工程坐標(biāo)轉(zhuǎn)換方法C#代碼實(shí)現(xiàn)-創(chuàng)新互聯(lián)

目錄
  • 1. 前言
  • 2. 計(jì)算總體框架
  • 3. C#代碼實(shí)現(xiàn)
    • 3.1 整體類的構(gòu)建
    • 3.2 橢球參數(shù)賦值
    • 3.3 轉(zhuǎn)換1、3(大地經(jīng)緯度坐標(biāo)與地心地固坐標(biāo)的轉(zhuǎn)換)
    • 3.4 投影轉(zhuǎn)換
    • 3.5 轉(zhuǎn)換2的實(shí)現(xiàn)(三參數(shù)、七參數(shù))
    • 3.6 轉(zhuǎn)換5的實(shí)現(xiàn)(四參數(shù)+高程擬合)
    • 3.7 調(diào)用過程
      • 3.7.1 一步法
      • 3.7.2 兩步法
  • 4. 總結(jié)

成都創(chuàng)新互聯(lián)服務(wù)項(xiàng)目包括夏河網(wǎng)站建設(shè)、夏河網(wǎng)站制作、夏河網(wǎng)頁制作以及夏河網(wǎng)絡(luò)營銷策劃等。多年來,我們專注于互聯(lián)網(wǎng)行業(yè),利用自身積累的技術(shù)優(yōu)勢、行業(yè)經(jīng)驗(yàn)、深度合作伙伴關(guān)系等,向廣大中小型企業(yè)、政府機(jī)構(gòu)等提供互聯(lián)網(wǎng)行業(yè)的解決方案,夏河網(wǎng)站推廣取得了明顯的社會效益與經(jīng)濟(jì)效益。目前,我們服務(wù)的客戶以成都為中心已經(jīng)輻射到夏河省份的部分城市,未來相信會繼續(xù)擴(kuò)大服務(wù)區(qū)域并繼續(xù)獲得客戶的支持與信任!1. 前言

在前面的文章中系統(tǒng)的闡述了工程坐標(biāo)的轉(zhuǎn)換類別和轉(zhuǎn)換的方法。關(guān)于轉(zhuǎn)換代碼實(shí)現(xiàn),有很多的類庫:

  • GDAL
  • SharpProj - Providing OSGEO PROJ for .Net (Core)
  • ProjNet (for GeoAPI)

這里針對GPS接收的WGS84橢球的經(jīng)緯度轉(zhuǎn)換為地方坐標(biāo)系的問題,利用C#,對工程坐標(biāo)轉(zhuǎn)換方法和步驟做出詳細(xì)的解答。不基于任何類庫和函數(shù)庫,也未使用矩陣庫,可以便利的將代碼移植到任何語言。


2. 計(jì)算總體框架

根據(jù)上一篇文章中對七參數(shù)、四參數(shù)、高程擬合在坐標(biāo)轉(zhuǎn)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(jié)的總結(jié)圖,按照計(jì)算的流程重新繪制。
在這里插入圖片描述
根據(jù)上圖可知,預(yù)將WGS84橢球的GPS坐標(biāo)需要經(jīng)過5次轉(zhuǎn)換。其中,

  1. 轉(zhuǎn)換1、轉(zhuǎn)換3在charlee44的博客:大地經(jīng)緯度坐標(biāo)與地心地固坐標(biāo)的轉(zhuǎn)換中詳細(xì)講解了,并且有C++代碼的實(shí)現(xiàn),利用C#重構(gòu)即可。
  2. 轉(zhuǎn)換2、轉(zhuǎn)換5,以及他們的組合,在我的上一篇文章(工程)坐標(biāo)轉(zhuǎn)換類別和方法也詳細(xì)的講解了。

因此,根據(jù)計(jì)算原理,直接可以利用C#代碼實(shí)現(xiàn)。


3. C#代碼實(shí)現(xiàn) 3.1 整體類的構(gòu)建

5個(gè)轉(zhuǎn)換是對點(diǎn)的操作,不妨構(gòu)建自定義點(diǎn)類MyPoint,在這個(gè)類中定義轉(zhuǎn)換方法。在實(shí)現(xiàn)轉(zhuǎn)換方法之前,需要定義數(shù)據(jù)屬性,以承載轉(zhuǎn)換參數(shù)和轉(zhuǎn)換數(shù)據(jù)。代碼框架如下:

internal class MyPoint
{// 定義橢球類型。這里僅列舉了4中國內(nèi)常見的橢球類型
	// 國際橢球可以增加自行定義	
	public enum EllipsoidType
	     { WGS84,
	         CGCS2000,
	         西安80,
	         北京54
	     }
	    //大地坐標(biāo)經(jīng)度、維度、高度
	    public double L {get; set; }
	    public double B {get; set; }
	    public double H {get; set; }
	
	    //空間坐標(biāo)系
	    public double X {get; set; }
	    public double Y {get; set; }
	    public double Z {get; set; }
	
	    //七參數(shù)轉(zhuǎn)換后的空間坐標(biāo)
	    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;    //橢球參數(shù)
	
	    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; }
	
	    //七參數(shù) 三個(gè)線性平移量-單位米 三個(gè)旋轉(zhuǎn)平移量-十進(jìn)制秒為單位(運(yùn)算時(shí)注意轉(zhuǎn)換為度) 比例因子-單位百萬分率 (ppm)
	    //測量隊(duì)給出的七參數(shù)單位與計(jì)算的單位不同,要進(jìn)行單位轉(zhuǎn)化 1 秒=0.0000048481373323 弧度
	    //尺度因子有兩種單位的表示形式,一種結(jié)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(diǎn),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 橢球參數(shù)賦值

常見的橢球參數(shù)值在我的文章經(jīng)緯度坐標(biāo)轉(zhuǎn)換為工程坐標(biāo)可以找到,這里選取與上述代碼對應(yīng)的4類橢球,并在上述MyPoint類中增加函數(shù)EllipsoidParam(EllipsoidType type)。

////// 橢球參數(shù)設(shè)置
//////橢球類型private void EllipsoidParam(EllipsoidType type)
{// CGCS2000 橢球參數(shù)
    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(zhuǎn)換1、3(大地經(jīng)緯度坐標(biāo)與地心地固坐標(biāo)的轉(zhuǎn)換)

charlee44的博客有C++代碼的實(shí)現(xiàn),現(xiàn)在利用C#重構(gòu)即可。上述MyPoint類中增加BLH2XYZ(EllipsoidType type)XYZ2BLH(EllipsoidType type)兩個(gè)函數(shù)。

////// 經(jīng)緯度坐標(biāo)轉(zhuǎn)空間直角坐標(biāo)
//////橢球類型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;
}

////// 空間直角坐標(biāo)轉(zhuǎn)經(jīng)緯度坐標(biāo)
//////橢球類型public void XYZ2BLH(EllipsoidType type)
{EllipsoidParam(type);

    // 這里轉(zhuǎn)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(jì)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(zhuǎn)換

此處僅實(shí)現(xiàn)了常見的高斯-克里格投影。上述MyPoint類中增加GaussProjection(EllipsoidType type, ProjectionSetting prjSetting)函數(shù)。

////// 利用高斯投影將指定橢球類型的經(jīng)緯度坐標(biāo)轉(zhuǎn)為投影坐標(biāo)
//////橢球類型///投影設(shè)置實(shí)例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(gè)投影參數(shù)設(shè)置類,獨(dú)立于MyPoint類,用于設(shè)定中央經(jīng)線、東偏等投影參數(shù)。

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; }
		}

		////// 設(shè)置全部的投影參數(shù)
		//////////////////public ProjectionSetting(double centerL, double centerB, 
			double pseudoEast, double pseudoNorth,
			double prjScale)
		{	CenterL = centerL;
			CenterB = centerB;
			PseudoEast = pseudoEast;
			PseudoNorth = pseudoNorth;
			PrjScale = prjScale;
		}

		////// 僅設(shè)置中央經(jīng)線和東偏
		/////////public ProjectionSetting(double centerL, double pseudoEast)
		{CenterL = centerL;
            CenterB = 0.0;
            PseudoEast = pseudoEast;
            PseudoNorth = 0.0;
            PrjScale = 1.0;
        }

		////// 默認(rèn)常用投影參數(shù),中央經(jīng)線120°,東偏500000
		///public ProjectionSetting()
		{CenterL = 120.0;
            CenterB = 0.0;
            PseudoEast = 500000;
            PseudoNorth = 0.0;
            PrjScale = 1.0;
        }
	}
3.5 轉(zhuǎn)換2的實(shí)現(xiàn)(三參數(shù)、七參數(shù))

上述MyPoint類中增加SevenParamTrans(Datum7Paras datum7Paras)TreeParamTrans(Datum3Paras datum3Paras)函數(shù)。

////// 利用7參數(shù)進(jìn)行坐標(biāo)系之間轉(zhuǎn)換
//////7參數(shù)實(shí)例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;
}

////// 利用3參數(shù)進(jìn)行坐標(biāo)系之間轉(zhuǎn)換
//////3參數(shù)實(shí)例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;
}

Datum3ParasDatum7Paras是獨(dú)立于MyPoint類,用于設(shè)定坐標(biāo)轉(zhuǎn)換參數(shù)。

////// 7參數(shù)
    ///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(zhuǎn)換5的實(shí)現(xiàn)(四參數(shù)+高程擬合)

上述MyPoint類中增加Transform4Para(Trans4Paras transPara)函數(shù)。此處,高程擬合僅實(shí)現(xiàn)了已知一個(gè)測點(diǎn)的固定改正差。

////// 投影坐標(biāo)獲取后,進(jìn)一步利用4參數(shù)轉(zhuǎn)換坐標(biāo)
//////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(dú)立于MyPoint類,用于設(shè)定坐標(biāo)轉(zhuǎn)換參數(shù)。

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 調(diào)用過程

里面的參數(shù),因?yàn)楸C茉?,做出了隨機(jī)更改,實(shí)際使用時(shí)可根據(jù)自己情況賦值。

3.7.1 一步法
// 實(shí)例化計(jì)算參數(shù)
MyPoint p = new MyPoint();.

p.L=113.256;
p.B=31.565;
p.H=5.216;
 
// 經(jīng)緯度轉(zhuǎn)空間坐標(biāo)
p.BLH2XYZ();

// 實(shí)例化七參數(shù)
Datum7Paras datum7Paras = new Datum7Paras(
    489.2994563566, 141.1525159753, 15.74421120568,
    -0.164423, 4.141573, -4.808299,
    -6.56482989958);

p.SevenParamTrans(datum7Paras);

// 空間坐標(biāo)轉(zhuǎn)回經(jīng)緯度
p.XYZ2BLH(EllipsoidType.WGS84);

// 高斯投影 經(jīng)緯度轉(zhuǎn)平面坐標(biāo)
// 實(shí)例化投影參數(shù)類
ProjectionSetting projectionSetting = new ProjectionSetting(120,500000);
p.GaussProjection(EllipsoidType.WGS84, projectionSetting);
3.7.2 兩步法
// 實(shí)例化計(jì)算參數(shù)
MyPoint p = new MyPoint();.

p.SetLBH(113.256,31.565,5.216);
 
// 經(jīng)緯度轉(zhuǎn)空間坐標(biāo)
p.BLH2XYZ();

// 實(shí)例化七參數(shù)
Datum7Paras datum7Paras = new Datum7Paras(
    489.2994563566, 141.1525159753, 15.74421120568,
    -0.164423, 4.141573, -4.808299,
    -6.56482989958);

p.SevenParamTrans(datum7Paras);

// 空間坐標(biāo)轉(zhuǎn)回經(jīng)緯度
p.XYZ2BLH(EllipsoidType.WGS84);

// 高斯投影 經(jīng)緯度轉(zhuǎn)平面坐標(biāo)
// 實(shí)例化投影參數(shù)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(jié)

至此,關(guān)于工程坐標(biāo)系轉(zhuǎn)化,即GPS接收的WGS84橢球的經(jīng)緯度轉(zhuǎn)換為地方坐標(biāo)系的問題,基本全部實(shí)現(xiàn)。代碼正確性和準(zhǔn)確性的驗(yàn)證是與 南方GPS工具箱做對比。例如,采用上述的一步法,在設(shè)定好坐標(biāo)、7參數(shù)、投影參數(shù)后,計(jì)算發(fā)現(xiàn),與南方GPS工具箱在y方向偏差1mm。結(jié)果如下圖:
在這里插入圖片描述

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