/* * Geodesic.js * Transcription of Geodesic.[ch]pp into JavaScript. * * See the documentation for the C++ class. The conversion is a literal * conversion from C++. * * The algorithms are derived in * * Charles F. F. Karney, * Algorithms for geodesics, J. Geodesy 87, 43-55 (2013); * https://doi.org/10.1007/s00190-012-0578-z * Addenda: https://geographiclib.sourceforge.io/geod-addenda.html * * Copyright (c) Charles Karney (2011-2022) <karney@alum.mit.edu> and licensed * under the MIT/X11 License. For more information, see * https://geographiclib.sourceforge.io/ */// Load AFTER Math.js// To allow swap via [y, x] = [x, y]/* jshint esversion: 6 */geodesic.Geodesic = {};geodesic.GeodesicLine = {};geodesic.PolygonArea = {};(function( /** * @exports geodesic/Geodesic * @description Solve geodesic problems via the * {@link module:geodesic/Geodesic.Geodesic Geodesic} class. */ g, l, p, m, c) { "use strict"; var GEOGRAPHICLIB_GEODESIC_ORDER = 6, nA1_ = GEOGRAPHICLIB_GEODESIC_ORDER, nA2_ = GEOGRAPHICLIB_GEODESIC_ORDER, nA3_ = GEOGRAPHICLIB_GEODESIC_ORDER, nA3x_ = nA3_, nC3x_, nC4x_, maxit1_ = 20, maxit2_ = maxit1_ + m.digits + 10, tol0_ = m.epsilon, tol1_ = 200 * tol0_, tol2_ = Math.sqrt(tol0_), tolb_ = tol0_, xthresh_ = 1000 * tol2_, CAP_NONE = 0, CAP_ALL = 0x1F, OUT_ALL = 0x7F80, astroid, A1m1f_coeff, C1f_coeff, C1pf_coeff, A2m1f_coeff, C2f_coeff, A3_coeff, C3_coeff, C4_coeff; // N.B. Number.MIN_VALUE is denormalized; divide by Number.EPSILON to get min // normalized positive number. g.tiny_ = Math.sqrt(Number.MIN_VALUE/Number.EPSILON); g.nC1_ = GEOGRAPHICLIB_GEODESIC_ORDER; g.nC1p_ = GEOGRAPHICLIB_GEODESIC_ORDER; g.nC2_ = GEOGRAPHICLIB_GEODESIC_ORDER; g.nC3_ = GEOGRAPHICLIB_GEODESIC_ORDER; g.nC4_ = GEOGRAPHICLIB_GEODESIC_ORDER; nC3x_ = (g.nC3_ * (g.nC3_ - 1)) / 2; nC4x_ = (g.nC4_ * (g.nC4_ + 1)) / 2; g.CAP_C1 = 1<<0; g.CAP_C1p = 1<<1; g.CAP_C2 = 1<<2; g.CAP_C3 = 1<<3; g.CAP_C4 = 1<<4; g.NONE = 0; g.ARC = 1<<6; g.LATITUDE = 1<<7 | CAP_NONE; g.LONGITUDE = 1<<8 | g.CAP_C3; g.AZIMUTH = 1<<9 | CAP_NONE; g.DISTANCE = 1<<10 | g.CAP_C1; g.STANDARD = g.LATITUDE | g.LONGITUDE | g.AZIMUTH | g.DISTANCE; g.DISTANCE_IN = 1<<11 | g.CAP_C1 | g.CAP_C1p; g.REDUCEDLENGTH = 1<<12 | g.CAP_C1 | g.CAP_C2; g.GEODESICSCALE = 1<<13 | g.CAP_C1 | g.CAP_C2; g.AREA = 1<<14 | g.CAP_C4; g.ALL = OUT_ALL| CAP_ALL; g.LONG_UNROLL = 1<<15; g.OUT_MASK = OUT_ALL| g.LONG_UNROLL; g.SinCosSeries = function(sinp, sinx, cosx, c) { // Evaluate // y = sinp ? sum(c[i] * sin( 2*i * x), i, 1, n) : // sum(c[i] * cos((2*i+1) * x), i, 0, n-1) // using Clenshaw summation. N.B. c[0] is unused for sin series // Approx operation count = (n + 5) mult and (2 * n + 2) add var k = c.length, // Point to one beyond last element n = k - (sinp ? 1 : 0), ar = 2 * (cosx - sinx) * (cosx + sinx), // 2 * cos(2 * x) y0 = n & 1 ? c[--k] : 0, y1 = 0; // accumulators for sum // Now n is even n = Math.floor(n/2); while (n--) { // Unroll loop x 2, so accumulators return to their original role y1 = ar * y0 - y1 + c[--k]; y0 = ar * y1 - y0 + c[--k]; } return (sinp ? 2 * sinx * cosx * y0 : // sin(2 * x) * y0 cosx * (y0 - y1)); // cos(x) * (y0 - y1) }; astroid = function(x, y) { // Solve k^4+2*k^3-(x^2+y^2-1)*k^2-2*y^2*k-y^2 = 0 for positive // root k. This solution is adapted from Geocentric::Reverse. var k, p = m.sq(x), q = m.sq(y), r = (p + q - 1) / 6, S, r2, r3, disc, u, T3, T, ang, v, uv, w; if ( !(q === 0 && r <= 0) ) { // Avoid possible division by zero when r = 0 by multiplying // equations for s and t by r^3 and r, resp. S = p * q / 4; // S = r^3 * s r2 = m.sq(r); r3 = r * r2; // The discriminant of the quadratic equation for T3. This is // zero on the evolute curve p^(1/3)+q^(1/3) = 1 disc = S * (S + 2 * r3); u = r; if (disc >= 0) { T3 = S + r3; // Pick the sign on the sqrt to maximize abs(T3). This // minimizes loss of precision due to cancellation. The // result is unchanged because of the way the T is used // in definition of u. T3 += T3 < 0 ? -Math.sqrt(disc) : Math.sqrt(disc); // T3 = (r * t)^3 // N.B. cbrt always returns the real root. cbrt(-8) = -2. T = m.cbrt(T3); // T = r * t // T can be zero; but then r2 / T -> 0. u += T + (T !== 0 ? r2 / T : 0); } else { // T is complex, but the way u is defined the result is real. ang = Math.atan2(Math.sqrt(-disc), -(S + r3)); // There are three possible cube roots. We choose the // root which avoids cancellation. Note that disc < 0 // implies that r < 0. u += 2 * r * Math.cos(ang / 3); } v = Math.sqrt(m.sq(u) + q); // guaranteed positive // Avoid loss of accuracy when u < 0. uv = u < 0 ? q / (v - u) : u + v; // u+v, guaranteed positive w = (uv - q) / (2 * v); // positive? // Rearrange expression for k to avoid loss of accuracy due to // subtraction. Division by 0 not possible because uv > 0, w >= 0. k = uv / (Math.sqrt(uv + m.sq(w)) + w); // guaranteed positive } else { // q == 0 && r <= 0 // y = 0 with |x| <= 1. Handle this case directly. // for y small, positive root is k = abs(y)/sqrt(1-x^2) k = 0; } return k; }; A1m1f_coeff = [ // (1-eps)*A1-1, polynomial in eps2 of order 3 +1, 4, 64, 0, 256 ]; // The scale factor A1-1 = mean value of (d/dsigma)I1 - 1 g.A1m1f = function(eps) { var p = Math.floor(nA1_/2), t = m.polyval(p, A1m1f_coeff, 0, m.sq(eps)) / A1m1f_coeff[p + 1]; return (t + eps) / (1 - eps); }; C1f_coeff = [ // C1[1]/eps^1, polynomial in eps2 of order 2 -1, 6, -16, 32, // C1[2]/eps^2, polynomial in eps2 of order 2 -9, 64, -128, 2048, // C1[3]/eps^3, polynomial in eps2 of order 1 +9, -16, 768, // C1[4]/eps^4, polynomial in eps2 of order 1 +3, -5, 512, // C1[5]/eps^5, polynomial in eps2 of order 0 -7, 1280, // C1[6]/eps^6, polynomial in eps2 of order 0 -7, 2048 ]; // The coefficients C1[l] in the Fourier expansion of B1 g.C1f = function(eps, c) { var eps2 = m.sq(eps), d = eps, o = 0, l, p; for (l = 1; l <= g.nC1_; ++l) { // l is index of C1p[l] p = Math.floor((g.nC1_ - l) / 2); // order of polynomial in eps^2 c[l] = d * m.polyval(p, C1f_coeff, o, eps2) / C1f_coeff[o + p + 1]; o += p + 2; d *= eps; } }; C1pf_coeff = [ // C1p[1]/eps^1, polynomial in eps2 of order 2 +205, -432, 768, 1536, // C1p[2]/eps^2, polynomial in eps2 of order 2 +4005, -4736, 3840, 12288, // C1p[3]/eps^3, polynomial in eps2 of order 1 -225, 116, 384, // C1p[4]/eps^4, polynomial in eps2 of order 1 -7173, 2695, 7680, // C1p[5]/eps^5, polynomial in eps2 of order 0 +3467, 7680, // C1p[6]/eps^6, polynomial in eps2 of order 0 +38081, 61440 ]; // The coefficients C1p[l] in the Fourier expansion of B1p g.C1pf = function(eps, c) { var eps2 = m.sq(eps), d = eps, o = 0, l, p; for (l = 1; l <= g.nC1p_; ++l) { // l is index of C1p[l] p = Math.floor((g.nC1p_ - l) / 2); // order of polynomial in eps^2 c[l] = d * m.polyval(p, C1pf_coeff, o, eps2) / C1pf_coeff[o + p + 1]; o += p + 2; d *= eps; } }; A2m1f_coeff = [ // (eps+1)*A2-1, polynomial in eps2 of order 3 -11, -28, -192, 0, 256 ]; // The scale factor A2-1 = mean value of (d/dsigma)I2 - 1 g.A2m1f = function(eps) { var p = Math.floor(nA2_/2), t = m.polyval(p, A2m1f_coeff, 0, m.sq(eps)) / A2m1f_coeff[p + 1]; return (t - eps) / (1 + eps); }; C2f_coeff = [ // C2[1]/eps^1, polynomial in eps2 of order 2 +1, 2, 16, 32, // C2[2]/eps^2, polynomial in eps2 of order 2 +35, 64, 384, 2048, // C2[3]/eps^3, polynomial in eps2 of order 1 +15, 80, 768, // C2[4]/eps^4, polynomial in eps2 of order 1 +7, 35, 512, // C2[5]/eps^5, polynomial in eps2 of order 0 +63, 1280, // C2[6]/eps^6, polynomial in eps2 of order 0 +77, 2048 ]; // The coefficients C2[l] in the Fourier expansion of B2 g.C2f = function(eps, c) { var eps2 = m.sq(eps), d = eps, o = 0, l, p; for (l = 1; l <= g.nC2_; ++l) { // l is index of C2[l] p = Math.floor((g.nC2_ - l) / 2); // order of polynomial in eps^2 c[l] = d * m.polyval(p, C2f_coeff, o, eps2) / C2f_coeff[o + p + 1]; o += p + 2; d *= eps; } }; /** * @class * @property {number} a the equatorial radius (meters). * @property {number} f the flattening. * @summary Initialize a Geodesic object for a specific ellipsoid. * @classdesc Performs geodesic calculations on an ellipsoid of revolution. * The routines for solving the direct and inverse problems return an * object with some of the following fields set: lat1, lon1, azi1, lat2, * lon2, azi2, s12, a12, m12, M12, M21, S12. See {@tutorial 2-interface}, * section "The results". * @example * var geodesic = require("geographiclib-geodesic"), * geod = geodesic.Geodesic.WGS84; * var inv = geod.Inverse(1,2,3,4); * console.log("lat1 = " + inv.lat1 + ", lon1 = " + inv.lon1 + * ", lat2 = " + inv.lat2 + ", lon2 = " + inv.lon2 + * ",\nazi1 = " + inv.azi1 + ", azi2 = " + inv.azi2 + * ", s12 = " + inv.s12); * @param {number} a the equatorial radius of the ellipsoid (meters). * @param {number} f the flattening of the ellipsoid. Setting f = 0 gives * a sphere (on which geodesics are great circles). Negative f gives a * prolate ellipsoid. * @throws an error if the parameters are illegal. */ g.Geodesic = function(a, f) { this.a = a; this.f = f; this._f1 = 1 - this.f; this._e2 = this.f * (2 - this.f); this._ep2 = this._e2 / m.sq(this._f1); // e2 / (1 - e2) this._n = this.f / ( 2 - this.f); this._b = this.a * this._f1; // authalic radius squared this._c2 = (m.sq(this.a) + m.sq(this._b) * (this._e2 === 0 ? 1 : (this._e2 > 0 ? m.atanh(Math.sqrt(this._e2)) : Math.atan(Math.sqrt(-this._e2))) / Math.sqrt(Math.abs(this._e2))))/2; // The sig12 threshold for "really short". Using the auxiliary sphere // solution with dnm computed at (bet1 + bet2) / 2, the relative error in // the azimuth consistency check is sig12^2 * abs(f) * min(1, 1-f/2) / 2. // (Error measured for 1/100 < b/a < 100 and abs(f) >= 1/1000. For a given // f and sig12, the max error occurs for lines near the pole. If the old // rule for computing dnm = (dn1 + dn2)/2 is used, then the error increases // by a factor of 2.) Setting this equal to epsilon gives sig12 = etol2. // Here 0.1 is a safety factor (error decreased by 100) and max(0.001, // abs(f)) stops etol2 getting too large in the nearly spherical case. this._etol2 = 0.1 * tol2_ / Math.sqrt( Math.max(0.001, Math.abs(this.f)) * Math.min(1, 1 - this.f/2) / 2 ); if (!(isFinite(this.a) && this.a > 0)) throw new Error("Equatorial radius is not positive"); if (!(isFinite(this._b) && this._b > 0)) throw new Error("Polar semi-axis is not positive"); this._A3x = new Array(nA3x_); this._C3x = new Array(nC3x_); this._C4x = new Array(nC4x_); this.A3coeff(); this.C3coeff(); this.C4coeff(); }; A3_coeff = [ // A3, coeff of eps^5, polynomial in n of order 0 -3, 128, // A3, coeff of eps^4, polynomial in n of order 1 -2, -3, 64, // A3, coeff of eps^3, polynomial in n of order 2 -1, -3, -1, 16, // A3, coeff of eps^2, polynomial in n of order 2 +3, -1, -2, 8, // A3, coeff of eps^1, polynomial in n of order 1 +1, -1, 2, // A3, coeff of eps^0, polynomial in n of order 0 +1, 1 ]; // The scale factor A3 = mean value of (d/dsigma)I3 g.Geodesic.prototype.A3coeff = function() { var o = 0, k = 0, j, p; for (j = nA3_ - 1; j >= 0; --j) { // coeff of eps^j p = Math.min(nA3_ - j - 1, j); // order of polynomial in n this._A3x[k++] = m.polyval(p, A3_coeff, o, this._n) / A3_coeff[o + p + 1]; o += p + 2; } }; C3_coeff = [ // C3[1], coeff of eps^5, polynomial in n of order 0 +3, 128, // C3[1], coeff of eps^4, polynomial in n of order 1 +2, 5, 128, // C3[1], coeff of eps^3, polynomial in n of order 2 -1, 3, 3, 64, // C3[1], coeff of eps^2, polynomial in n of order 2 -1, 0, 1, 8, // C3[1], coeff of eps^1, polynomial in n of order 1 -1, 1, 4, // C3[2], coeff of eps^5, polynomial in n of order 0 +5, 256, // C3[2], coeff of eps^4, polynomial in n of order 1 +1, 3, 128, // C3[2], coeff of eps^3, polynomial in n of order 2 -3, -2, 3, 64, // C3[2], coeff of eps^2, polynomial in n of order 2 +1, -3, 2, 32, // C3[3], coeff of eps^5, polynomial in n of order 0 +7, 512, // C3[3], coeff of eps^4, polynomial in n of order 1 -10, 9, 384, // C3[3], coeff of eps^3, polynomial in n of order 2 +5, -9, 5, 192, // C3[4], coeff of eps^5, polynomial in n of order 0 +7, 512, // C3[4], coeff of eps^4, polynomial in n of order 1 -14, 7, 512, // C3[5], coeff of eps^5, polynomial in n of order 0 +21, 2560 ]; // The coefficients C3[l] in the Fourier expansion of B3 g.Geodesic.prototype.C3coeff = function() { var o = 0, k = 0, l, j, p; for (l = 1; l < g.nC3_; ++l) { // l is index of C3[l] for (j = g.nC3_ - 1; j >= l; --j) { // coeff of eps^j p = Math.min(g.nC3_ - j - 1, j); // order of polynomial in n this._C3x[k++] = m.polyval(p, C3_coeff, o, this._n) / C3_coeff[o + p + 1]; o += p + 2; } } }; C4_coeff = [ // C4[0], coeff of eps^5, polynomial in n of order 0 +97, 15015, // C4[0], coeff of eps^4, polynomial in n of order 1 +1088, 156, 45045, // C4[0], coeff of eps^3, polynomial in n of order 2 -224, -4784, 1573, 45045, // C4[0], coeff of eps^2, polynomial in n of order 3 -10656, 14144, -4576, -858, 45045, // C4[0], coeff of eps^1, polynomial in n of order 4 +64, 624, -4576, 6864, -3003, 15015, // C4[0], coeff of eps^0, polynomial in n of order 5 +100, 208, 572, 3432, -12012, 30030, 45045, // C4[1], coeff of eps^5, polynomial in n of order 0 +1, 9009, // C4[1], coeff of eps^4, polynomial in n of order 1 -2944, 468, 135135, // C4[1], coeff of eps^3, polynomial in n of order 2 +5792, 1040, -1287, 135135, // C4[1], coeff of eps^2, polynomial in n of order 3 +5952, -11648, 9152, -2574, 135135, // C4[1], coeff of eps^1, polynomial in n of order 4 -64, -624, 4576, -6864, 3003, 135135, // C4[2], coeff of eps^5, polynomial in n of order 0 +8, 10725, // C4[2], coeff of eps^4, polynomial in n of order 1 +1856, -936, 225225, // C4[2], coeff of eps^3, polynomial in n of order 2 -8448, 4992, -1144, 225225, // C4[2], coeff of eps^2, polynomial in n of order 3 -1440, 4160, -4576, 1716, 225225, // C4[3], coeff of eps^5, polynomial in n of order 0 -136, 63063, // C4[3], coeff of eps^4, polynomial in n of order 1 +1024, -208, 105105, // C4[3], coeff of eps^3, polynomial in n of order 2 +3584, -3328, 1144, 315315, // C4[4], coeff of eps^5, polynomial in n of order 0 -128, 135135, // C4[4], coeff of eps^4, polynomial in n of order 1 -2560, 832, 405405, // C4[5], coeff of eps^5, polynomial in n of order 0 +128, 99099 ]; g.Geodesic.prototype.C4coeff = function() { var o = 0, k = 0, l, j, p; for (l = 0; l < g.nC4_; ++l) { // l is index of C4[l] for (j = g.nC4_ - 1; j >= l; --j) { // coeff of eps^j p = g.nC4_ - j - 1; // order of polynomial in n this._C4x[k++] = m.polyval(p, C4_coeff, o, this._n) / C4_coeff[o + p + 1]; o += p + 2; } } }; g.Geodesic.prototype.A3f = function(eps) { // Evaluate A3 return m.polyval(nA3x_ - 1, this._A3x, 0, eps); }; g.Geodesic.prototype.C3f = function(eps, c) { // Evaluate C3 coeffs // Elements c[1] thru c[nC3_ - 1] are set var mult = 1, o = 0, l, p; for (l = 1; l < g.nC3_; ++l) { // l is index of C3[l] p = g.nC3_ - l - 1; // order of polynomial in eps mult *= eps; c[l] = mult * m.polyval(p, this._C3x, o, eps); o += p + 1; } }; g.Geodesic.prototype.C4f = function(eps, c) { // Evaluate C4 coeffs // Elements c[0] thru c[g.nC4_ - 1] are set var mult = 1, o = 0, l, p; for (l = 0; l < g.nC4_; ++l) { // l is index of C4[l] p = g.nC4_ - l - 1; // order of polynomial in eps c[l] = mult * m.polyval(p, this._C4x, o, eps); o += p + 1; mult *= eps; } }; // return s12b, m12b, m0, M12, M21 g.Geodesic.prototype.Lengths = function(eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2, outmask, C1a, C2a) { // Return m12b = (reduced length)/_b; also calculate s12b = // distance/_b, and m0 = coefficient of secular term in // expression for reduced length. outmask &= g.OUT_MASK; var vals = {}, m0x = 0, J12 = 0, A1 = 0, A2 = 0, B1, B2, l, csig12, t; if (outmask & (g.DISTANCE | g.REDUCEDLENGTH | g.GEODESICSCALE)) { A1 = g.A1m1f(eps); g.C1f(eps, C1a); if (outmask & (g.REDUCEDLENGTH | g.GEODESICSCALE)) { A2 = g.A2m1f(eps); g.C2f(eps, C2a); m0x = A1 - A2; A2 = 1 + A2; } A1 = 1 + A1; } if (outmask & g.DISTANCE) { B1 = g.SinCosSeries(true, ssig2, csig2, C1a) - g.SinCosSeries(true, ssig1, csig1, C1a); // Missing a factor of _b vals.s12b = A1 * (sig12 + B1); if (outmask & (g.REDUCEDLENGTH | g.GEODESICSCALE)) { B2 = g.SinCosSeries(true, ssig2, csig2, C2a) - g.SinCosSeries(true, ssig1, csig1, C2a); J12 = m0x * sig12 + (A1 * B1 - A2 * B2); } } else if (outmask & (g.REDUCEDLENGTH | g.GEODESICSCALE)) { // Assume here that nC1_ >= nC2_ for (l = 1; l <= g.nC2_; ++l) C2a[l] = A1 * C1a[l] - A2 * C2a[l]; J12 = m0x * sig12 + (g.SinCosSeries(true, ssig2, csig2, C2a) - g.SinCosSeries(true, ssig1, csig1, C2a)); } if (outmask & g.REDUCEDLENGTH) { vals.m0 = m0x; // Missing a factor of _b. // Add parens around (csig1 * ssig2) and (ssig1 * csig2) to ensure // accurate cancellation in the case of coincident points. vals.m12b = dn2 * (csig1 * ssig2) - dn1 * (ssig1 * csig2) - csig1 * csig2 * J12; } if (outmask & g.GEODESICSCALE) { csig12 = csig1 * csig2 + ssig1 * ssig2; t = this._ep2 * (cbet1 - cbet2) * (cbet1 + cbet2) / (dn1 + dn2); vals.M12 = csig12 + (t * ssig2 - csig2 * J12) * ssig1 / dn1; vals.M21 = csig12 - (t * ssig1 - csig1 * J12) * ssig2 / dn2; } return vals; }; // return sig12, salp1, calp1, salp2, calp2, dnm g.Geodesic.prototype.InverseStart = function(sbet1, cbet1, dn1, sbet2, cbet2, dn2, lam12, slam12, clam12, C1a, C2a) { // Return a starting point for Newton's method in salp1 and calp1 // (function value is -1). If Newton's method doesn't need to be // used, return also salp2 and calp2 and function value is sig12. // salp2, calp2 only updated if return val >= 0. var vals = {}, // bet12 = bet2 - bet1 in [0, pi); bet12a = bet2 + bet1 in (-pi, 0] sbet12 = sbet2 * cbet1 - cbet2 * sbet1, cbet12 = cbet2 * cbet1 + sbet2 * sbet1, sbet12a, shortline, omg12, sbetm2, somg12, comg12, t, ssig12, csig12, x, y, lamscale, betscale, k2, eps, cbet12a, bet12a, m12b, m0, nvals, k, omg12a, lam12x; vals.sig12 = -1; // Return value // Volatile declaration needed to fix inverse cases // 88.202499451857 0 -88.202499451857 179.981022032992859592 // 89.262080389218 0 -89.262080389218 179.992207982775375662 // 89.333123580033 0 -89.333123580032997687 179.99295812360148422 // which otherwise fail with g++ 4.4.4 x86 -O3 sbet12a = sbet2 * cbet1; sbet12a += cbet2 * sbet1; shortline = cbet12 >= 0 && sbet12 < 0.5 && cbet2 * lam12 < 0.5; if (shortline) { sbetm2 = m.sq(sbet1 + sbet2); // sin((bet1+bet2)/2)^2 // = (sbet1 + sbet2)^2 / ((sbet1 + sbet2)^2 + (cbet1 + cbet2)^2) sbetm2 /= sbetm2 + m.sq(cbet1 + cbet2); vals.dnm = Math.sqrt(1 + this._ep2 * sbetm2); omg12 = lam12 / (this._f1 * vals.dnm); somg12 = Math.sin(omg12); comg12 = Math.cos(omg12); } else { somg12 = slam12; comg12 = clam12; } vals.salp1 = cbet2 * somg12; vals.calp1 = comg12 >= 0 ? sbet12 + cbet2 * sbet1 * m.sq(somg12) / (1 + comg12) : sbet12a - cbet2 * sbet1 * m.sq(somg12) / (1 - comg12); ssig12 = m.hypot(vals.salp1, vals.calp1); csig12 = sbet1 * sbet2 + cbet1 * cbet2 * comg12; if (shortline && ssig12 < this._etol2) { // really short lines vals.salp2 = cbet1 * somg12; vals.calp2 = sbet12 - cbet1 * sbet2 * (comg12 >= 0 ? m.sq(somg12) / (1 + comg12) : 1 - comg12); // norm(vals.salp2, vals.calp2); t = m.hypot(vals.salp2, vals.calp2); vals.salp2 /= t; vals.calp2 /= t; // Set return value vals.sig12 = Math.atan2(ssig12, csig12); } else if (Math.abs(this._n) > 0.1 || // Skip astroid calc if too eccentric csig12 >= 0 || ssig12 >= 6 * Math.abs(this._n) * Math.PI * m.sq(cbet1)) { // Nothing to do, zeroth order spherical approximation is OK } else { // Scale lam12 and bet2 to x, y coordinate system where antipodal // point is at origin and singular point is at y = 0, x = -1. lam12x = Math.atan2(-slam12, -clam12); // lam12 - pi if (this.f >= 0) { // In fact f == 0 does not get here // x = dlong, y = dlat k2 = m.sq(sbet1) * this._ep2; eps = k2 / (2 * (1 + Math.sqrt(1 + k2)) + k2); lamscale = this.f * cbet1 * this.A3f(eps) * Math.PI; betscale = lamscale * cbet1; x = lam12x / lamscale; y = sbet12a / betscale; } else { // f < 0 // x = dlat, y = dlong cbet12a = cbet2 * cbet1 - sbet2 * sbet1; bet12a = Math.atan2(sbet12a, cbet12a); // In the case of lon12 = 180, this repeats a calculation made // in Inverse. nvals = this.Lengths(this._n, Math.PI + bet12a, sbet1, -cbet1, dn1, sbet2, cbet2, dn2, cbet1, cbet2, g.REDUCEDLENGTH, C1a, C2a); m12b = nvals.m12b; m0 = nvals.m0; x = -1 + m12b / (cbet1 * cbet2 * m0 * Math.PI); betscale = x < -0.01 ? sbet12a / x : -this.f * m.sq(cbet1) * Math.PI; lamscale = betscale / cbet1; y = lam12 / lamscale; } if (y > -tol1_ && x > -1 - xthresh_) { // strip near cut if (this.f >= 0) { vals.salp1 = Math.min(1, -x); vals.calp1 = -Math.sqrt(1 - m.sq(vals.salp1)); } else { vals.calp1 = Math.max(x > -tol1_ ? 0 : -1, x); vals.salp1 = Math.sqrt(1 - m.sq(vals.calp1)); } } else { // Estimate alp1, by solving the astroid problem. // // Could estimate alpha1 = theta + pi/2, directly, i.e., // calp1 = y/k; salp1 = -x/(1+k); for f >= 0 // calp1 = x/(1+k); salp1 = -y/k; for f < 0 (need to check) // // However, it's better to estimate omg12 from astroid and use // spherical formula to compute alp1. This reduces the mean number of // Newton iterations for astroid cases from 2.24 (min 0, max 6) to 2.12 // (min 0 max 5). The changes in the number of iterations are as // follows: // // change percent // 1 5 // 0 78 // -1 16 // -2 0.6 // -3 0.04 // -4 0.002 // // The histogram of iterations is (m = number of iterations estimating // alp1 directly, n = number of iterations estimating via omg12, total // number of trials = 148605): // // iter m n // 0 148 186 // 1 13046 13845 // 2 93315 102225 // 3 36189 32341 // 4 5396 7 // 5 455 1 // 6 56 0 // // Because omg12 is near pi, estimate work with omg12a = pi - omg12 k = astroid(x, y); omg12a = lamscale * ( this.f >= 0 ? -x * k/(1 + k) : -y * (1 + k)/k ); somg12 = Math.sin(omg12a); comg12 = -Math.cos(omg12a); // Update spherical estimate of alp1 using omg12 instead of // lam12 vals.salp1 = cbet2 * somg12; vals.calp1 = sbet12a - cbet2 * sbet1 * m.sq(somg12) / (1 - comg12); } } // Sanity check on starting guess. Backwards check allows NaN through. // jshint -W018 if (!(vals.salp1 <= 0)) { // norm(vals.salp1, vals.calp1); t = m.hypot(vals.salp1, vals.calp1); vals.salp1 /= t; vals.calp1 /= t; } else { vals.salp1 = 1; vals.calp1 = 0; } return vals; }; // return lam12, salp2, calp2, sig12, ssig1, csig1, ssig2, csig2, eps, // domg12, dlam12, g.Geodesic.prototype.Lambda12 = function(sbet1, cbet1, dn1, sbet2, cbet2, dn2, salp1, calp1, slam120, clam120, diffp, C1a, C2a, C3a) { var vals = {}, t, salp0, calp0, somg1, comg1, somg2, comg2, somg12, comg12, B312, eta, k2, nvals; if (sbet1 === 0 && calp1 === 0) // Break degeneracy of equatorial line. This case has already been // handled. calp1 = -g.tiny_; // sin(alp1) * cos(bet1) = sin(alp0) salp0 = salp1 * cbet1; calp0 = m.hypot(calp1, salp1 * sbet1); // calp0 > 0 // tan(bet1) = tan(sig1) * cos(alp1) // tan(omg1) = sin(alp0) * tan(sig1) = tan(omg1)=tan(alp1)*sin(bet1) vals.ssig1 = sbet1; somg1 = salp0 * sbet1; vals.csig1 = comg1 = calp1 * cbet1; // norm(vals.ssig1, vals.csig1); t = m.hypot(vals.ssig1, vals.csig1); vals.ssig1 /= t; vals.csig1 /= t; // norm(somg1, comg1); -- don't need to normalize! // Enforce symmetries in the case abs(bet2) = -bet1. Need to be careful // about this case, since this can yield singularities in the Newton // iteration. // sin(alp2) * cos(bet2) = sin(alp0) vals.salp2 = cbet2 !== cbet1 ? salp0 / cbet2 : salp1; // calp2 = sqrt(1 - sq(salp2)) // = sqrt(sq(calp0) - sq(sbet2)) / cbet2 // and subst for calp0 and rearrange to give (choose positive sqrt // to give alp2 in [0, pi/2]). vals.calp2 = cbet2 !== cbet1 || Math.abs(sbet2) !== -sbet1 ? Math.sqrt(m.sq(calp1 * cbet1) + (cbet1 < -sbet1 ? (cbet2 - cbet1) * (cbet1 + cbet2) : (sbet1 - sbet2) * (sbet1 + sbet2))) / cbet2 : Math.abs(calp1); // tan(bet2) = tan(sig2) * cos(alp2) // tan(omg2) = sin(alp0) * tan(sig2). vals.ssig2 = sbet2; somg2 = salp0 * sbet2; vals.csig2 = comg2 = vals.calp2 * cbet2; // norm(vals.ssig2, vals.csig2); t = m.hypot(vals.ssig2, vals.csig2); vals.ssig2 /= t; vals.csig2 /= t; // norm(somg2, comg2); -- don't need to normalize! // sig12 = sig2 - sig1, limit to [0, pi] vals.sig12 = Math.atan2(Math.max(0, vals.csig1 * vals.ssig2 - vals.ssig1 * vals.csig2), vals.csig1 * vals.csig2 + vals.ssig1 * vals.ssig2); // omg12 = omg2 - omg1, limit to [0, pi] somg12 = Math.max(0, comg1 * somg2 - somg1 * comg2); comg12 = comg1 * comg2 + somg1 * somg2; // eta = omg12 - lam120 eta = Math.atan2(somg12 * clam120 - comg12 * slam120, comg12 * clam120 + somg12 * slam120); k2 = m.sq(calp0) * this._ep2; vals.eps = k2 / (2 * (1 + Math.sqrt(1 + k2)) + k2); this.C3f(vals.eps, C3a); B312 = (g.SinCosSeries(true, vals.ssig2, vals.csig2, C3a) - g.SinCosSeries(true, vals.ssig1, vals.csig1, C3a)); vals.domg12 = -this.f * this.A3f(vals.eps) * salp0 * (vals.sig12 + B312); vals.lam12 = eta + vals.domg12; if (diffp) { if (vals.calp2 === 0) vals.dlam12 = -2 * this._f1 * dn1 / sbet1; else { nvals = this.Lengths(vals.eps, vals.sig12, vals.ssig1, vals.csig1, dn1, vals.ssig2, vals.csig2, dn2, cbet1, cbet2, g.REDUCEDLENGTH, C1a, C2a); vals.dlam12 = nvals.m12b; vals.dlam12 *= this._f1 / (vals.calp2 * cbet2); } } return vals; }; /** * @summary Solve the inverse geodesic problem. * @param {number} lat1 the latitude of the first point in degrees. * @param {number} lon1 the longitude of the first point in degrees. * @param {number} lat2 the latitude of the second point in degrees. * @param {number} lon2 the longitude of the second point in degrees. * @param {bitmask} [outmask = STANDARD] which results to include. * @return {object} the requested results * @description The lat1, lon1, lat2, lon2, and a12 fields of the result are * always set. For details on the outmask parameter, see {@tutorial * 2-interface}, "The outmask and caps parameters". */ g.Geodesic.prototype.Inverse = function(lat1, lon1, lat2, lon2, outmask) { var r, vals; if (!outmask) outmask = g.STANDARD; if (outmask === g.LONG_UNROLL) outmask |= g.STANDARD; outmask &= g.OUT_MASK; r = this.InverseInt(lat1, lon1, lat2, lon2, outmask); vals = r.vals; if (outmask & g.AZIMUTH) { vals.azi1 = m.atan2d(r.salp1, r.calp1); vals.azi2 = m.atan2d(r.salp2, r.calp2); } return vals; }; g.Geodesic.prototype.InverseInt = function(lat1, lon1, lat2, lon2, outmask) { var vals = {}, lon12, lon12s, lonsign, t, swapp, latsign, sbet1, cbet1, sbet2, cbet2, s12x, m12x, dn1, dn2, lam12, slam12, clam12, sig12, calp1, salp1, calp2, salp2, C1a, C2a, C3a, meridian, nvals, ssig1, csig1, ssig2, csig2, eps, omg12, dnm, numit, salp1a, calp1a, salp1b, calp1b, tripn, tripb, v, dv, dalp1, sdalp1, cdalp1, nsalp1, lengthmask, salp0, calp0, alp12, k2, A4, C4a, B41, B42, somg12, comg12, domg12, dbet1, dbet2, salp12, calp12, sdomg12, cdomg12; // Compute longitude difference (AngDiff does this carefully). Result is // in [-180, 180] but -180 is only for west-going geodesics. 180 is for // east-going and meridional geodesics. vals.lat1 = lat1 = m.LatFix(lat1); vals.lat2 = lat2 = m.LatFix(lat2); // If really close to the equator, treat as on equator. lat1 = m.AngRound(lat1); lat2 = m.AngRound(lat2); lon12 = m.AngDiff(lon1, lon2); lon12s = lon12.e; lon12 = lon12.d; if (outmask & g.LONG_UNROLL) { vals.lon1 = lon1; vals.lon2 = (lon1 + lon12) + lon12s; } else { vals.lon1 = m.AngNormalize(lon1); vals.lon2 = m.AngNormalize(lon2); } // Make longitude difference positive. lonsign = m.copysign(1, lon12); lon12 *= lonsign; lon12s *= lonsign; lam12 = lon12 * m.degree; // Calculate sincos of lon12 + error (this applies AngRound internally). t = m.sincosde(lon12, lon12s); slam12 = t.s; clam12 = t.c; lon12s = (180 - lon12) - lon12s; // the supplementary longitude difference // Swap points so that point with higher (abs) latitude is point 1 // If one latitude is a nan, then it becomes lat1. swapp = Math.abs(lat1) < Math.abs(lat2) || isNaN(lat2) ? -1 : 1; if (swapp < 0) { lonsign *= -1; [lat2, lat1] = [lat1, lat2]; // swap(lat1, lat2); } // Make lat1 <= 0 latsign = m.copysign(1, -lat1); lat1 *= latsign; lat2 *= latsign; // Now we have // // 0 <= lon12 <= 180 // -90 <= lat1 <= 0 // lat1 <= lat2 <= -lat1 // // longsign, swapp, latsign register the transformation to bring the // coordinates to this canonical form. In all cases, 1 means no change was // made. We make these transformations so that there are few cases to // check, e.g., on verifying quadrants in atan2. In addition, this // enforces some symmetries in the results returned. t = m.sincosd(lat1); sbet1 = this._f1 * t.s; cbet1 = t.c; // norm(sbet1, cbet1); t = m.hypot(sbet1, cbet1); sbet1 /= t; cbet1 /= t; // Ensure cbet1 = +epsilon at poles cbet1 = Math.max(g.tiny_, cbet1); t = m.sincosd(lat2); sbet2 = this._f1 * t.s; cbet2 = t.c; // norm(sbet2, cbet2); t = m.hypot(sbet2, cbet2); sbet2 /= t; cbet2 /= t; // Ensure cbet2 = +epsilon at poles cbet2 = Math.max(g.tiny_, cbet2); // If cbet1 < -sbet1, then cbet2 - cbet1 is a sensitive measure of the // |bet1| - |bet2|. Alternatively (cbet1 >= -sbet1), abs(sbet2) + sbet1 is // a better measure. This logic is used in assigning calp2 in Lambda12. // Sometimes these quantities vanish and in that case we force bet2 = +/- // bet1 exactly. An example where is is necessary is the inverse problem // 48.522876735459 0 -48.52287673545898293 179.599720456223079643 // which failed with Visual Studio 10 (Release and Debug) if (cbet1 < -sbet1) { if (cbet2 === cbet1) sbet2 = m.copysign(sbet1, sbet2); } else { if (Math.abs(sbet2) === -sbet1) cbet2 = cbet1; } dn1 = Math.sqrt(1 + this._ep2 * m.sq(sbet1)); dn2 = Math.sqrt(1 + this._ep2 * m.sq(sbet2)); // index zero elements of these arrays are unused C1a = new Array(g.nC1_ + 1); C2a = new Array(g.nC2_ + 1); C3a = new Array(g.nC3_); meridian = lat1 === -90 || slam12 === 0; if (meridian) { // Endpoints are on a single full meridian, so the geodesic might // lie on a meridian. calp1 = clam12; salp1 = slam12; // Head to the target longitude calp2 = 1; salp2 = 0; // At the target we're heading north // tan(bet) = tan(sig) * cos(alp) ssig1 = sbet1; csig1 = calp1 * cbet1; ssig2 = sbet2; csig2 = calp2 * cbet2; // sig12 = sig2 - sig1 sig12 = Math.atan2(Math.max(0, csig1 * ssig2 - ssig1 * csig2), csig1 * csig2 + ssig1 * ssig2); nvals = this.Lengths(this._n, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2, outmask | g.DISTANCE | g.REDUCEDLENGTH, C1a, C2a); s12x = nvals.s12b; m12x = nvals.m12b; // Ignore m0 if (outmask & g.GEODESICSCALE) { vals.M12 = nvals.M12; vals.M21 = nvals.M21; } // Add the check for sig12 since zero length geodesics might yield // m12 < 0. Test case was // // echo 20.001 0 20.001 0 | GeodSolve -i // // In fact, we will have sig12 > pi/2 for meridional geodesic // which is not a shortest path. if (sig12 < 1 || m12x >= 0) { // Need at least 2, to handle 90 0 90 180 if (sig12 < 3 * g.tiny_ || // Prevent negative s12 or m12 for short lines (sig12 < tol0_ && (s12x < 0 || m12x < 0))) sig12 = m12x = s12x = 0; m12x *= this._b; s12x *= this._b; vals.a12 = sig12 / m.degree; } else // m12 < 0, i.e., prolate and too close to anti-podal meridian = false; } somg12 = 2; if (!meridian && sbet1 === 0 && // and sbet2 == 0 (this.f <= 0 || lon12s >= this.f * 180)) { // Geodesic runs along equator calp1 = calp2 = 0; salp1 = salp2 = 1; s12x = this.a * lam12; sig12 = omg12 = lam12 / this._f1; m12x = this._b * Math.sin(sig12); if (outmask & g.GEODESICSCALE) vals.M12 = vals.M21 = Math.cos(sig12); vals.a12 = lon12 / this._f1; } else if (!meridian) { // Now point1 and point2 belong within a hemisphere bounded by a // meridian and geodesic is neither meridional or equatorial. // Figure a starting point for Newton's method nvals = this.InverseStart(sbet1, cbet1, dn1, sbet2, cbet2, dn2, lam12, slam12, clam12, C1a, C2a); sig12 = nvals.sig12; salp1 = nvals.salp1; calp1 = nvals.calp1; if (sig12 >= 0) { salp2 = nvals.salp2; calp2 = nvals.calp2; // Short lines (InverseStart sets salp2, calp2, dnm) dnm = nvals.dnm; s12x = sig12 * this._b * dnm; m12x = m.sq(dnm) * this._b * Math.sin(sig12 / dnm); if (outmask & g.GEODESICSCALE) vals.M12 = vals.M21 = Math.cos(sig12 / dnm); vals.a12 = sig12 / m.degree; omg12 = lam12 / (this._f1 * dnm); } else { // Newton's method. This is a straightforward solution of f(alp1) = // lambda12(alp1) - lam12 = 0 with one wrinkle. f(alp) has exactly one // root in the interval (0, pi) and its derivative is positive at the // root. Thus f(alp) is positive for alp > alp1 and negative for alp < // alp1. During the course of the iteration, a range (alp1a, alp1b) is // maintained which brackets the root and with each evaluation of // f(alp) the range is shrunk if possible. Newton's method is // restarted whenever the derivative of f is negative (because the new // value of alp1 is then further from the solution) or if the new // estimate of alp1 lies outside (0,pi); in this case, the new starting // guess is taken to be (alp1a + alp1b) / 2. numit = 0; // Bracketing range salp1a = g.tiny_; calp1a = 1; salp1b = g.tiny_; calp1b = -1; for (tripn = false, tripb = false;; ++numit) { // the WGS84 test set: mean = 1.47, sd = 1.25, max = 16 // WGS84 and random input: mean = 2.85, sd = 0.60 nvals = this.Lambda12(sbet1, cbet1, dn1, sbet2, cbet2, dn2, salp1, calp1, slam12, clam12, numit < maxit1_, C1a, C2a, C3a); v = nvals.lam12; salp2 = nvals.salp2; calp2 = nvals.calp2; sig12 = nvals.sig12; ssig1 = nvals.ssig1; csig1 = nvals.csig1; ssig2 = nvals.ssig2; csig2 = nvals.csig2; eps = nvals.eps; domg12 = nvals.domg12; dv = nvals.dlam12; // Reversed test to allow escape with NaNs // jshint -W018 if (tripb || !(Math.abs(v) >= (tripn ? 8 : 1) * tol0_) || numit == maxit2_) break; // Update bracketing values if (v > 0 && (numit < maxit1_ || calp1/salp1 > calp1b/salp1b)) { salp1b = salp1; calp1b = calp1; } else if (v < 0 && (numit < maxit1_ || calp1/salp1 < calp1a/salp1a)) { salp1a = salp1; calp1a = calp1; } if (numit < maxit1_ && dv > 0) { dalp1 = -v/dv; if (Math.abs(dalp1) < Math.PI) { sdalp1 = Math.sin(dalp1); cdalp1 = Math.cos(dalp1); nsalp1 = salp1 * cdalp1 + calp1 * sdalp1; if (nsalp1 > 0) { calp1 = calp1 * cdalp1 - salp1 * sdalp1; salp1 = nsalp1; // norm(salp1, calp1); t = m.hypot(salp1, calp1); salp1 /= t; calp1 /= t; // In some regimes we don't get quadratic convergence because // slope -> 0. So use convergence conditions based on epsilon // instead of sqrt(epsilon). tripn = Math.abs(v) <= 16 * tol0_; continue; } } } // Either dv was not positive or updated value was outside legal // range. Use the midpoint of the bracket as the next estimate. // This mechanism is not needed for the WGS84 ellipsoid, but it does // catch problems with more eccentric ellipsoids. Its efficacy is // such for the WGS84 test set with the starting guess set to alp1 = // 90deg: // the WGS84 test set: mean = 5.21, sd = 3.93, max = 24 // WGS84 and random input: mean = 4.74, sd = 0.99 salp1 = (salp1a + salp1b)/2; calp1 = (calp1a + calp1b)/2; // norm(salp1, calp1); t = m.hypot(salp1, calp1); salp1 /= t; calp1 /= t; tripn = false; tripb = (Math.abs(salp1a - salp1) + (calp1a - calp1) < tolb_ || Math.abs(salp1 - salp1b) + (calp1 - calp1b) < tolb_); } lengthmask = outmask | (outmask & (g.REDUCEDLENGTH | g.GEODESICSCALE) ? g.DISTANCE : g.NONE); nvals = this.Lengths(eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2, lengthmask, C1a, C2a); s12x = nvals.s12b; m12x = nvals.m12b; // Ignore m0 if (outmask & g.GEODESICSCALE) { vals.M12 = nvals.M12; vals.M21 = nvals.M21; } m12x *= this._b; s12x *= this._b; vals.a12 = sig12 / m.degree; if (outmask & g.AREA) { // omg12 = lam12 - domg12 sdomg12 = Math.sin(domg12); cdomg12 = Math.cos(domg12); somg12 = slam12 * cdomg12 - clam12 * sdomg12; comg12 = clam12 * cdomg12 + slam12 * sdomg12; } } } if (outmask & g.DISTANCE) vals.s12 = 0 + s12x; // Convert -0 to 0 if (outmask & g.REDUCEDLENGTH) vals.m12 = 0 + m12x; // Convert -0 to 0 if (outmask & g.AREA) { // From Lambda12: sin(alp1) * cos(bet1) = sin(alp0) salp0 = salp1 * cbet1; calp0 = m.hypot(calp1, salp1 * sbet1); // calp0 > 0 if (calp0 !== 0 && salp0 !== 0) { // From Lambda12: tan(bet) = tan(sig) * cos(alp) ssig1 = sbet1; csig1 = calp1 * cbet1; ssig2 = sbet2; csig2 = calp2 * cbet2; k2 = m.sq(calp0) * this._ep2; eps = k2 / (2 * (1 + Math.sqrt(1 + k2)) + k2); // Multiplier = a^2 * e^2 * cos(alpha0) * sin(alpha0). A4 = m.sq(this.a) * calp0 * salp0 * this._e2; // norm(ssig1, csig1); t = m.hypot(ssig1, csig1); ssig1 /= t; csig1 /= t; // norm(ssig2, csig2); t = m.hypot(ssig2, csig2); ssig2 /= t; csig2 /= t; C4a = new Array(g.nC4_); this.C4f(eps, C4a); B41 = g.SinCosSeries(false, ssig1, csig1, C4a); B42 = g.SinCosSeries(false, ssig2, csig2, C4a); vals.S12 = A4 * (B42 - B41); } else // Avoid problems with indeterminate sig1, sig2 on equator vals.S12 = 0; if (!meridian && somg12 == 2) { somg12 = Math.sin(omg12); comg12 = Math.cos(omg12); } if (!meridian && comg12 > -0.7071 && // Long difference not too big sbet2 - sbet1 < 1.75) { // Lat difference not too big // Use tan(Gamma/2) = tan(omg12/2) // * (tan(bet1/2)+tan(bet2/2))/(1+tan(bet1/2)*tan(bet2/2)) // with tan(x/2) = sin(x)/(1+cos(x)) domg12 = 1 + comg12; dbet1 = 1 + cbet1; dbet2 = 1 + cbet2; alp12 = 2 * Math.atan2( somg12 * (sbet1*dbet2 + sbet2*dbet1), domg12 * (sbet1*sbet2 + dbet1*dbet2) ); } else { // alp12 = alp2 - alp1, used in atan2 so no need to normalize salp12 = salp2 * calp1 - calp2 * salp1; calp12 = calp2 * calp1 + salp2 * salp1; // The right thing appears to happen if alp1 = +/-180 and alp2 = 0, viz // salp12 = -0 and alp12 = -180. However this depends on the sign // being attached to 0 correctly. The following ensures the correct // behavior. if (salp12 === 0 && calp12 < 0) { salp12 = g.tiny_ * calp1; calp12 = -1; } alp12 = Math.atan2(salp12, calp12); } vals.S12 += this._c2 * alp12; vals.S12 *= swapp * lonsign * latsign; // Convert -0 to 0 vals.S12 += 0; } // Convert calp, salp to azimuth accounting for lonsign, swapp, latsign. if (swapp < 0) { [salp2, salp1] = [salp1, salp2]; // swap(salp1, salp2); [calp2, calp1] = [calp1, calp2]; // swap(calp1, calp2); if (outmask & g.GEODESICSCALE) { [vals.M21, vals.M12] = [vals.M12, vals.M21]; //swap(vals.M12, vals.M21); } } salp1 *= swapp * lonsign; calp1 *= swapp * latsign; salp2 *= swapp * lonsign; calp2 *= swapp * latsign; return {vals: vals, salp1: salp1, calp1: calp1, salp2: salp2, calp2: calp2}; }; /** * @summary Solve the general direct geodesic problem. * @param {number} lat1 the latitude of the first point in degrees. * @param {number} lon1 the longitude of the first point in degrees. * @param {number} azi1 the azimuth at the first point in degrees. * @param {bool} arcmode is the next parameter an arc length? * @param {number} s12_a12 the (arcmode ? arc length : distance) from the * first point to the second in (arcmode ? degrees : meters). * @param {bitmask} [outmask = STANDARD] which results to include. * @return {object} the requested results. * @description The lat1, lon1, azi1, and a12 fields of the result are always * set; s12 is included if arcmode is false. For details on the outmask * parameter, see {@tutorial 2-interface}, "The outmask and caps * parameters". */ g.Geodesic.prototype.GenDirect = function(lat1, lon1, azi1, arcmode, s12_a12, outmask) { var line; if (!outmask) outmask = g.STANDARD; else if (outmask === g.LONG_UNROLL) outmask |= g.STANDARD; // Automatically supply DISTANCE_IN if necessary if (!arcmode) outmask |= g.DISTANCE_IN; line = new l.GeodesicLine(this, lat1, lon1, azi1, outmask); return line.GenPosition(arcmode, s12_a12, outmask); }; /** * @summary Solve the direct geodesic problem. * @param {number} lat1 the latitude of the first point in degrees. * @param {number} lon1 the longitude of the first point in degrees. * @param {number} azi1 the azimuth at the first point in degrees. * @param {number} s12 the distance from the first point to the second in * meters. * @param {bitmask} [outmask = STANDARD] which results to include. * @return {object} the requested results. * @description The lat1, lon1, azi1, s12, and a12 fields of the result are * always set. For details on the outmask parameter, see {@tutorial * 2-interface}, "The outmask and caps parameters". */ g.Geodesic.prototype.Direct = function(lat1, lon1, azi1, s12, outmask) { return this.GenDirect(lat1, lon1, azi1, false, s12, outmask); }; /** * @summary Solve the direct geodesic problem with arc length. * @param {number} lat1 the latitude of the first point in degrees. * @param {number} lon1 the longitude of the first point in degrees. * @param {number} azi1 the azimuth at the first point in degrees. * @param {number} a12 the arc length from the first point to the second in * degrees. * @param {bitmask} [outmask = STANDARD] which results to include. * @return {object} the requested results. * @description The lat1, lon1, azi1, and a12 fields of the result are * always set. For details on the outmask parameter, see {@tutorial * 2-interface}, "The outmask and caps parameters". */ g.Geodesic.prototype.ArcDirect = function(lat1, lon1, azi1, a12, outmask) { return this.GenDirect(lat1, lon1, azi1, true, a12, outmask); }; /** * @summary Create a {@link module:geodesic/GeodesicLine.GeodesicLine * GeodesicLine} object. * @param {number} lat1 the latitude of the first point in degrees. * @param {number} lon1 the longitude of the first point in degrees. * @param {number} azi1 the azimuth at the first point in degrees. * degrees. * @param {bitmask} [caps = STANDARD | DISTANCE_IN] which capabilities to * include. * @return {object} the * {@link module:geodesic/GeodesicLine.GeodesicLine * GeodesicLine} object * @description For details on the caps parameter, see {@tutorial * 2-interface}, "The outmask and caps parameters". */ g.Geodesic.prototype.Line = function(lat1, lon1, azi1, caps) { return new l.GeodesicLine(this, lat1, lon1, azi1, caps); }; /** * @summary Define a {@link module:geodesic/GeodesicLine.GeodesicLine * GeodesicLine} in terms of the direct geodesic problem specified in terms * of distance. * @param {number} lat1 the latitude of the first point in degrees. * @param {number} lon1 the longitude of the first point in degrees. * @param {number} azi1 the azimuth at the first point in degrees. * degrees. * @param {number} s12 the distance between point 1 and point 2 (meters); it * can be negative. * @param {bitmask} [caps = STANDARD | DISTANCE_IN] which capabilities to * include. * @return {object} the * {@link module:geodesic/GeodesicLine.GeodesicLine * GeodesicLine} object * @description This function sets point 3 of the GeodesicLine to correspond * to point 2 of the direct geodesic problem. For details on the caps * parameter, see {@tutorial 2-interface}, "The outmask and caps * parameters". */ g.Geodesic.prototype.DirectLine = function(lat1, lon1, azi1, s12, caps) { return this.GenDirectLine(lat1, lon1, azi1, false, s12, caps); }; /** * @summary Define a {@link module:geodesic/GeodesicLine.GeodesicLine * GeodesicLine} in terms of the direct geodesic problem specified in terms * of arc length. * @param {number} lat1 the latitude of the first point in degrees. * @param {number} lon1 the longitude of the first point in degrees. * @param {number} azi1 the azimuth at the first point in degrees. * degrees. * @param {number} a12 the arc length between point 1 and point 2 (degrees); * it can be negative. * @param {bitmask} [caps = STANDARD | DISTANCE_IN] which capabilities to * include. * @return {object} the * {@link module:geodesic/GeodesicLine.GeodesicLine * GeodesicLine} object * @description This function sets point 3 of the GeodesicLine to correspond * to point 2 of the direct geodesic problem. For details on the caps * parameter, see {@tutorial 2-interface}, "The outmask and caps * parameters". */ g.Geodesic.prototype.ArcDirectLine = function(lat1, lon1, azi1, a12, caps) { return this.GenDirectLine(lat1, lon1, azi1, true, a12, caps); }; /** * @summary Define a {@link module:geodesic/GeodesicLine.GeodesicLine * GeodesicLine} in terms of the direct geodesic problem specified in terms * of either distance or arc length. * @param {number} lat1 the latitude of the first point in degrees. * @param {number} lon1 the longitude of the first point in degrees. * @param {number} azi1 the azimuth at the first point in degrees. * degrees. * @param {bool} arcmode boolean flag determining the meaning of the * s12_a12. * @param {number} s12_a12 if arcmode 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 {bitmask} [caps = STANDARD | DISTANCE_IN] which capabilities to * include. * @return {object} the * {@link module:geodesic/GeodesicLine.GeodesicLine * GeodesicLine} object * @description This function sets point 3 of the GeodesicLine to correspond * to point 2 of the direct geodesic problem. For details on the caps * parameter, see {@tutorial 2-interface}, "The outmask and caps * parameters". */ g.Geodesic.prototype.GenDirectLine = function(lat1, lon1, azi1, arcmode, s12_a12, caps) { var t; if (!caps) caps = g.STANDARD | g.DISTANCE_IN; // Automatically supply DISTANCE_IN if necessary if (!arcmode) caps |= g.DISTANCE_IN; t = new l.GeodesicLine(this, lat1, lon1, azi1, caps); t.GenSetDistance(arcmode, s12_a12); return t; }; /** * @summary Define a {@link module:geodesic/GeodesicLine.GeodesicLine * GeodesicLine} in terms of the inverse geodesic problem. * @param {number} lat1 the latitude of the first point in degrees. * @param {number} lon1 the longitude of the first point in degrees. * @param {number} lat2 the latitude of the second point in degrees. * @param {number} lon2 the longitude of the second point in degrees. * @param {bitmask} [caps = STANDARD | DISTANCE_IN] which capabilities to * include. * @return {object} the * {@link module:geodesic/GeodesicLine.GeodesicLine * GeodesicLine} object * @description This function sets point 3 of the GeodesicLine to correspond * to point 2 of the inverse geodesic problem. For details on the caps * parameter, see {@tutorial 2-interface}, "The outmask and caps * parameters". */ g.Geodesic.prototype.InverseLine = function(lat1, lon1, lat2, lon2, caps) { var r, t, azi1; if (!caps) caps = g.STANDARD | g.DISTANCE_IN; r = this.InverseInt(lat1, lon1, lat2, lon2, g.ARC); azi1 = m.atan2d(r.salp1, r.calp1); // Ensure that a12 can be converted to a distance if (caps & (g.OUT_MASK & g.DISTANCE_IN)) caps |= g.DISTANCE; t = new l.GeodesicLine(this, lat1, lon1, azi1, caps, r.salp1, r.calp1); t.SetArc(r.vals.a12); return t; }; /** * @summary Create a {@link module:geodesic/PolygonArea.PolygonArea * PolygonArea} object. * @param {bool} [polyline = false] if true the new PolygonArea object * describes a polyline instead of a polygon. * @return {object} the * {@link module:geodesic/PolygonArea.PolygonArea * PolygonArea} object */ g.Geodesic.prototype.Polygon = function(polyline) { return new p.PolygonArea(this, polyline); }; /** * @summary a {@link module:geodesic/Geodesic.Geodesic Geodesic} object * initialized for the WGS84 ellipsoid. * @constant {object} */ g.WGS84 = new g.Geodesic(c.WGS84.a, c.WGS84.f);})(geodesic.Geodesic, geodesic.GeodesicLine, geodesic.PolygonArea, geodesic.Math, geodesic.Constants);
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