Esempio n. 1
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        /**
         * The general position function.  {@link #Position(double, int) Position}
         * and {@link #ArcPosition(double, int) ArcPosition} are defined in terms of
         * this function.
         * <p>
         * @param arcmode boolean flag determining the meaning of the second
         *   parameter; if arcmode is false, then the GeodesicLine object must have
         *   been constructed with <i>caps</i> |= {@link GeodesicMask#DISTANCE_IN}.
         * @param s12_a12 if <i>arcmode</i> is false, this is the distance between
         *   point 1 and point 2 (meters); otherwise it is the arc length between
         *   point 1 and point 2 (degrees); it can be negative.
         * @param outmask a bitor'ed combination of {@link GeodesicMask} values
         *   specifying which results should be returned.
         * @return a {@link GeodesicData} object with the requested results.
         * <p>
         * The {@link GeodesicMask} values possible for <i>outmask</i> are
         * <ul>
         * <li>
         *   <i>outmask</i> |= {@link GeodesicMask#LATITUDE} for the latitude
         *   <i>lat2</i>;
         * <li>
         *   <i>outmask</i> |= {@link GeodesicMask#LONGITUDE} for the latitude
         *   <i>lon2</i>;
         * <li>
         *   <i>outmask</i> |= {@link GeodesicMask#AZIMUTH} for the latitude
         *   <i>azi2</i>;
         * <li>
         *   <i>outmask</i> |= {@link GeodesicMask#DISTANCE} for the distance
         *   <i>s12</i>;
         * <li>
         *   <i>outmask</i> |= {@link GeodesicMask#REDUCEDLENGTH} for the reduced
         *   length <i>m12</i>;
         * <li>
         *   <i>outmask</i> |= {@link GeodesicMask#GEODESICSCALE} for the geodesic
         *   scales <i>M12</i> and <i>M21</i>;
         * <li>
         *   <i>outmask</i> |= {@link GeodesicMask#ALL} for all of the above;
         * <li>
         *   <i>outmask</i> |= {@link GeodesicMask#LONG_UNROLL} to unroll <i>lon2</i>
         *   (instead of reducing it to the range [&minus;180&deg;, 180&deg;]).
         * </ul>
         * <p>
         * Requesting a value which the GeodesicLine object is not capable of
         * computing is not an error; Double.NaN is returned instead.
         **********************************************************************/

        public GeodesicData Position(bool 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.Latitude1  = _lat1; r.InitialAzimuth = _azi1;
            r.Longitude1 = ((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.ArcLength = s12_a12;
                sig12       = Math2.ToRadians(s12_a12);
                {
                    Pair p = GeoMath.SinCosD(s12_a12);
                    ssig12 = p.First; csig12 = p.Second;
                }
            }
            else
            {
                // Interpret s12_a12 as distance
                r.Distance = 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
                        sssig2 = _ssig1 * csig12 + _csig1 * ssig12,
                        scsig2 = _csig1 * csig12 - _ssig1 * ssig12;
                    B12 = Geodesic.SinCosSeries(true, sssig2, scsig2, _C1a);
                    double serr = (1 + _A1m1) * (sig12 + (B12 - _B11)) - s12_a12 / _b;
                    sig12  = sig12 - serr / Math.Sqrt(1 + _k2 * GeoMath.Square(sssig2));
                    ssig12 = Math.Sin(sig12); csig12 = Math.Cos(sig12);
                    // Update B12 below
                }
                r.ArcLength = Math2.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.Square(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.Distance = _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 = Math2.ToDegrees(lam12);
                r.Longitude2 = ((outmask & GeodesicMask.LONG_UNROLL) != 0) ? _lon1 + lon12 :
                               GeoMath.AngNormalize(r.Longitude1 + GeoMath.AngNormalize(lon12));
            }

            if ((outmask & GeodesicMask.LATITUDE) != 0)
            {
                r.Latitude2 = GeoMath.Atan2d(sbet2, _f1 * cbet2);
            }

            if ((outmask & GeodesicMask.AZIMUTH) != 0)
            {
                r.FinalAzimuth = 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.ReducedLength = _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.GeodesicScale12 = csig12 + (t * ssig2 - csig2 * J12) * _ssig1 / _dn1;
                    r.GeodesicScale21 = 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.Square(_salp0) + GeoMath.Square(_calp0) * _csig1 * csig2;
                }
                r.AreaUnderGeodesic = _c2 * Math.Atan2(salp12, calp12) + _A4 * (B42 - _B41);
            }

            return(r);
        }