public static XYCoord Mercator(ellipsoid ellip, LBCoord _lbc, double _log1, double _log0, double _lat0) { Ellipsoid _ellip = new Ellipsoid(ellip); double e1 = _ellip.e1; double e2 = _ellip.e2; double FE = 0; double FN = 0; //result+="ellipsoid.Clarke1866\n"; double a = _ellip.a; double log0 = _log0 * Math.PI / 180.0; double lat0 = _lat0 * Math.PI / 180.0; double log = _lbc.lon * Math.PI / 180.0; double lat = _lbc.lat * Math.PI / 180.0; double log1 = tools.toRad(_log1); double k0 = Math.Cos(log1) / Math.Sqrt(1 - Math.Pow(e1 * Math.Sin(log1), 2)); double E = FE + a * k0 * (lat - lat0); double N = FN + a * k0 * Math.Log( Math.Tan(Math.PI / 4 + log / 2) * Math.Pow((1 - e1 * Math.Sin(log)) / (1 + e1 * Math.Sin(log)), e1 / 2), Math.E); return(new XYCoord(E, N)); }
/// <summary> /// /// </summary> /// <param name="ellip">椭圆体</param> /// <param name="isSouth_hemisphere">是否南半球 UTM的“false easting”值为500km,而南半球UTM带的“false northing”为10000km</param> /// <param name="_xyc">投影经纬度</param> /// <param name="_log0">起始经度</param> /// <param name="_lat0">起始维度</param> /// <param name="result"></param> /// <returns></returns> public static LBCoord reverseUTM(ellipsoid ellip, bool isSouth_hemisphere, XYCoord _xyc, double _log0, double _lat0) { Ellipsoid _ellip = new Ellipsoid(ellip); double e1 = _ellip.e1; double e2 = _ellip.e2; double k0 = 0.9996; double FE = 500000; double FN = 0; if (isSouth_hemisphere) { FN = 10000000; } double a = _ellip.a; double log0 = _log0 * Math.PI / 180.0; double lat0 = _lat0 * Math.PI / 180.0; double E = _xyc.X; double N = _xyc.Y; double M0 = a * ((1 - Math.Pow(e1, 2) / 4 - 3 * Math.Pow(e1, 4) / 64 - 5 * Math.Pow(e1, 6) / 256) * log0 - (3 * Math.Pow(e1, 2) / 8 + 3 * Math.Pow(e1, 4) / 32 + 45 * Math.Pow(e1, 6) / 1024) * Math.Sin(2 * log0) + (15 * Math.Pow(e1, 4) / 256 + 45 * Math.Pow(e1, 6) / 1024) * Math.Sin(4 * log0) - (35 * Math.Pow(e1, 6) / 3027) * Math.Sin(6 * log0)); double M1 = M0 + (N - FN) / k0; double miu1 = M1 / (a * (1 - e1 * e1 / 4 - 3 * Math.Pow(e1, 4) / 64 - 5 * Math.Pow(e1, 6) / 256)); double _e1 = (1 - Math.Sqrt(1 - e1 * e1)) / (1 + Math.Sqrt(1 - e1 * e1)); double log1 = miu1 + ((3 * _e1 / 2 - 27 * _e1 * _e1 * _e1 / 32) * Math.Sin(2 * miu1) + (21 * _e1 * _e1 / 16 - 55 * Math.Pow(_e1, 4) / 32) * Math.Sin(4 * miu1) + (151 * Math.Pow(_e1, 3) / 96) * Math.Sin(6 * miu1) + (1097 * Math.Pow(_e1, 4)) * Math.Sin(8 * miu1)); double T1 = Math.Pow(Math.Tan(log1), 2); double C1 = Math.Pow(e2 * Math.Cos(log1), 2); double v1 = a / Math.Sqrt(1 - Math.Pow(e1 * Math.Sin(log1), 2)); double D = (E - FE) / (v1 * k0); double rol1 = a * (1 - e1 * e1) / Math.Pow(1 - Math.Pow(e1 * Math.Sin(log1), 2), 1.5); double log = log1 - (v1 * Math.Tan(log1) / rol1) * (D * D / 2 - (5 + 3 * T1 + 10 * C1 - 4 * C1 * C1 - 9 * e2 * e2) * Math.Pow(D, 4) / 24 + (61 + 90 * T1 + 298 * C1 + 45 * T1 - 252 * e2 * e2 - 3 * C1 * C1) * Math.Pow(D, 6) / 720); double lat = lat0 + (D - (1 + 2 * T1 + C1) * Math.Pow(D, 3) / 6 + (5 - 2 * C1 + 28 * T1 - 3 * C1 * C1 + 8 * Math.Pow(e2, 2) + 24 * T1 * T1) * Math.Pow(D, 5) / 120) / Math.Cos(log1); return(new LBCoord(tools.toDegree(lat), tools.toDegree(log))); }
public Ellipsoid(ellipsoid _ellipsoid) { switch (_ellipsoid) { case ellipsoid.Everest: this.a = 6377276; this.b = 6356075; break; case ellipsoid.Bassel: this.a = 6377379; this.b = 6356079; break; case ellipsoid.Clarke1880: this.a = 6378249; this.b = 6356515; break; case ellipsoid.Clarke1866: this.a = 6378206.400; this.b = 6356584; break; case ellipsoid.Hayford: this.a = 6378388; this.b = 6356912; break; case ellipsoid.Krassovsky: this.a = 6378245; this.b = 6356863.0188; break; case ellipsoid.IUGG: this.a = 6378160; this.b = 6356775; break; case ellipsoid.IAG75: this.a = 6378140; this.b = 6356755.2882; break; case ellipsoid.WGS84: this.a = 6378137; this.b = 6356752.3142; break; } this.alpha = (this.a - this.b) / this.a; this.e1 = Math.Sqrt(2 * this.alpha - this.alpha * this.alpha); this.e2 = Math.Sqrt(this.e1 * this.e1 / (1 - this.e1 * this.e1)); }
public static XYCoord UTM(ellipsoid ellip, bool isSouth_hemisphere, LBCoord _lbc, double _log0, double _lat0) { Ellipsoid _ellip = new Ellipsoid(ellip); double e1 = _ellip.e1; double e2 = _ellip.e2; double k0 = 0.9996; double FE = 500000; double FN = 0; if (isSouth_hemisphere) { FN = 10000000; } double a = _ellip.a; double log0 = _log0 * Math.PI / 180.0; double lat0 = _lat0 * Math.PI / 180.0; double log = _lbc.lon * Math.PI / 180.0; double lat = _lbc.lat * Math.PI / 180.0; double T = Math.Tan(log) * Math.Tan(log); double C = e1 * e1 * Math.Pow(Math.Cos(log), 2) / (1 - e1 * e1); double A = (lat - lat0) * Math.Cos(log); double v = a / Math.Pow(1 - e1 * e1 * Math.Sin(log) * Math.Sin(log), 0.5); double M = a * ((1 - Math.Pow(e1, 2) / 4 - 3 * Math.Pow(e1, 4) / 64 - 5 * Math.Pow(e1, 6) / 256) * log - (3 * Math.Pow(e1, 2) / 8 + 3 * Math.Pow(e1, 4) / 32 + 45 * Math.Pow(e1, 6) / 1024) * Math.Sin(2 * log) + (15 * Math.Pow(e1, 4) / 256 + 45 * Math.Pow(e1, 6) / 1024) * Math.Sin(4 * log) - (35 * Math.Pow(e1, 6) / 3027) * Math.Sin(6 * log)); double M0 = a * ((1 - Math.Pow(e1, 2) / 4 - 3 * Math.Pow(e1, 4) / 64 - 5 * Math.Pow(e1, 6) / 256) * log0 - (3 * Math.Pow(e1, 2) / 8 + 3 * Math.Pow(e1, 4) / 32 + 45 * Math.Pow(e1, 6) / 1024) * Math.Sin(2 * log0) + (15 * Math.Pow(e1, 4) / 256 + 45 * Math.Pow(e1, 6) / 1024) * Math.Sin(4 * log0) - (35 * Math.Pow(e1, 6) / 3027) * Math.Sin(6 * log0)); double E = FE + k0 * v * (A + (1 - T + C) * Math.Pow(A, 3) / 6 + (5 - 18 * T + T * T + 72 * C - 58 * e2 * e2) * Math.Pow(A, 5) / 120); double N = FN + k0 * (M - M0 + v * Math.Tan(log) * (A * A / 2 + (5 - T + 9 * C + 4 * C * C) * Math.Pow(A, 4) / 24 + (61 - 58 * T + T * T + 600 * C - 330 * e2 * e2) * Math.Pow(A, 6) / 720)); return(new XYCoord(E, N)); }
public static LBCoord reverseMercator(ellipsoid ellip, XYCoord _xyc, double _log1, double _log0, double _lat0) { Ellipsoid _ellip = new Ellipsoid(ellip); double e1 = _ellip.e1; double e2 = _ellip.e2; double FE = 0; double FN = 0; //result+="ellipsoid.Clarke1866\n"; double a = _ellip.a; //a=6377563.396; //e1=Math.Sqrt(0.00667054); //e2=Math.Sqrt(0.00671534); double lat0 = _lat0 * Math.PI / 180.0; double E = _xyc.X; double N = _xyc.Y; double log1 = tools.toRad(_log1); double k0 = Math.Cos(log1) / Math.Sqrt(1 - Math.Pow(e1 * Math.Sin(log1), 2)); double t = Math.Pow(Math.E, (FN - N) / (a * k0)); double x = Math.PI / 2 - 2 * Math.Atan(t); double log = x + (e1 * e1 / 2 + 5 * Math.Pow(e1, 4) / 24 + Math.Pow(e1, 6) / 12 + 13 * Math.Pow(e1, 8) / 360) * Math.Sin(2 * x) + (7 * Math.Pow(e1, 4) / 48 + 29 * Math.Pow(e1, 6) / 240 + 811 * Math.Pow(e1, 8) / 11520) * Math.Sin(4 * x) + (7 * Math.Pow(e1, 6) / 120 + 81 * Math.Pow(e1, 8) / 1120) * Math.Sin(6 * x) + (4279 * Math.Pow(e1, 8) / 161280) * Math.Sin(8 * x); //double log=log1; //double templog=log+1; //while(log!=templog) //{ // templog=log; // log=Math.PI/2-2*Math.Atan(Math.Pow(Math.E,-N/k0)*Math.Pow(Math.E,e1/2*Math.Log((1-e1*Math.Sin(log))/(1+e1*Math.Sin(log)),Math.E))); //} double lat = (E - FE) / (a * k0) + lat0; return(new LBCoord(tools.toDegree(lat), tools.toDegree(log))); }
private static ellipsoid getEllipsoid(int selection, double? majorradius, double? inverse_f) { int no_selections = 9; ellipsoid[] ells = new ellipsoid[10]; ells[0] = new ellipsoid() { name = "Sphere", a = 180 * 60 / Math.PI, invf = double.PositiveInfinity }; ells[1] = new ellipsoid() { name = "WGS84", a = 6378.137 / 1.852, invf = 298.257223563 }; ells[2] = new ellipsoid() { name = "NAD27", a = 6378.2064 / 1.852, invf = 294.9786982138 }; ells[3] = new ellipsoid() { name = "International", a = 6378.388 / 1.852, invf = 297.0 }; ells[4] = new ellipsoid() { name = "Krasovsky", a = 6378.245 / 1.852, invf = 298.3 }; ells[5] = new ellipsoid() { name = "Bessel", a = 6377.397155 / 1.852, invf = 299.1528 }; ells[6] = new ellipsoid() { name = "WGS72", a = 6378.135 / 1.852, invf = 298.26 }; ells[7] = new ellipsoid() { name = "WGS66", a = 6378.145 / 1.852, invf = 298.25 }; ells[8] = new ellipsoid() { name = "FAI sphere", a = 6371.0 / 1.852, invf = 1000000000.0 }; ells[9] = new ellipsoid() { name = "User", a = 0.0, invf = 0.0 }; // last one! if (selection == no_selections) { // user defined ells[no_selections].name = "User"; ells[no_selections].a = majorradius.Value / 1.852; ells[no_selections].invf = inverse_f.Value; if (ells[no_selections].invf == double.PositiveInfinity) { ells[no_selections].invf = 1000000000.0; } } return ells[selection]; }
private static point direct_ell(double glat1, double glon1, double faz, double s, ellipsoid ellipse) { // glat1 initial geodetic latitude in radians N positive // glon1 initial geodetic longitude in radians E positive // faz forward azimuth in radians // s distance in units of a (=nm) double EPS = 0.00000000005; double r, tu, sf, cf, b, cu, su, sa, c2a, x, c, d, y, sy = 0.0, cy = 0.0, cz = 0.0, e = 0.0; double glat2, glon2, baz, f; if ((Math.Abs(Math.Cos(glat1)) < EPS) && !(Math.Abs(Math.Sin(faz)) < EPS)) { // alert("Only N-S courses are meaningful, starting at a pole!") } double a = ellipse.a; f = 1.0 / ellipse.invf; r = 1.0 - f; tu = r * Math.Tan(glat1); sf = Math.Sin(faz); cf = Math.Cos(faz); if (cf == 0.0) { b = 0.0; } else { b = 2.0 * Math.Atan2(tu, cf); } cu = 1.0 / Math.Sqrt(1 + tu * tu); su = tu * cu; sa = cu * sf; c2a = 1.0 - sa * sa; x = 1.0 + Math.Sqrt(1.0 + c2a * (1.0 / (r * r) - 1.0)); x = (x - 2.0) / x; c = 1.0 - x; c = (x * x / 4.0 + 1.0) / c; d = (0.375 * x * x - 1.0) * x; tu = s / (r * a * c); y = tu; c = y + 1; while (Math.Abs(y - c) > EPS) { sy = Math.Sin(y); cy = Math.Cos(y); cz = Math.Cos(b + y); e = 2.0 * cz * cz - 1.0; c = y; x = e * cy; y = e + e - 1.0; y = (((sy * sy * 4.0 - 3.0) * y * cz * d / 6.0 + x) * d / 4.0 - cz) * sy * d + tu; } b = cu * cy * cf - su * sy; c = r * Math.Sqrt(sa * sa + b * b); d = su * cy + cu * sy * cf; glat2 = modlat(Math.Atan2(d, c)); c = cu * cy - su * sy * cf; x = atan2(sy * sf, c); c = ((-3.0 * c2a + 4.0) * f + 4.0) * c2a * f / 16.0; d = ((e * cy * c + cz) * sy * c + y) * sa; glon2 = modlon(glon1 + x - (1.0 - c) * d * f); // fix date line problems baz = modcrs(Math.Atan2(sa, b) + Math.PI); point retval = new point() { lat = glat2, lon = glon2, c = baz }; return retval; }
static crsd crsdist_ell(double glat1, double glon1, double glat2, double glon2, ellipsoid ellipse) { // glat1 initial geodetic latitude in radians N positive // glon1 initial geodetic longitude in radians E positive // glat2 final geodetic latitude in radians N positive // glon2 final geodetic longitude in radians E positive double a = ellipse.a; double f = 1 / ellipse.invf; double r, tu1, tu2, cu1, su1, cu2, s1, b1, f1; double x, sx = 0.0, cx = 0.0, sy = 0.0, cy = 0.0, y = 0.0, sa, c2a = 0.0, cz = 0.0, e = 0.0, c, d; double EPS = 0.00000000005; double faz, baz, s; double iter = 1.0; double MAXITER = 100.0; if ((glat1 + glat2 == 0.0) && (Math.Abs(glon1 - glon2) == Math.PI)) { glat1 = glat1 + 0.00001; // allow algorithm to complete } if (glat1 == glat2 && (glon1 == glon2 || Math.Abs(Math.Abs(glon1 - glon2) - 2 * Math.PI) < EPS)) { return new crsd(); } r = 1 - f; tu1 = r * Math.Tan(glat1); tu2 = r * Math.Tan(glat2); cu1 = 1.0 / Math.Sqrt(1.0 + tu1 * tu1); su1 = cu1 * tu1; cu2 = 1.0 / Math.Sqrt(1.0 + tu2 * tu2); s1 = cu1 * cu2; b1 = s1 * tu2; f1 = b1 * tu1; x = glon2 - glon1; d = x + 1; // force one pass while ((Math.Abs(d - x) > EPS) && (iter < MAXITER)) { iter = iter + 1; sx = Math.Sin(x); cx = Math.Cos(x); tu1 = cu2 * sx; tu2 = b1 - su1 * cu2 * cx; sy = Math.Sqrt(tu1 * tu1 + tu2 * tu2); cy = s1 * cx + f1; y = Math.Atan2(sy, cy); sa = s1 * sx / sy; c2a = 1 - sa * sa; cz = f1 + f1; if (c2a > 0.0) cz = cy - cz / c2a; e = cz * cz * 2.0 - 1.0; c = ((-3.0 * c2a + 4.0) * f + 4.0) * c2a * f / 16.0; d = x; x = ((e * cy * c + cz) * sy * c + y) * sa; x = (1.0 - c) * x * f + glon2 - glon1; } faz = modcrs(Math.Atan2(tu1, tu2)); baz = modcrs(Math.Atan2(cu1 * sx, b1 * cx - su1 * cu2) + Math.PI); x = Math.Sqrt((1.0 / (r * r) - 1.0) * c2a + 1.0); x += 1; x = (x - 2.0) / x; c = 1.0 - x; c = (x * x / 4.0 + 1.0) / c; d = (0.375 * x * x - 1.0) * x; x = e * cy; s = ((((sy * sy * 4.0 - 3.0) * (1.0 - e - e) * cz * d / 6.0 - x) * d / 4.0 + cz) * sy * d + y) * c * a * r; return new crsd() { d = s, crs12 = faz, crs21 = baz }; }
public static LBCoord reversLambert(ellipsoid ellip, XYCoord _xyc, double _log1, double _log2, double _log0, double _lat0, ref string result) { Ellipsoid _ellip = new Ellipsoid(ellip); double e = _ellip.e1; result += "e:" + e.ToString() + " a:" + _ellip.a.ToString() + "\n"; result += "-------------------------------------\n"; double log1 = _log1 * Math.PI / 180.0; double log2 = _log2 * Math.PI / 180.0; double log0 = _log0 * Math.PI / 180.0; double lat0 = _lat0 * Math.PI / 180.0; double E = _xyc.X; double N = _xyc.Y; result += "l1:" + log1.ToString() + "\n"; result += "l2:" + log2.ToString() + "\n"; result += "log0:" + log0.ToString() + "\n"; result += "lat0:" + lat0.ToString() + "\n"; result += "E:" + E.ToString() + "\n"; result += "N:" + N.ToString() + "\n"; result += "-----------------------\n"; double m1 = Math.Cos(log1) / Math.Sqrt(1 - e * e * Math.Sin(log1) * Math.Sin(log1)); double m2 = Math.Cos(log2) / Math.Sqrt(1 - e * e * Math.Sin(log2) * Math.Sin(log2)); result += "m1:" + m1.ToString() + "\n"; result += "m1:" + m2.ToString() + "\n"; double t1 = Lam_gett(log1, e); double t2 = Lam_gett(log2, e); double tF = Lam_gett(log0, e); result += "t1:" + t1.ToString() + "\n"; result += "t2:" + t2.ToString() + "\n"; result += "tF:" + tF.ToString() + "\n"; double n = Math.Log(m1 / m2, Math.E) / Math.Log(t1 / t2, Math.E); double F = m1 / (n * Math.Pow(t1, n)); double rF = _ellip.a * (F * Math.Pow(tF, n)); result += "n:" + n.ToString() + "\n"; result += "F:" + F.ToString() + "\n"; result += "rF:" + rF.ToString() + "\n"; double EF = 0; double NF = 0.0; double tht = Math.Atan((E - EF) / (rF - (N - NF))); double r = Math.Sqrt((E - EF) * (E - EF) + (rF - (N - NF)) * (rF - (N - NF))); if (n < 0) { r = -r; } double t = Math.Pow(r / (_ellip.a * F), 1 / n); result += "tht:" + tht.ToString() + "\n"; result += "r:" + r.ToString() + "\n"; result += "t:" + t.ToString() + "\n"; double log = Math.PI / 2 - 2 * Math.Atan(t); double prelog = log + 1; while (log != prelog) { prelog = log; log = Math.PI / 2 - 2 * Math.Atan(t * Math.Pow((1 - e * Math.Sin(log)) / (1 + e * Math.Sin(log)), e / 2)); } double lat = tht / n + lat0; return(new LBCoord(lat / Math.PI * 180, log / Math.PI * 180)); }
public static XYCoord lambert(ellipsoid ellip, LBCoord _lbc, double _log1, double _log2, double _log0, double _lat0, ref string result) { Ellipsoid _ellip = new Ellipsoid(ellip); double e = _ellip.e1; //result+="ellipsoid.Clarke1866\n"; result += "e:" + e.ToString() + " a:" + _ellip.a.ToString() + "\n"; result += "-------------------------------------\n"; double log1 = _log1 * Math.PI / 180.0; double log2 = _log2 * Math.PI / 180.0; result += "log1:" + log1.ToString() + "\n"; result += "log1:" + log2.ToString() + "\n"; double log0 = _log0 * Math.PI / 180.0; double lat0 = _lat0 * Math.PI / 180.0; result += "log0:" + log0.ToString() + "\n"; result += "lat0:" + lat0.ToString() + "\n"; double log = _lbc.lon * Math.PI / 180.0; double lat = _lbc.lat * Math.PI / 180.0; result += "log:" + log.ToString() + "\n"; result += "lat:" + lat.ToString() + "\n"; //double jiao=Math.Asin(e*Math.Sin(l)); result += "-------------------------------------\n"; double m1 = Math.Cos(log1) / Math.Sqrt(1 - e * e * Math.Sin(log1) * Math.Sin(log1)); double m2 = Math.Cos(log2) / Math.Sqrt(1 - e * e * Math.Sin(log2) * Math.Sin(log2)); result += "m1:" + m1.ToString() + "\n"; result += "m1:" + m2.ToString() + "\n"; double t1 = Lam_gett(log1, e); double t2 = Lam_gett(log2, e); double tF = Lam_gett(log0, e); double t = Lam_gett(log, e); result += "t1:" + t1.ToString() + "\n"; result += "t2:" + t2.ToString() + "\n"; result += "tF:" + tF.ToString() + "\n"; result += "t:" + t.ToString() + "\n"; double n = Math.Log(m1 / m2, Math.E) / Math.Log(t1 / t2, Math.E); double F = m1 / (n * Math.Pow(t1, n)); double r = _ellip.a * F * Math.Pow(t, n); double rF = _ellip.a * (F * Math.Pow(tF, n)); double tht = n * (lat - lat0); result += "a:" + _ellip.a.ToString() + "\n"; result += "n:" + n.ToString() + "\n"; result += "F:" + F.ToString() + "\n"; result += "r:" + r.ToString() + "\n"; result += "rF:" + rF.ToString() + "\n"; result += "tht:" + tht.ToString() + "\n"; return(new XYCoord(r * Math.Sin(tht), rF - r * Math.Cos(tht))); }
public static LBCoord reVersAlbers(ellipsoid ellip, XYCoord _xyc, double _log1, double _log2, double _log0, double _lat0, ref string result) { Ellipsoid _ellip = new Ellipsoid(ellip); double e = _ellip.e1; result += "e:" + e.ToString() + " a:" + _ellip.a.ToString() + "\n"; result += "-------------------------------------\n"; double l1 = _log1 * Math.PI / 180.0; double l2 = _log2 * Math.PI / 180.0; double l0 = _log0 * Math.PI / 180.0; double lmt0 = _lat0 * Math.PI / 180.0; double E = _xyc.X; double N = _xyc.Y; result += "l1:" + l1.ToString() + "\n"; result += "l2:" + l2.ToString() + "\n"; result += "l0:" + l0.ToString() + "\n"; result += "lmt0:" + lmt0.ToString() + "\n"; result += "E:" + E.ToString() + "\n"; result += "N:" + N.ToString() + "\n"; result += "-----------------------\n"; double alpha1 = getalpha(_ellip, l1); double alpha2 = getalpha(_ellip, l2); double alpha0 = getalpha(_ellip, l0); double m1 = Math.Cos(l1) / Math.Sqrt(1 - e * e * Math.Sin(l1) * Math.Sin(l1)); double m2 = Math.Cos(l2) / Math.Sqrt(1 - e * e * Math.Sin(l2) * Math.Sin(l2)); result += "m1:" + m1.ToString() + "\nm2:" + m2.ToString() + "\n"; double n = (m1 * m1 - m2 * m2) / (alpha2 - alpha1); double c = (m1 * m1 * alpha2 - m2 * m2 * alpha1) / (alpha2 - alpha1); result += "n:" + n.ToString() + "\nc:" + c.ToString() + "\n"; double rol0 = (_ellip.a * Math.Sqrt(c - n * alpha0)) / n; double tht = Math.Atan(E / (rol0 - N)); double rol = Math.Sqrt(E * E + (rol0 - N) * (rol0 - N)); double alpha = (c - rol * rol * n * n / (_ellip.a * _ellip.a)) / n; //λO + (θ / n) ?' + (e2/3 + 31e4/180 + 517e6/5040) . sin 2?'] + [(23e4/360 + 251e6/3780) . sin 4?'] //+ [(761e6/45360) . sin 6?'] result += "rol0:" + rol0.ToString() + "\nrol:" + rol.ToString() + "\n"; double beta = Math.Asin(alpha / (1 - (1 - e * e) / (2 * e) * Math.Log((1 - e) / (1 + e), Math.E))); double lmt = (lmt0 + (tht / n)) / Math.PI * 180.0; double l = beta + (e * e / 3 + 31 * Math.Pow(e, 4) / 180 + 517 * Math.Pow(e, 6) / 5040) * Math.Sin(2 * beta) + (23 * Math.Pow(e, 4) / 360 + 251 * Math.Pow(e, 6) / 3780) * Math.Sin(4 * beta) + 761 * Math.Pow(e, 6) / 45360 * Math.Sin(6 * beta); return(new LBCoord(lmt, (l / Math.PI * 180.0))); }
public static XYCoord albers(ellipsoid ellip, LBCoord _lbc, double _log1, double _log2, double _log0, double _lat0, ref string result) { Ellipsoid _ellip = new Ellipsoid(ellip); double e = _ellip.e1; result += "e:" + e.ToString() + " a:" + _ellip.a.ToString() + "\n"; result += "-------------------------------------\n"; double l1 = _log1 * Math.PI / 180.0; double l2 = _log2 * Math.PI / 180.0; double l0 = _log0 * Math.PI / 180.0; double lmt0 = _lat0 * Math.PI / 180.0; double l = _lbc.lon * Math.PI / 180.0; double lmt = _lbc.lat * Math.PI / 180.0; result += "l1:" + l1.ToString() + "\n"; result += "l2:" + l2.ToString() + "\n"; result += "l0:" + l0.ToString() + "\n"; result += "lmt0:" + lmt0.ToString() + "\n"; result += "l:" + l.ToString() + "\n"; result += "lmt:" + lmt.ToString() + "\n"; result += "-----------------------\n"; double alpha0 = getalpha(_ellip, l0); double alpha1 = getalpha(_ellip, l1); double alpha2 = getalpha(_ellip, l2); double alpha = getalpha(_ellip, l); result += "alpha0:" + alpha0.ToString() + "\n"; result += "alpha1:" + alpha1.ToString() + "\n"; result += "alpha2:" + alpha2.ToString() + "\n"; result += "alpha:" + alpha.ToString() + "\n"; double m1 = Math.Cos(l1) / Math.Pow(1 - e * e * Math.Sin(l1) * Math.Sin(l1), 0.5); double m2 = Math.Cos(l2) / Math.Pow(1 - e * e * Math.Sin(l2) * Math.Sin(l2), 0.5); result += "m1:" + m1.ToString() + "\n"; result += "m2:" + m2.ToString() + "\n"; double n = (m1 * m1 - m2 * m2) / (alpha2 - alpha1); //double c=_ellip.a*_ellip.a*(m1*m1+n*alpha1); double c = (m1 * m1 * alpha2 - m2 * m2 * alpha1) / (alpha2 - alpha1); result += "n:" + n.ToString() + "\n"; result += "c:" + c.ToString() + "\n"; double tht = n * (lmt - lmt0); double rol = (_ellip.a * Math.Sqrt(c - n * alpha)) / n; double rol0 = (_ellip.a * Math.Sqrt(c - n * alpha0)) / n; result += "tht:" + tht.ToString() + "\n"; result += "rol:" + rol.ToString() + "\n"; result += "rol0:" + rol0.ToString() + "\n"; double E = rol * Math.Sin(tht); double N = rol0 - (rol * Math.Cos(tht)); XYCoord xyc; xyc.X = E; xyc.Y = N; return(xyc); }