工程坐标转换方法C#代码实现
<p></p><div class="toc"><div class="toc-container-header">目录</div><ul><li>1. 前言</li><li>2. 计算总体框架</li><li>3. C#代码实现<ul><li>3.1 整体类的构建</li><li>3.2 椭球参数赋值</li><li>3.3 转换1、3（大地经纬度坐标与地心地固坐标的转换）</li><li>3.4 投影转换</li><li>3.5 转换2的实现（三参数、七参数）</li><li>3.6 转换5的实现（四参数+高程拟合）</li><li>3.7 调用过程<ul><li>3.7.1 一步法</li><li>3.7.2 两步法</li></ul></li></ul></li><li>4. 总结</li></ul></div><p></p><h1 id="1-前言">1. 前言</h1>
<p>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：</p>
<ul>
<li>GDAL</li>
<li>SharpProj - Providing OSGEO PROJ for .Net (Core)</li>
<li>ProjNet (for GeoAPI)</li>
</ul>
<p>这里<strong>针对GPS接收的WGS84椭球的经纬度转换为地方坐标系的问题</strong>，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。</p>
<hr>
<h1 id="2-计算总体框架">2. 计算总体框架</h1>
<p>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。<br>
<img src="https://img2023.cnblogs.com/blog/2605793/202212/2605793-20221204204521129-1041359551.png" alt="image" loading="lazy"></p>
<p>根据上图可知，预将WGS84椭球的GPS坐标需要经过<strong>5次转换</strong>。其中，</p>
<ol>
<li>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。</li>
<li>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。</li>
</ol>
<p>因此，根据计算原理，直接可以利用C#代码实现。</p>
<hr>
<h1 id="3-c代码实现">3. C#代码实现</h1>
<h2 id="31-整体类的构建">3.1 整体类的构建</h2>
<p>5个转换是对点的操作，不妨构建自定义点类<code>MyPoint</code>，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：</p>
<pre><code class="language-csharp">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;
}
</code></pre>
<h2 id="32-椭球参数赋值">3.2 椭球参数赋值</h2>
<p>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<strong>在上述<code>MyPoint</code>类中增加函数<code>EllipsoidParam(EllipsoidType type)</code></strong>。</p>
<pre><code class="language-csharp">/// <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
}
</code></pre>
<h2 id="33-转换13大地经纬度坐标与地心地固坐标的转换">3.3 转换1、3（大地经纬度坐标与地心地固坐标的转换）</h2>
<p>charlee44的博客有C++代码的实现，现在利用C#重构即可。<strong>上述<code>MyPoint</code>类中增加<code>BLH2XYZ(EllipsoidType type)</code>和<code>XYZ2BLH(EllipsoidType type)</code>两个函数</strong>。</p>
<pre><code class="language-csharp">/// <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);
}
</code></pre>
<h2 id="34-投影转换">3.4 投影转换</h2>
<p>此处仅实现了常见的<strong>高斯-克里格</strong>投影。<strong>上述<code>MyPoint</code>类中增加<code>GaussProjection(EllipsoidType type, ProjectionSetting prjSetting)</code>函数</strong>。</p>
<pre><code class="language-csharp">/// <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;
}
</code></pre>
<p>其中，<code>ProjectionSetting</code>是一个投影参数设置类，<strong>独立于<code>MyPoint</code>类</strong>，用于设定<strong>中央经线、东偏等投影参数</strong>。</p>
<pre><code class="language-csharp">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;
}
}
</code></pre>
<h2 id="35-转换2的实现三参数七参数">3.5 转换2的实现（三参数、七参数）</h2>
<p><strong>上述<code>MyPoint</code>类中增加<code>SevenParamTrans(Datum7Paras datum7Paras)</code>和<code>TreeParamTrans(Datum3Paras datum3Paras)</code>函数</strong>。</p>
<pre><code class="language-csharp">/// <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;
}
</code></pre>
<p><code>Datum3Paras</code>和<code>Datum7Paras</code>是<strong>独立于<code>MyPoint</code>类</strong>，用于设定<strong>坐标转换参数</strong>。</p>
<pre><code class="language-csharp"> /// <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;
}
}
</code></pre>
<pre><code class="language-csharp"> 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;
}
}
</code></pre>
<h2 id="36-转换5的实现四参数高程拟合">3.6 转换5的实现（四参数+高程拟合）</h2>
<p><strong>上述<code>MyPoint</code>类中增加<code>Transform4Para(Trans4Paras transPara)</code>函数</strong>。此处，高程拟合仅实现了已知一个测点的<strong>固定改正差</strong>。</p>
<pre><code class="language-csharp">/// <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;
}
</code></pre>
<p><code>Trans4Paras</code>是<strong>独立于<code>MyPoint</code>类</strong>，用于设定<strong>坐标转换参数</strong>。</p>
<pre><code class="language-csharp"> 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()
{
}
}
</code></pre>
<h2 id="37-调用过程">3.7 调用过程</h2>
<p><strong>里面的参数，因为保密原因，做出了随机更改</strong>，实际使用时可根据自己情况赋值。</p>
<h3 id="371-一步法">3.7.1 一步法</h3>
<pre><code class="language-csharp">// 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);
</code></pre>
<h3 id="372-两步法">3.7.2 两步法</h3>
<pre><code class="language-csharp">// 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);
</code></pre>
<hr>
<h1 id="4-总结">4. 总结</h1>
<p>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 <strong>南方GPS工具箱</strong>做对比。例如，采用上述的<strong>一步法</strong>，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：<br>
<img src="https://img2023.cnblogs.com/blog/2605793/202212/2605793-20221204204605291-625669898.png" alt="image" loading="lazy"></p>
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<div>作者：Aidan</div>
<div>出处：http://www.cnblogs.com/AidanLee/
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<p>个性签名：独学而无友，则孤陋而寡闻。做一个灵魂有趣的人！</p>
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来源：https://www.cnblogs.com/AidanLee/p/16950730.html
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