/**
* Constructor for a geodesic line staring at latitude <i>lat1</i>, longitude
* <i>lon1</i>, and azimuth <i>azi1</i> (all in degrees) with a subset of the
* capabilities included.
* <p>
* @param g A {@link Geodesic} object used to compute the necessary
* information about the GeodesicLine.
* @param lat1 latitude of point 1 (degrees).
* @param lon1 longitude of point 1 (degrees).
* @param azi1 azimuth at point 1 (degrees).
* @param caps bitor'ed combination of {@link GeodesicMask} values
* specifying the capabilities the GeodesicLine object should possess,
* i.e., which quantities can be returned in calls to {@link #Position
* Position}.
* <p>
* The {@link GeodesicMask} values are
* <ul>
* <li>
* <i>caps</i> |= {@link GeodesicMask#LATITUDE} for the latitude
* <i>lat2</i>; this is added automatically;
* <li>
* <i>caps</i> |= {@link GeodesicMask#LONGITUDE} for the latitude
* <i>lon2</i>;
* <li>
* <i>caps</i> |= {@link GeodesicMask#AZIMUTH} for the latitude
* <i>azi2</i>; this is added automatically;
* <li>
* <i>caps</i> |= {@link GeodesicMask#DISTANCE} for the distance
* <i>s12</i>;
* <li>
* <i>caps</i> |= {@link GeodesicMask#REDUCEDLENGTH} for the reduced length
* <i>m12</i>;
* <li>
* <i>caps</i> |= {@link GeodesicMask#GEODESICSCALE} for the geodesic
* scales <i>M12</i> and <i>M21</i>;
* <li>
* <i>caps</i> |= {@link GeodesicMask#AREA} for the area <i>S12</i>;
* <li>
* <i>caps</i> |= {@link GeodesicMask#DISTANCE_IN} permits the length of
* the geodesic to be given in terms of <i>s12</i>; without this capability
* the length can only be specified in terms of arc length;
* <li>
* <i>caps</i> |= {@link GeodesicMask#ALL} for all of the above.
* </ul>
**********************************************************************/
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.equatorialRadius;
_f = g.ellipsoidFlattening;
_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.Square(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.Square(_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.Square(_a) * _calp0 * _salp0 * g._e2;
_B41 = Geodesic.SinCosSeries(false, _ssig1, _csig1, _C4a);
}
}