中央子午线

UTM坐标系，需要确定给定UTM区域的中央子午线。
分为三分度和六分度。

三分度

3度带：中央子午线计算公式：中央子午线L=3 ×N 。N=当地经度/3，N值进行四舍五入后即为3度带的带号。

六分度

6度带：中央子午线计算公式：中央子午线L=6 ×（N＋1）－3 。N=[当地经度/6]，N值不进行四舍五入，只取整数部分，（N＋1）即为6度带的带号。
代号查询：
https://www.docin.com/p-1652560117.html

注意

下面的转换代码，用的是六分度的中央子午线，范围为（-177,177）。

UTM转经纬度

引入头文件
#include “CoorConv.hpp”

 double x = 690829.75249613554;double y = 3118616.9477559421;WGS84Corr t;//长沙的zone为49  长沙的中央子午线经度为111，推出zone为49//return DegToRad(-183.0 + (zone * 6.0));UTMXYToLatLon(x, y, 49,false,t);double lat = RadToDeg(t.lat);  //注意弧度转角度！！！double log = RadToDeg(t.log);

经纬度转UTM

    WGS84Corr t;t.lat = 28.17951;t.log = 112.943878;LatLonToUTMXY(DegToRad(t.lat), DegToRad(t.log),49,test);std::cout << test.x << "  " << test.y << std::endl;

相关的头文件！直接引入就可以用！

//CoorConv.hpp
#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;  //UTM坐标系typedef struct tagWGS84Corr
{double lat;double log;
}WGS84Corr;  //经纬度
/*
* DegToRad
*
* Converts degrees to radians.
* 将度数转换为弧度
*/
inline double DegToRad (double deg)
{return (deg / 180.0 * pi);
}/*
* RadToDeg
*
* Converts radians to degrees.
* 将弧度转换为度数
*/
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.  计算从赤道到a点的椭圆距离给定纬度。
*
* 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.
*     phi-点的纬度，以弧度为单位。
* 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.
*     点到赤道的椭圆距离，以米为单位
*/
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
* UTMC中央子午线
* Determines the central meridian for the given UTM zone.
* 确定给定UTM区域的中央子午线
* Inputs:
*     zone - An integer value designating the UTM zone, range [1,60].
*     zone-  指定UTM区域的整数值，范围[1,60]
* Returns:
*   The central meridian for the given UTM zone, in radians, or zero
*   给定UTM区域的中央子午线，以弧度为单位
*   if the UTM zone parameter is outside the range [1,60].
*    如果UTM区域参数不在[1,60]范围内，返回0
*   Range of the central meridian is the radian equivalent of [-177,+177].
*   中央子午线的范围是[-177，+ 177]的弧度
*/
inline double UTMCentralMeridian (int zone)
{return DegToRad(-183.0 + (zone * 6.0));
}/*
* FootpointLatitude
*
* Computes the footpoint latitude for use in converting transverse
* 计算用于转换横向的立足点纬度
* 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.
*   y - UTM北坐标，以米为单位
* Returns:
*   The footpoint latitude, in radians.
*   返回立足点的纬度，以弧度为单位
*
*/
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.
**将纬度/经度对转换为x和y坐标，横向墨卡托投影。 请注意，横轴墨卡托与UTM不同； 需要比例因子在它们之间进行转换。
* 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.
*    phi-点的纬度，以弧度为单位。
*    lambda-点的经度，以弧度为单位。
*    lambda0-要使用的中央子午线的经度，以弧度为单位。
* Outputs:
*    xy - A 2-element array containing the x and y coordinates
*         of the computed point.
*    xy-一个2元素的数组，其中包含计算点的x和y坐标
* 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 belowso a normal human being can read the expressions for eastingand 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.
*  将“横向墨卡托”投影中的x和y坐标转换为纬度/经度对。
*  请注意，横轴墨卡托与UTM不同；需要比例因子在它们之间进行转换。
* 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.
* 输入：
*    x-点的东移，以米为单位。
*    y-点的北，以米为单位。
*    lambda0-要使用的中央子午线的经度，以弧度为单位。
*
*输出：
*     philambda-包含纬度和经度的2元素，单位为弧度。
* 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(sm_a, 2.0) - pow(sm_b, 2.0))   / pow(sm_b, 2.0);/* Precalculate cos (phif) */cf = cos (phif);/* Precalculate nuf2 */nuf2 = ep2 * pow (cf, 2.0);/* Precalculate Nf and initialize Nfpow */Nf = pow(sm_a, 2.0) / (sm_b * sqrt(1 + nuf2));Nfpow = Nf;/* Precalculate tf */tf = tan (phif);tf2 = tf * tf;tf4 = tf2 * tf2;/* Precalculate fractional coefficients for x**n in the equationsbelow 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);/* Calculate latitude */philambda.lat = phif + x2frac * x2poly * (x * x) + x4frac * x4poly * pow(x, 4.0) + x6frac * x6poly * pow(x, 6.0) + x8frac * x8poly * pow(x, 8.0);/* Calculate longitude */philambda.log = lambda0 + x1frac * x + x3frac * x3poly * pow(x, 3.0) + x5frac * x5poly * pow(x, 5.0) + x7frac * x7poly * pow(x, 7.0);
}/*
* LatLonToUTMXY
*
* Converts a latitude/longitude pair to x and y coordinates in the
* Universal Transverse Mercator projection.
* 将纬度/经度对转换为x和y坐标
* 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.
* 输入：
*   lat-点的纬度，以弧度为单位。
*   lon-点的经度，以弧度为单位。
*   zone-用于计算x和y值的UTM区域。
*   如果区域小于1或大于60，则例程将根据lon的值确定适当的区域。
* Outputs:
*   xy - A 2-element array where the UTM x and y values will be stored.
*   xy-2元素数组，将存储UTM x和y值
* Returns:
*   void
*
*/
void LatLonToUTMXY (double lat, double lon, int zone, UTMCoor &xy)
{MapLatLonToXY (lat, lon, UTMCentralMeridian(zone), xy);/* Adjust easting and northing for UTM system. */xy.x = xy.x * UTMScaleFactor + 500000.0;xy.y = xy.y * UTMScaleFactor;if (xy.y < 0.0)xy.y += 10000000.0;
}/*
* UTMXYToLatLon
*
* Converts x and y coordinates in the Universal Transverse Mercator
* projection to a latitude/longitude pair.
* 在通用横轴墨卡托中转换x和y坐标投影到纬度/经度对。
*
* 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.
* 输入：
*    x-点的东移，以米为单位。
*    y-点的北，以米为单位。
*    zone-点所在的UTM区域。
*    southhemi-如果该点在南半球，则为true；否则为true。
*    否则为false。
* Outputs:
*   latlon - A 2-element array containing the latitude and
*            longitude of the point, in radians.
*
* Returns:
*   The function does not return a value.
*
*/
void UTMXYToLatLon (double x, double y, int zone, bool southhemi, WGS84Corr &latlon)
{double cmeridian;x -= 500000.0;x /= UTMScaleFactor;/* If in southern hemisphere, adjust y accordingly. */if (southhemi)y -= 10000000.0;y /= UTMScaleFactor;cmeridian = UTMCentralMeridian (zone);MapXYToLatLon (x, y, cmeridian, latlon);
}#endif //__COORCONV_H__

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UTM大地坐标系与经纬度转换算法C++

中央子午线

三分度

六分度

注意

UTM转经纬度

经纬度转UTM

相关的头文件！直接引入就可以用！

UTM大地坐标系与经纬度转换算法C++相关推荐

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