工程座標轉換方法C#程式碼實現

Aidan_Lee發表於2022-12-04
C#

目錄

1. 前言

在前面的文章中系統的闡述了工程座標的轉換類別和轉換的方法。關於轉換程式碼實現，有很多的類庫：

這裡針對GPS接收的WGS84橢球的經緯度轉換為地方座標系的問題，利用C#，對工程座標轉換方法和步驟做出詳細的解答。不基於任何類庫和函式庫，也未使用矩陣庫，可以便利的將程式碼移植到任何語言。

2. 計算總體框架

根據上一篇文章中對七引數、四引數、高程擬合在座標轉換的作用和使用條件的闡述，我們可以將上一篇文章第7節的總結圖，按照計算的流程重新繪製。
image

根據上圖可知，預將WGS84橢球的GPS座標需要經過5次轉換。其中，

  1. 轉換1、轉換3在charlee44的部落格：大地經緯度座標與地心地固座標的轉換中詳細講解了，並且有C++程式碼的實現，利用C#重構即可。
  2. 轉換2、轉換5，以及他們的組合，在我的上一篇文章(工程)座標轉換類別和方法也詳細的講解了。

因此，根據計算原理，直接可以利用C#程式碼實現。

3. C#程式碼實現

3.1 整體類的構建

5個轉換是對點的操作，不妨構建自定義點類MyPoint，在這個類中定義轉換方法。在實現轉換方法之前，需要定義資料屬性，以承載轉換引數和轉換資料。程式碼框架如下：

internal class MyPoint
{
	// 定義橢球型別。這裡僅列舉了4中國內常見的橢球型別
	// 國際橢球可以增加自行定義	
	public enum EllipsoidType
	     {
	         WGS84,
	         CGCS2000,
	         西安80,
	         北京54
	     }
	    //大地座標經度、維度、高度
	    public double L { get; set; }
	    public double B { get; set; }
	    public double H { get; set; }
	
	    //空間座標系
	    public double X { get; set; }
	    public double Y { get; set; }
	    public double Z { get; set; }
	
	    //七引數轉換後的空間座標
	    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;    //橢球引數
	
	    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; }
	
	    //七引數 三個線性平移量-單位米 三個旋轉平移量-十進位制秒為單位（運算時注意轉換為度） 比例因子-單位百萬分率 (ppm)
	    //測量隊給出的七引數單位與計算的單位不同，要進行單位轉化 1 秒=0.0000048481373323 弧度
	    //尺度因子有兩種單位的表示形式，一種結果約為1，如1.0000045，用k表示；
	    //另一種就是ppm的表示形式，稍微比1大一點，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 橢球引數賦值

常見的橢球引數值在我的文章經緯度座標轉換為工程座標可以找到，這裡選取與上述程式碼對應的4類橢球，並在上述MyPoint類中增加函式EllipsoidParam(EllipsoidType type)。

/// <summary>
/// 橢球引數設定
/// </summary>
/// <param name="type">橢球型別</param>
private void EllipsoidParam(EllipsoidType type)
{
    // CGCS2000 橢球引數
    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 轉換1、3（大地經緯度座標與地心地固座標的轉換）

charlee44的部落格有C++程式碼的實現，現在利用C#重構即可。上述MyPoint類中增加BLH2XYZ(EllipsoidType type)和XYZ2BLH(EllipsoidType type)兩個函式。

/// <summary>
/// 經緯度座標轉空間直角座標
/// </summary>
/// <param name="type">橢球型別</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>
/// 空間直角座標轉經緯度座標
/// </summary>
/// <param name="type">橢球型別</param>
public void XYZ2BLH(EllipsoidType type)
{
    EllipsoidParam(type);

    // 這裡轉出來的B L是弧度
    this.L = Math.Atan(this.Y2 / this.X2) + Math.PI;
    
    this.L = this.L * 180 / Math.PI;
    // B需要迭代計算
    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 投影轉換

此處僅實現了常見的高斯-克里格投影。上述MyPoint類中增加GaussProjection(EllipsoidType type, ProjectionSetting prjSetting)函式。

/// <summary>
/// 利用高斯投影將指定橢球型別的經緯度座標轉為投影座標
/// </summary>
/// <param name="type">橢球型別</param>
/// <param name="prjSetting">投影設定例項</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);       // 卯酉圈曲率半徑
    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為自赤道量起的子午線弧長
    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;

    // 假東 假北偏移
    
    this.Xs += prjSetting.PseudoNorth;
    this.Ys += prjSetting.PseudoEast;
}

其中，ProjectionSetting是一個投影引數設定類，獨立於MyPoint類，用於設定中央經線、東偏等投影引數。

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>
		/// 設定全部的投影引數
		/// </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>
		/// 僅設定中央經線和東偏
		/// </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>
		/// 預設常用投影引數，中央經線120°，東偏500000
		/// </summary>
		public ProjectionSetting()
		{
            CenterL = 120.0;
            CenterB = 0.0;
            PseudoEast = 500000;
            PseudoNorth = 0.0;
            PrjScale = 1.0;
        }
	}

3.5 轉換2的實現（三引數、七引數）

上述MyPoint類中增加SevenParamTrans(Datum7Paras datum7Paras)和TreeParamTrans(Datum3Paras datum3Paras)函式。

/// <summary>
/// 利用7引數進行座標系之間轉換
/// </summary>
/// <param name="datum7Paras">7引數例項</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引數進行座標系之間轉換
/// </summary>
/// <param name="datum3Paras">3引數例項</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是獨立於MyPoint類，用於設定座標轉換引數。

   /// <summary>
    /// 7引數
    /// </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 轉換5的實現（四引數+高程擬合）

上述MyPoint類中增加Transform4Para(Trans4Paras transPara)函式。此處，高程擬合僅實現了已知一個測點的固定改正差。

/// <summary>
/// 投影座標獲取後，進一步利用4引數轉換座標
/// </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是獨立於MyPoint類，用於設定座標轉換引數。

    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 呼叫過程

裡面的引數，因為保密原因，做出了隨機更改，實際使用時可根據自己情況賦值。

3.7.1 一步法

// 例項化計算引數
MyPoint p = new MyPoint();.

p.L=113.256;
p.B=31.565;
p.H=5.216;
 
// 經緯度轉空間座標
p.BLH2XYZ();

// 例項化七引數
Datum7Paras datum7Paras = new Datum7Paras(
    489.2994563566, 141.1525159753, 15.74421120568,
    -0.164423, 4.141573, -4.808299,
    -6.56482989958);

p.SevenParamTrans(datum7Paras);

// 空間座標轉回經緯度
p.XYZ2BLH(EllipsoidType.WGS84);

// 高斯投影 經緯度轉平面座標
// 例項化投影引數類
ProjectionSetting projectionSetting = new ProjectionSetting(120,500000);
p.GaussProjection(EllipsoidType.WGS84, projectionSetting);

3.7.2 兩步法

// 例項化計算引數
MyPoint p = new MyPoint();.

p.SetLBH(113.256,31.565,5.216);
 
// 經緯度轉空間座標
p.BLH2XYZ();

// 例項化七引數
Datum7Paras datum7Paras = new Datum7Paras(
    489.2994563566, 141.1525159753, 15.74421120568,
    -0.164423, 4.141573, -4.808299,
    -6.56482989958);

p.SevenParamTrans(datum7Paras);

// 空間座標轉回經緯度
p.XYZ2BLH(EllipsoidType.WGS84);

// 高斯投影 經緯度轉平面座標
// 例項化投影引數類
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. 總結

至此，關於工程座標系轉化，即GPS接收的WGS84橢球的經緯度轉換為地方座標系的問題，基本全部實現。程式碼正確性和準確性的驗證是與 南方GPS工具箱做對比。例如，採用上述的一步法，在設定好座標、7引數、投影引數後，計算發現，與南方GPS工具箱在y方向偏差1mm。結果如下圖：
image

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