UTM与WGS84坐标系互转C/C++实现

#ifndef __COORCONV_H__ #define __COORCONV_H__ #include <cmath> double pi = 3.14159265358979; /* Ellipsoid model constants (actual values here are for WGS84) */ double sm_a = 6378137.0; double sm_b = 6356752.314; double sm_EccSquared = 6.69437999013e-03; double UTMScaleFactor = 0.9996; typedef struct tagUTMCorr { double x; double y; }UTMCoor; typedef struct tagWGS84Corr { double lat; double log; }WGS84Corr; /* * DegToRad * * Converts degrees to radians. * */ inline double DegToRad (double deg) { return (deg / 180.0 * pi); } /* * RadToDeg * * Converts radians to degrees. * */ inline double RadToDeg (double rad) { return (rad / pi * 180.0); } /* * ArcLengthOfMeridian * * Computes the ellipsoidal distance from the equator to a point at a * given latitude. * * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J., * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994. * * Inputs: * phi - Latitude of the point, in radians. * * Globals: * sm_a - Ellipsoid model major axis. * sm_b - Ellipsoid model minor axis. * * Returns: * The ellipsoidal distance of the point from the equator, in meters. * */ double ArcLengthOfMeridian (double phi) { double alpha, beta, gamma, delta, epsilon, n; double result; /* Precalculate n */ n = (sm_a - sm_b) / (sm_a + sm_b); /* Precalculate alpha */ alpha = ((sm_a + sm_b) / 2.0) * (1.0 + (pow(n, 2.0) / 4.0) + (pow(n, 4.0) / 64.0)); /* Precalculate beta */ beta = (-3.0 * n / 2.0) + (9.0 * pow(n, 3.0) / 16.0) + (-3.0 * pow(n, 5.0) / 32.0); /* Precalculate gamma */ gamma = (15.0 * pow(n, 2.0) / 16.0) + (-15.0 * pow(n, 4.0) / 32.0); /* Precalculate delta */ delta = (-35.0 * pow(n, 3.0) / 48.0) + (105.0 * pow(n, 5.0) / 256.0); /* Precalculate epsilon */ epsilon = (315.0 * pow(n, 4.0) / 512.0); /* Now calculate the sum of the series and return */ result = alpha * (phi + (beta * sin(2.0 * phi)) + (gamma * sin(4.0 * phi)) + (delta * sin(6.0 * phi)) + (epsilon * sin(8.0 * phi))); return result; } /* * UTMCentralMeridian * * Determines the central meridian for the given UTM zone. * * Inputs: * zone - An integer value designating the UTM zone, range [1,60]. * * Returns: * The central meridian for the given UTM zone, in radians, or zero * if the UTM zone parameter is outside the range [1,60]. * Range of the central meridian is the radian equivalent of [-177,+177]. * */ inline double UTMCentralMeridian (int zone) { return DegToRad(-183.0 + (zone * 6.0)); } /* * FootpointLatitude * * Computes the footpoint latitude for use in converting transverse * Mercator coordinates to ellipsoidal coordinates. * * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J., * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994. * * Inputs: * y - The UTM northing coordinate, in meters. * * Returns: * The footpoint latitude, in radians. * */ double FootpointLatitude (double y) { double y_, alpha_, beta_, gamma_, delta_, epsilon_, n; double result; /* Precalculate n (Eq. 10.18) */ n = (sm_a - sm_b) / (sm_a + sm_b); /* Precalculate alpha_ (Eq. 10.22) */ /* (Same as alpha in Eq. 10.17) */ alpha_ = ((sm_a + sm_b) / 2.0) * (1 + (pow(n, 2.0) / 4) + (pow(n, 4.0) / 64)); /* Precalculate y_ (Eq. 10.23) */ y_ = y / alpha_; /* Precalculate beta_ (Eq. 10.22) */ beta_ = (3.0 * n / 2.0) + (-27.0 * pow(n, 3.0) / 32.0) + (269.0 * pow(n, 5.0) / 512.0); /* Precalculate gamma_ (Eq. 10.22) */ gamma_ = (21.0 * pow(n, 2.0) / 16.0) + (-55.0 * pow(n, 4.0) / 32.0); /* Precalculate delta_ (Eq. 10.22) */ delta_ = (151.0 * pow (n, 3.0) / 96.0) + (-417.0 * pow (n, 5.0) / 128.0); /* Precalculate epsilon_ (Eq. 10.22) */ epsilon_ = (1097.0 * pow(n, 4.0) / 512.0); /* Now calculate the sum of the series (Eq. 10.21) */ result = y_ + (beta_ * sin(2.0 * y_)) + (gamma_ * sin(4.0 * y_)) + (delta_ * sin(6.0 * y_)) + (epsilon_ * sin(8.0 * y_)); return result; } /* * MapLatLonToXY * * Converts a latitude/longitude pair to x and y coordinates in the * Transverse Mercator projection. Note that Transverse Mercator is not * the same as UTM; a scale factor is required to convert between them. * * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J., * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994. * * Inputs: * phi - Latitude of the point, in radians. * lambda - Longitude of the point, in radians. * lambda0 - Longitude of the central meridian to be used, in radians. * * Outputs: * xy - A 2-element array containing the x and y coordinates * of the computed point. * * Returns: * The function does not return a value. * */ void MapLatLonToXY (double phi, double lambda, double lambda0, UTMCoor &xy) { double N, nu2, ep2, t, t2, l; double l3coef, l4coef, l5coef, l6coef, l7coef, l8coef; double tmp; /* Precalculate ep2 */ ep2 = (pow(sm_a, 2.0) - pow(sm_b, 2.0)) / pow(sm_b, 2.0); /* Precalculate nu2 */ nu2 = ep2 * pow(cos(phi), 2.0); /* Precalculate N */ N = pow(sm_a, 2.0) / (sm_b * sqrt(1 + nu2)); /* Precalculate t */ t = tan (phi); t2 = t * t; tmp = (t2 * t2 * t2) - pow (t, 6.0); /* Precalculate l */ l = lambda - lambda0; /* Precalculate coefficients for l**n in the equations below so a normal human being can read the expressions for easting and northing -- l**1 and l**2 have coefficients of 1.0 */ l3coef = 1.0 - t2 + nu2; l4coef = 5.0 - t2 + 9 * nu2 + 4.0 * (nu2 * nu2); l5coef = 5.0 - 18.0 * t2 + (t2 * t2) + 14.0 * nu2 - 58.0 * t2 * nu2; l6coef = 61.0 - 58.0 * t2 + (t2 * t2) + 270.0 * nu2 - 330.0 * t2 * nu2; l7coef = 61.0 - 479.0 * t2 + 179.0 * (t2 * t2) - (t2 * t2 * t2); l8coef = 1385.0 - 3111.0 * t2 + 543.0 * (t2 * t2) - (t2 * t2 * t2); /* Calculate easting (x) */ xy.x = N * cos (phi) * l + (N / 6.0 * pow(cos(phi), 3.0) * l3coef * pow(l, 3.0)) + (N / 120.0 * pow(cos(phi), 5.0) * l5coef * pow(l, 5.0)) + (N / 5040.0 * pow(cos (phi), 7.0) * l7coef * pow(l, 7.0)); /* Calculate northing (y) */ xy.y = ArcLengthOfMeridian (phi) + (t / 2.0 * N * pow(cos(phi), 2.0) * pow(l, 2.0)) + (t / 24.0 * N * pow(cos(phi), 4.0) * l4coef * pow(l, 4.0)) + (t / 720.0 * N * pow(cos(phi), 6.0) * l6coef * pow(l, 6.0)) + (t / 40320.0 * N * pow(cos(phi), 8.0) * l8coef * pow(l, 8.0)); } /* * MapXYToLatLon * * Converts x and y coordinates in the Transverse Mercator projection to * a latitude/longitude pair. Note that Transverse Mercator is not * the same as UTM; a scale factor is required to convert between them. * * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J., * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994. * * Inputs: * x - The easting of the point, in meters. * y - The northing of the point, in meters. * lambda0 - Longitude of the central meridian to be used, in radians. * * Outputs: * philambda - A 2-element containing the latitude and longitude * in radians. * * Returns: * The function does not return a value. * * Remarks: * The local variables Nf, nuf2, tf, and tf2 serve the same purpose as * N, nu2, t, and t2 in MapLatLonToXY, but they are computed with respect * to the footpoint latitude phif. * * x1frac, x2frac, x2poly, x3poly, etc. are to enhance readability and * to optimize computations. * */ void MapXYToLatLon (double x, double y, double lambda0, WGS84Corr &philambda) { double phif, Nf, Nfpow, nuf2, ep2, tf, tf2, tf4, cf; double x1frac, x2frac, x3frac, x4frac, x5frac, x6frac, x7frac, x8frac; double x2poly, x3poly, x4poly, x5poly, x6poly, x7poly, x8poly; /* Get the value of phif, the footpoint latitude. */ phif = FootpointLatitude (y); /* Precalculate ep2 */ ep2 = (pow(