0 * ssig2, comg2 = csig2, // No need to normalize
        E = GeoMath.copysign(1, _salp0);            // east or west going?
      // omg12 = omg2 - omg1
      double omg12 = ((outmask & GeodesicMask.LONG_UNROLL) != 0)
        ? E * (sig12
               - (Math.atan2(  ssig2, csig2) - Math.atan2(  _ssig1, _csig1))
               + (Math.atan2(E*somg2, comg2) - Math.atan2(E*_somg1, _comg1)))
        : Math.atan2(somg2 * _comg1 - comg2 * _somg1,
                     comg2 * _comg1 + somg2 * _somg1);
      double lam12 = omg12 + _A3c *
        ( sig12 + (Geodesic.SinCosSeries(true, ssig2, csig2, _C3a)
                   - _B31));
      double lon12 = Math.toDegrees(lam12);
      r.lon2 = ((outmask & GeodesicMask.LONG_UNROLL) != 0) ? _lon1 + lon12 :
        GeoMath.AngNormalize(r.lon1 + GeoMath.AngNormalize(lon12));
    }
 
    if ((outmask & GeodesicMask.LATITUDE) != 0)
      r.lat2 = GeoMath.atan2d(sbet2, _f1 * cbet2);
 
    if ((outmask & GeodesicMask.AZIMUTH) != 0)
      r.azi2 = GeoMath.atan2d(salp2, calp2);
 
    if ((outmask &
         (GeodesicMask.REDUCEDLENGTH | GeodesicMask.GEODESICSCALE)) != 0) {
      double
        B22 = Geodesic.SinCosSeries(true, ssig2, csig2, _C2a),
        AB2 = (1 + _A2m1) * (B22 - _B21),
        J12 = (_A1m1 - _A2m1) * sig12 + (AB1 - AB2);
      if ((outmask & GeodesicMask.REDUCEDLENGTH) != 0)
        // Add parens around (_csig1 * ssig2) and (_ssig1 * csig2) to ensure
        // accurate cancellation in the case of coincident points.
        r.m12 = _b * ((dn2 * (_csig1 * ssig2) - _dn1 * (_ssig1 * csig2))
                    - _csig1 * csig2 * J12);
      if ((outmask & GeodesicMask.GEODESICSCALE) != 0) {
        double t = _k2 * (ssig2 - _ssig1) * (ssig2 + _ssig1) / (_dn1 + dn2);
        r.M12 = csig12 + (t *  ssig2 -  csig2 * J12) * _ssig1 / _dn1;
        r.M21 = csig12 - (t * _ssig1 - _csig1 * J12) *  ssig2 /  dn2;
      }
    }
 
    if ((outmask & GeodesicMask.AREA) != 0) {
      double
        B42 = Geodesic.SinCosSeries(false, ssig2, csig2, _C4a);
      double salp12, calp12;
      if (_calp0 == 0 || _salp0 == 0) {
        // alp12 = alp2 - alp1, used in atan2 so no need to normalize
        salp12 = salp2 * _calp1 - calp2 * _salp1;
        calp12 = calp2 * _calp1 + salp2 * _salp1;
      } else {
        // tan(alp) = tan(alp0) * sec(sig)
        // tan(alp2-alp1) = (tan(alp2) -tan(alp1)) / (tan(alp2)*tan(alp1)+1)
        // = calp0 * salp0 * (csig1-csig2) / (salp0^2 + calp0^2 * csig1*csig2)
        // If csig12 > 0, write
        //   csig1 - csig2 = ssig12 * (csig1 * ssig12 / (1 + csig12) + ssig1)
        // else
        //   csig1 - csig2 = csig1 * (1 - csig12) + ssig12 * ssig1
        // No need to normalize
        salp12 = _calp0 * _salp0 *
          (csig12 <= 0 ? _csig1 * (1 - csig12) + ssig12 * _ssig1 :
           ssig12 * (_csig1 * ssig12 / (1 + csig12) + _ssig1));
        calp12 = GeoMath.sq(_salp0) + GeoMath.sq(_calp0) * _csig1 * csig2;
      }
      r.S12 = _c2 * Math.atan2(salp12, calp12) + _A4 * (B42 - _B41);
    }
 
    return r;
  }
 
  public void SetDistance(double s13) {
    _s13 = s13;
    GeodesicData g = Position(false, _s13, 0);
    _a13 = g.a12;
  }
 
  void SetArc(double a13) {
    _a13 = a13;
    GeodesicData g = Position(true, _a13, GeodesicMask.DISTANCE);
    _s13 = g.s12;
  }
 
  public void GenSetDistance(boolean arcmode, double s13_a13) {
    if (arcmode)
      SetArc(s13_a13);
    else
      SetDistance(s13_a13);
  }
 
  private boolean Init() { return _caps != 0; }
 
  public double Latitude()
  { return Init() ? _lat1 : Double.NaN; }
 
  public double Longitude()
  { return Init() ? _lon1 : Double.NaN; }
 
  public double Azimuth()
  { return Init() ? _azi1 : Double.NaN; }
 
  public Pair AzimuthCosines() {
    return new Pair(Init() ? _salp1 : Double.NaN,
                    Init() ? _calp1 : Double.NaN);
  }
 
  public double EquatorialAzimuth() {
    return Init() ?
      GeoMath.atan2d(_salp0, _calp0) : Double.NaN;
  }
 
  public Pair EquatorialAzimuthCosines() {
    return new Pair(Init() ? _salp0 : Double.NaN,
                    Init() ? _calp0 : Double.NaN);
  }
 
  public double EquatorialArc() {
    return Init() ?
      GeoMath.atan2d(_ssig1, _csig1) : Double.NaN;
  }
 
  public double MajorRadius()
  { return Init() ? _a : Double.NaN; }
 
  public double Flattening()
  { return Init() ? _f : Double.NaN; }
 
  public int Capabilities() { return _caps; }
 
  public boolean Capabilities(int testcaps) {
    testcaps &= GeodesicMask.OUT_ALL;
    return (_caps & testcaps) == testcaps;
  }
 
  public double GenDistance(boolean arcmode)
  { return Init() ? (arcmode ? _a13 : _s13) : Double.NaN; }
 
  public double Distance() { return GenDistance(false); }
 
  public double Arc() { return GenDistance(true); }
 
}