目录
1. 前言
在前面的文章中系统的阐述了工程坐标的转换类别和转换的方法。关于转换代码实现，有很多的类库：
这里针对GPS接收的WGS84椭球的经纬度转换为地方坐标系的问题，利用C#，对工程坐标转换方法和步骤做出详细的解答。不基于任何类库和函数库，也未使用矩阵库，可以便利的将代码移植到任何语言。
2. 计算总体框架
根据上一篇文章中对七参数、四参数、高程拟合在坐标转换的作用和使用条件的阐述，我们可以将上一篇文章第7节的总结图，按照计算的流程重新绘制。
根据上图可知，预将WGS84椭球的GPS坐标需要经过5次转换。其中，
- 转换1、转换3在charlee44的博客：大地经纬度坐标与地心地固坐标的转换中详细讲解了，并且有C++代码的实现，利用C#重构即可。
- 转换2、转换5，以及他们的组合，在我的上一篇文章(工程)坐标转换类别和方法也详细的讲解了。
因此，根据计算原理，直接可以利用C#代码实现。
3. C#代码实现
3.1 整体类的构建
5个转换是对点的操作，不妨构建自定义点类MyPoint，在这个类中定义转换方法。在实现转换方法之前，需要定义数据属性，以承载转换参数和转换数据。代码框架如下：
internal class MyPoint { // 定义椭球类型。这里仅列举了4中国内常见的椭球类型 // 国际椭球可以增加自行定义 public enum EllipsoidType { WGS84, CGCS2000, 西安80, 北京54 } //大地坐标经度、维度、高度 public double L { get; set; } public double B { get; set; } public double H { get; set; } //空间坐标系 public double X { get; set; } public double Y { get; set; } public double Z { get; set; } //七参数转换后的空间坐标 public double X2 { get; set; } public double Y2 { get; set; } public double Z2 { get; set; } private double a = 0, f = 0, b = 0, e = 0, e2 = 0; //椭球参数 private readonly double rho = 180 / Math.PI; private readonly double d2r = Math.PI / 180; public double Xs { get; set; } public double Ys { get; set; } public double Hs { get; set; } //七参数 三个线性平移量-单位米 三个旋转平移量-十进制秒为单位（运算时注意转换为度） 比例因子-单位百万分率 (ppm) //测量队给出的七参数单位与计算的单位不同，要进行单位转化 1 秒=0.0000048481373323 弧度 //尺度因子有两种单位的表示形式，一种结果约为1，如1.0000045，用k表示； //另一种就是ppm的表示形式，稍微比1大一点，如4.5，用m表示。k=m/1000000 private double dx = 0, dy = 0, dz = 0, rx = 0, ry = 0, rz = 0, m = 0, k = 0; } 3.2 椭球参数赋值
常见的椭球参数值在我的文章经纬度坐标转换为工程坐标可以找到，这里选取与上述代码对应的4类椭球，并在上述MyPoint类中增加函数EllipsoidParam(EllipsoidType type)。
/// <summary> /// 椭球参数设置 /// </summary> /// <param name="type">椭球类型</param> private void EllipsoidParam(EllipsoidType type) { // CGCS2000 椭球参数 if (type == EllipsoidType.CGCS2000) { this.a = 6378137; this.f = 1 / 298.257222101; } // 西安 80 else if (type == EllipsoidType.西安80) { this.a = 6378140; this.f = 1 / 298.257; } // 北京 54 else if (type == EllipsoidType.北京54) { this.a = 6378245; this.f = 1 / 298.3; } // WGS-84 else { this.a = 6378137; this.f = 1 / 298.257223563; } this.b = this.a * (1 - this.f); this.e = Math.Sqrt(this.a * this.a - this.b * this.b) / this.a; //第一偏心率 this.e2 = Math.Sqrt(this.a * this.a - this.b * this.b) / this.b; //第二偏心率 } 3.3 转换1、3（大地经纬度坐标与地心地固坐标的转换）
charlee44的博客有C++代码的实现，现在利用C#重构即可。上述MyPoint类中增加BLH2XYZ(EllipsoidType type)和XYZ2BLH(EllipsoidType type)两个函数。
/// <summary> /// 经纬度坐标转空间直角坐标 /// </summary> /// <param name="type">椭球类型</param> public void BLH2XYZ(EllipsoidType type = EllipsoidType.WGS84) { EllipsoidParam(type); double sB = Math.Sin(this.B * d2r); double cB = Math.Cos(this.B * d2r); double sL = Math.Sin(this.L * d2r); double cL = Math.Cos(this.L * d2r); double N = this.a / (Math.Sqrt(1 - this.e * this.e * sB * sB)); this.X = (N + this.H) * cB * cL; this.Y = (N + this.H) * cB * sL; this.Z = (N * (1 - this.e * this.e) + this.H) * sB; this.X2 = this.X; this.Y2 = this.Y; this.Z2 = this.Z; } /// <summary> /// 空间直角坐标转经纬度坐标 /// </summary> /// <param name="type">椭球类型</param> public void XYZ2BLH(EllipsoidType type) { EllipsoidParam(type); // 这里转出来的B L是弧度 this.L = Math.Atan(this.Y2 / this.X2) + Math.PI; this.L = this.L * 180 / Math.PI; // B需要迭代计算 double B2 = Math.Atan(Z2 / Math.Sqrt(X2 * X2 + Y2 * Y2)); double B1; double N; while (true) { N = a / Math.Sqrt(1 - f * (2 - f) * Math.Sin(B2) * Math.Sin(B2)); B1 = Math.Atan((Z2 + N * f * (2 - f) * Math.Sin(B2)) / Math.Sqrt(X2 * X2 + Y2 * Y2)); if (Math.Abs(B1 - B2) < 1e-12) break; B2 = B1; } this.B = B2 * 180 / Math.PI; double sB = Math.Sin(this.B * d2r); double cB = Math.Cos(this.B * d2r); this.H = this.Z2 / sB - N * (1 - this.e * this.e); } 3.4 投影转换
此处仅实现了常见的高斯-克里格投影。上述MyPoint类中增加GaussProjection(EllipsoidType type, ProjectionSetting prjSetting)函数。
/// <summary> /// 利用高斯投影将指定椭球类型的经纬度坐标转为投影坐标 /// </summary> /// <param name="type">椭球类型</param> /// <param name="prjSetting">投影设置实例</param> public void GaussProjection(EllipsoidType type, ProjectionSetting prjSetting) { this.EllipsoidParam(type); double l = (this.L - prjSetting.CenterL) / this.rho; double cB = Math.Cos(this.B * this.d2r); double sB = Math.Sin(this.B * this.d2r); double s2b = Math.Sin(this.B * this.d2r * 2); double s4b = Math.Sin(this.B * this.d2r * 4); double s6b = Math.Sin(this.B * this.d2r * 6); double s8b = Math.Sin(this.B * this.d2r * 8); double N = this.a / Math.Sqrt(1 - this.e * this.e * sB * sB); // 卯酉圈曲率半径 double t = Math.Tan(this.B * this.d2r); double eta = this.e2 * cB; double m0 = this.a * (1 - this.e * this.e); double m2 = 3.0 / 2.0 * this.e * this.e * m0; double m4 = 5.0 / 4.0 * this.e * this.e * m2; double m6 = 7.0 / 6.0 * this.e * this.e * m4; double m8 = 9.0 / 8.0 * this.e * this.e * m6; double a0 = m0 + 1.0 / 2.0 * m2 + 3.0 / 8.0 * m4 + 5.0 / 16.0 * m6 + 35.0 / 128.0 * m8; double a2 = 1.0 / 2.0 * m2 + 1.0 / 2.0 * m4 + 15.0 / 32.0 * m6 + 7.0 / 16.0 * m8; double a4 = 1.0 / 8.0 * m4 + 3.0 / 16.0 * m6 + 7.0 / 32.0 * m8; double a6 = 1.0 / 32.0 * m6 + 1.0 / 16.0 * m8; double a8 = 1.0 / 128.0 * m8; // X1为自赤道量起的子午线弧长 double X1 = a0 * (this.B * this.d2r) - 1.0 / 2.0 * a2 * s2b + 1.0 / 4.0 * a4 * s4b - 1.0 / 6.0 * a6 * s6b + 1.0 / 8.0 * a8 * s8b; this.Xs = X1 + N / 2 * t * cB * cB * l * l + N / 24 * t * (5 - t * t + 9 * Math.Pow(eta, 2) + 4 * Math.Pow(eta, 4)) * Math.Pow(cB, 4) * Math.Pow(l, 4) + N / 720 * t * (61 - 58 * t * t + Math.Pow(t, 4)) * Math.Pow(cB, 6) * Math.Pow(l, 6); this.Ys = N * cB * l + N / 6 * (1 - t * t + eta * eta) * Math.Pow(cB, 3) * Math.Pow(l, 3) + N / 120 * (5 - 18 * t * t + Math.Pow(t, 4) + 14 * Math.Pow(eta, 2) - 58 * eta * eta * t * t) * Math.Pow(cB, 5) * Math.Pow(l, 5); this.Hs = this.H; // 假东 假北偏移 this.Xs += prjSetting.PseudoNorth; this.Ys += prjSetting.PseudoEast; } 其中，ProjectionSetting是一个投影参数设置类，独立于MyPoint类，用于设定中央经线、东偏等投影参数。
internal class ProjectionSetting { private double _centerL; public double CenterL { get { return _centerL; } set { _centerL = value; } } private double _centerB; public double CenterB { get { return _centerB; } set { _centerB = value; } } private double _pseudoEast; public double PseudoEast { get { return _pseudoEast; } set { _pseudoEast = value; } } private double _pseudoNorth; public double PseudoNorth { get { return _pseudoNorth; } set { _pseudoNorth = value; } } private double _prjScale; public double PrjScale { get { return _prjScale; } set { _prjScale = value; } } /// <summary> /// 设置全部的投影参数 /// </summary> /// <param name="centerL"></param> /// <param name="centerB"></param> /// <param name="pseudoEast"></param> /// <param name="pseudoNorth"></param> /// <param name="prjScale"></param> public ProjectionSetting(double centerL, double centerB, double pseudoEast, double pseudoNorth, double prjScale) { CenterL = centerL; CenterB = centerB; PseudoEast = pseudoEast; PseudoNorth = pseudoNorth; PrjScale = prjScale; } /// <summary> /// 仅设置中央经线和东偏 /// </summary> /// <param name="centerL"></param> /// <param name="pseudoEast"></param> public ProjectionSetting(double centerL, double pseudoEast) { CenterL = centerL; CenterB = 0.0; PseudoEast = pseudoEast; PseudoNorth = 0.0; PrjScale = 1.0; } /// <summary> /// 默认常用投影参数，中央经线120°，东偏500000 /// </summary> public ProjectionSetting() { CenterL = 120.0; CenterB = 0.0; PseudoEast = 500000; PseudoNorth = 0.0; PrjScale = 1.0; } } 3.5 转换2的实现（三参数、七参数）
上述MyPoint类中增加SevenParamTrans(Datum7Paras datum7Paras)和TreeParamTrans(Datum3Paras datum3Paras)函数。
/// <summary> /// 利用7参数进行坐标系之间转换 /// </summary> /// <param name="datum7Paras">7参数实例</param> public void SevenParamTrans(Datum7Paras datum7Paras) { this.dx = datum7Paras.Dx; this.dy = datum7Paras.Dy; this.dz = datum7Paras.Dz; this.rx = datum7Paras.Rx * 0.0000048481373323; //1 秒=0.0000048481373323 弧度 this.ry = datum7Paras.Ry * 0.0000048481373323; this.rz = datum7Paras.Rz * 0.0000048481373323; this.m = datum7Paras.PPM; this.k = this.m / 1000000; this.X2 = (1 + k) * (this.X + this.rz * this.Y - this.ry * this.Z) + this.dx; this.Y2 = (1 + k) * (-this.rz * this.X + this.Y + this.rx * this.Z) + this.dy; this.Z2 = (1 + k) * (this.ry * this.X - this.rx * this.Y + this.Z) + this.dz; } /// <summary> /// 利用3参数进行坐标系之间转换 /// </summary> /// <param name="datum3Paras">3参数实例</param> public void TreeParamTrans(Datum3Paras datum3Paras) { this.dx = datum3Paras.Dx; this.dy = datum3Paras.Dy; this.dz = datum3Paras.Dz; this.X2 = this.X + this.dx; this.Y2 = this.Y + this.dy; this.Z2 = this.Z + this.dz; } Datum3Paras和Datum7Paras是独立于MyPoint类，用于设定坐标转换参数。
/// <summary> /// 7参数 /// </summary> internal class Datum7Paras { private double _dx; public double Dx { get { return _dx; } set { _dx = value; } } private double _dy; public double Dy { get { return _dy; } set { _dy = value; } } private double _dz; public double Dz { get { return _dz; } set { _dz = value; } } private double _rx; public double Rx { get { return _rx; } set { _rx = value; } } private double _ry; public double Ry { get { return _ry; } set { _ry = value; } } private double _rz; public double Rz { get { return _rz; } set { _rz = value; } } private double _ppm; public double PPM { get { return _ppm; } set { _ppm = value; } } public Datum7Paras(double dx, double dy, double dz, double rx, double ry, double rz, double ppm) { _dx = dx; _dy = dy; _dz = dz; _rx = rx; _ry = ry; _rz = rz; _ppm = ppm; } } internal class Datum3Paras { private double _dx; public double Dx { get { return _dx; } set { _dx = value; } } private double _dy; public double Dy { get { return _dy; } set { _dy = value; } } private double _dz; public double Dz { get { return _dz; } set { _dz = value; } } public Datum3Paras(double dx, double dy, double dz) { Dx = dx; Dy = dy; Dz = dz; } } 3.6 转换5的实现（四参数+高程拟合）
上述MyPoint类中增加Transform4Para(Trans4Paras transPara)函数。此处，高程拟合仅实现了已知一个测点的固定改正差。
/// <summary> /// 投影坐标获取后，进一步利用4参数转换坐标 /// </summary> /// <param name="transPara"></param> public void Transform4Para(Trans4Paras transPara) { var X1 = transPara.Dx; var Y1 = transPara.Dy; var cosAngle = Math.Cos(transPara.A); var sinAngle = Math.Sin(transPara.A); X1 += transPara.K * (cosAngle * this.Xs - sinAngle * this.Ys); Y1 += transPara.K * (sinAngle * this.Xs + cosAngle * this.Ys); this.Xs = X1; this.Ys = Y1; // 固定改正差 this.Hs += transPara.Dh; } Trans4Paras是独立于MyPoint类，用于设定坐标转换参数。
internal class Trans4Paras { private double _dx; public double Dx { get { return _dx; } set { _dx = value; } } private double _dy; public double Dy { get { return _dy; } set { _dy = value; } } private double _a; public double A { get { return _a; } set { _a = value; } } private double _k; public double K { get { return _k; } set { _k = value; } } private double _dh; public double Dh { get { return _dh; } set { _dh = value; } } public Trans4Paras(double dx, double dy, double a, double k, double dh) { Dx = dx; Dy = dy; A = a; K = k; Dh = dh; } public Trans4Paras() { } } 3.7 调用过程
里面的参数，因为保密原因，做出了随机更改，实际使用时可根据自己情况赋值。
3.7.1 一步法
// 实例化计算参数 MyPoint p = new MyPoint();. p.L=113.256; p.B=31.565; p.H=5.216; // 经纬度转空间坐标 p.BLH2XYZ(); // 实例化七参数 Datum7Paras datum7Paras = new Datum7Paras( 489.2994563566, 141.1525159753, 15.74421120568, -0.164423, 4.141573, -4.808299, -6.56482989958); p.SevenParamTrans(datum7Paras); // 空间坐标转回经纬度 p.XYZ2BLH(EllipsoidType.WGS84); // 高斯投影 经纬度转平面坐标 // 实例化投影参数类 ProjectionSetting projectionSetting = new ProjectionSetting(120,500000); p.GaussProjection(EllipsoidType.WGS84, projectionSetting); 3.7.2 两步法
// 实例化计算参数 MyPoint p = new MyPoint();. p.SetLBH(113.256,31.565,5.216); // 经纬度转空间坐标 p.BLH2XYZ(); // 实例化七参数 Datum7Paras datum7Paras = new Datum7Paras( 489.2994563566, 141.1525159753, 15.74421120568, -0.164423, 4.141573, -4.808299, -6.56482989958); p.SevenParamTrans(datum7Paras); // 空间坐标转回经纬度 p.XYZ2BLH(EllipsoidType.WGS84); // 高斯投影 经纬度转平面坐标 // 实例化投影参数类 ProjectionSetting projectionSetting = new ProjectionSetting(120,500000); p.GaussProjection(EllipsoidType.WGS84, projectionSetting); Trans4Paras transformPara = new(6456.15957352521, -134618.390707439, 0.011104964500129, 1.00002537583871, 5.788); p.Transform4Para(transformPara); 4. 总结
至此，关于工程坐标系转化，即GPS接收的WGS84椭球的经纬度转换为地方坐标系的问题，基本全部实现。代码正确性和准确性的验证是与 南方GPS工具箱做对比。例如，采用上述的一步法，在设定好坐标、7参数、投影参数后，计算发现，与南方GPS工具箱在y方向偏差1mm。结果如下图：
