UTM投影坐标转WGS84大地坐标
程序员文章站
2022-04-04 12:57:26
...
public class UTMAndWGS84
{
static double pi = Math.PI;
/* Ellipsoid model constants (actual values here are for WGS84) */
static double sm_a = 6378137.0;
static double sm_b = 6356752.314;
static double sm_EccSquared = 6.69437999013e-03;
static double UTMScaleFactor = 0.9996;
/*
* DegToRad
*
* Converts degrees to radians.
*
*/
private static double DegToRad(double deg)
{
return (deg / 180.0 * pi);
}
/*
* RadToDeg
*
* Converts radians to degrees.
*
*/
private static 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.
*
*/
private static 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 + (Math.Pow(n, 2.0) / 4.0) + (Math.Pow(n, 4.0) / 64.0));
/* Precalculate beta */
beta = (-3.0 * n / 2.0) + (9.0 * Math.Pow(n, 3.0) / 16.0)
+ (-3.0 * Math.Pow(n, 5.0) / 32.0);
/* Precalculate gamma */
gamma = (15.0 * Math.Pow(n, 2.0) / 16.0)
+ (-15.0 * Math.Pow(n, 4.0) / 32.0);
/* Precalculate delta */
delta = (-35.0 * Math.Pow(n, 3.0) / 48.0)
+ (105.0 * Math.Pow(n, 5.0) / 256.0);
/* Precalculate epsilon */
epsilon = (315.0 * Math.Pow(n, 4.0) / 512.0);
/* Now calculate the sum of the series and return */
result = alpha
* (phi + (beta * Math.Sin(2.0 * phi))
+ (gamma * Math.Sin(4.0 * phi))
+ (delta * Math.Sin(6.0 * phi))
+ (epsilon * Math.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].
*
*/
private static double UTMCentralMeridian(double zone)
{
double cmeridian;
cmeridian = DegToRad(-183.0 + (zone * 6.0));
return cmeridian;
}
/*
* 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.
*
*/
private static 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 + (Math.Pow(n, 2.0) / 4) + (Math.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 * Math.Pow(n, 3.0) / 32.0)
+ (269.0 * Math.Pow(n, 5.0) / 512.0);
/* Precalculate gamma_ (Eq. 10.22) */
gamma_ = (21.0 * Math.Pow(n, 2.0) / 16.0)
+ (-55.0 * Math.Pow(n, 4.0) / 32.0);
/* Precalculate delta_ (Eq. 10.22) */
delta_ = (151.0 * Math.Pow(n, 3.0) / 96.0)
+ (-417.0 * Math.Pow(n, 5.0) / 128.0);
/* Precalculate epsilon_ (Eq. 10.22) */
epsilon_ = (1097.0 * Math.Pow(n, 4.0) / 512.0);
/* Now calculate the sum of the series (Eq. 10.21) */
result = y_ + (beta_ * Math.Sin(2.0 * y_))
+ (gamma_ * Math.Sin(4.0 * y_))
+ (delta_ * Math.Sin(6.0 * y_))
+ (epsilon_ * Math.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.
*
*/
private static void MapLatLonToXY(double phi, double lambda, double lambda0, out double[] xy)
{
double N, nu2, ep2, t, t2, l;
double l3coef, l4coef, l5coef, l6coef, l7coef, l8coef;
double tmp;
/* Precalculate ep2 */
ep2 = (Math.Pow(sm_a, 2.0) - Math.Pow(sm_b, 2.0)) / Math.Pow(sm_b, 2.0);
/* Precalculate nu2 */
nu2 = ep2 * Math.Pow(Math.Cos(phi), 2.0);
/* Precalculate N */
N = Math.Pow(sm_a, 2.0) / (sm_b * Math.Sqrt(1 + nu2));
/* Precalculate t */
t = Math.Tan(phi);
t2 = t * t;
tmp = (t2 * t2 * t2) - Math.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);
xy = new double[2];
/* Calculate easting (x) */
xy[0] = N * Math.Cos(phi) * l
+ (N / 6.0 * Math.Pow(Math.Cos(phi), 3.0) * l3coef * Math.Pow(l, 3.0))
+ (N / 120.0 * Math.Pow(Math.Cos(phi), 5.0) * l5coef * Math.Pow(l, 5.0))
+ (N / 5040.0 * Math.Pow(Math.Cos(phi), 7.0) * l7coef * Math.Pow(l, 7.0));
/* Calculate northing (y) */
xy[1] = ArcLengthOfMeridian(phi)
+ (t / 2.0 * N * Math.Pow(Math.Cos(phi), 2.0) * Math.Pow(l, 2.0))
+ (t / 24.0 * N * Math.Pow(Math.Cos(phi), 4.0) * l4coef * Math.Pow(l, 4.0))
+ (t / 720.0 * N * Math.Pow(Math.Cos(phi), 6.0) * l6coef * Math.Pow(l, 6.0))
+ (t / 40320.0 * N * Math.Pow(Math.Cos(phi), 8.0) * l8coef * Math.Pow(l, 8.0));
return;
}
/*
* 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.
*
*/
private static void MapXYToLatLon(double x, double y, double lambda0, out double[] xy)
{
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 = (Math.Pow(sm_a, 2.0) - Math.Pow(sm_b, 2.0))
/ Math.Pow(sm_b, 2.0);
/* Precalculate cos (phif) */
cf = Math.Cos(phif);
/* Precalculate nuf2 */
nuf2 = ep2 * Math.Pow(cf, 2.0);
/* Precalculate Nf and initialize Nfpow */
Nf = Math.Pow(sm_a, 2.0) / (sm_b * Math.Sqrt(1 + nuf2));
Nfpow = Nf;
/* Precalculate tf */
tf = Math.Tan(phif);
tf2 = tf * tf;
tf4 = tf2 * tf2;
/* Precalculate fractional coefficients for x**n in the equations
below to simplify the expressions for latitude and longitude. */
x1frac = 1.0 / (Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**2) */
x2frac = tf / (2.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**3) */
x3frac = 1.0 / (6.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**4) */
x4frac = tf / (24.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**5) */
x5frac = 1.0 / (120.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**6) */
x6frac = tf / (720.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**7) */
x7frac = 1.0 / (5040.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**8) */
x8frac = tf / (40320.0 * Nfpow);
/* Precalculate polynomial coefficients for x**n.
-- x**1 does not have a polynomial coefficient. */
x2poly = -1.0 - nuf2;
x3poly = -1.0 - 2 * tf2 - nuf2;
x4poly = 5.0 + 3.0 * tf2 + 6.0 * nuf2 - 6.0 * tf2 * nuf2
- 3.0 * (nuf2 * nuf2) - 9.0 * tf2 * (nuf2 * nuf2);
x5poly = 5.0 + 28.0 * tf2 + 24.0 * tf4 + 6.0 * nuf2 + 8.0 * tf2 * nuf2;
x6poly = -61.0 - 90.0 * tf2 - 45.0 * tf4 - 107.0 * nuf2
+ 162.0 * tf2 * nuf2;
x7poly = -61.0 - 662.0 * tf2 - 1320.0 * tf4 - 720.0 * (tf4 * tf2);
x8poly = 1385.0 + 3633.0 * tf2 + 4095.0 * tf4 + 1575 * (tf4 * tf2);
xy = new double[2];
/* Calculate latitude */
xy[0] = phif + x2frac * x2poly * (x * x)
+ x4frac * x4poly * Math.Pow(x, 4.0)
+ x6frac * x6poly * Math.Pow(x, 6.0)
+ x8frac * x8poly * Math.Pow(x, 8.0);
/* Calculate longitude */
xy[1] = lambda0 + x1frac * x
+ x3frac * x3poly * Math.Pow(x, 3.0)
+ x5frac * x5poly * Math.Pow(x, 5.0)
+ x7frac * x7poly * Math.Pow(x, 7.0);
return;
}
/*
* LatLonToUTMXY
*
* Converts a latitude/longitude pair to x and y coordinates in the
* Universal Transverse Mercator projection.
*
* Inputs:
* lat - Latitude of the point, in radians.
* lon - Longitude of the point, in radians.
* zone - UTM zone to be used for calculating values for x and y.
* If zone is less than 1 or greater than 60, the routine
* will determine the appropriate zone from the value of lon.
*
* Outputs:
* xy - A 2-element array where the UTM x and y values will be stored.
*
* Returns:
* The UTM zone used for calculating the values of x and y.
*
*/
public static double[] LatLonToUTMXY(double lat, double lon)
{
double zone = Math.Floor((lon + 180.0) / 6) + 1;
double[] xy = new double[2];
MapLatLonToXY(DegToRad(lat), DegToRad(lon), UTMCentralMeridian(zone), out xy);
/* Adjust easting and northing for UTM system. */
xy[0] = xy[0] * UTMScaleFactor + 500000.0;
xy[1] = xy[1] * UTMScaleFactor;
if (xy[1] < 0.0)
xy[1] = xy[1] + 10000000.0;
return new double[] { xy[0], xy[1], zone };
}
/*
* UTMXYToLatLon
*
* Converts x and y coordinates in the Universal Transverse Mercator
* projection to a latitude/longitude pair.
*
* Inputs:
* x - The easting of the point, in meters.
* y - The northing of the point, in meters.
* zone - The UTM zone in which the point lies.
* southhemi - True if the point is in the southern hemisphere;
* false otherwise.
*
* Outputs:
* latlon - A 2-element array containing the latitude and
* longitude of the point, in radians.
*
* Returns:
* The function does not return a value.
*
*/
public static Coordinate UTMXYToLatLon(double x, double y, double zone, bool southhemi)
{
double cmeridian;
x -= 500000.0;
x /= UTMScaleFactor;
/* If in southern hemisphere, adjust y accordingly. */
if (southhemi)
y -= 10000000.0;
y /= UTMScaleFactor;
cmeridian = UTMCentralMeridian(zone);
double[] xy = new double[2];
MapXYToLatLon(x, y, cmeridian, out xy);
Coordinate coordinate = new Coordinate();
coordinate.Latitude = RadToDeg(xy[0]);
coordinate.Lonitude = RadToDeg(xy[1]);
return coordinate;
}
}
上一篇： 2021年计算机专业大学排名及录取分数线一览表（2022参考）
下一篇： 虫草花是菌类吗