#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(
