(完整word版)高斯投影正反算 代码
高斯投影正反算c代码
高斯投影正反算程序设计一．程序设计流程本程序(de)设计思路如下：（1）,程序采用VS08版本作为开发平台,并采用C语言作为开发语言,设计为WindowsForm窗体程序形式.（2）,程序主要(de)算法来自于教材.但是本程序为了更加实用,添加了更多(de)解算基准,包括：WGS-84,国际椭球1975,克氏椭球,和2000国家大地坐标系.（3）,程序为了更方便(de)读取数据和输出数据,故需要自己定义了固定(de)数据输入格式和数据输出格式或形式,请老师注意查看.二．代码using System;using Systusing SystemponentModel;using System.Data;using System.Drawing;using System.Text;namespace Gauss{public partial class Form1 : Form{//大地坐标//Geodetic Coordinatepublic struct CRDGEODETIC{public double dLongitude;public double dLatitude;public double dHeight;}//笛卡尔坐标//Cartesian Coordinatepublic struct CRDCARTESIAN{public double x;public double y;public double z;}public Form1(){InitializeComponent();}private void button1_Click(object sender, EventArgs e) {double ee = 0;double a = 0;string tt;try{}catch{MessageBox.Show("Gauss Inverse: Choose datum error");return;}if (ttpareTo("克氏椭球")==0){a = 6378245.00;}if (ttpareTo("WGS-84") == 0){a = 6378.00;}if (ttpareTo("1975国际椭球") == 0){a = 6378140.00;ee =}if (ttpareTo("2000国家大地坐标系") == 0){a = 6378.0;}const double pai = 3.1415926;double b = Math.Sqrt(a a (1 - ee ee));double c = a a / b;double epp = Math.Sqrt((a a - b b) / b / b);CRDGEODETIC pcrdGeo;CRDCARTESIAN pcrdCar;double midlong;//求纬度string[] temp;double[] tempradius = new double[3];for (int i = 0; i < 3; i++){tempradius[i] = Convert.ToDouble(temp[i]);}pcrdGeo.dLatitude = tempradius[0] / 180.0 pai + tempradius[1] / 180.0 / 60.0 pai + tempradius[2] / 180 / 60.0 / 60 pai;//求经度for (int i = 0; i < 3; i++){tempradius[i] = Convert.ToDouble(temp[i]);}pcrdGeo.dLongitude = tempradius[0] / 180.0 pai + tempradius[1] / 180.0 / 60.0 pai + tempradius[2] / 180 / 60.0 / 60 pai;int deglon = Convert.ToInt32(pcrdGeo.dLongitude180 / pai);//求中央经度int num; //带号midlong = 0; //默认值,需要制定分带try{}catch{MessageBox.Show("Choose 3/6 error");return;}if (ttpareTo("3度带") == 0){num = Convert.ToInt32(deglon / 6 + 1);midlong = (6 num - 3) / 180.0 pai;}if (ttpareTo("6度带") == 0){num = Convert.ToInt32((deglon + 1.5) / 3);midlong = num 3 pai / 180;}double lp=pcrdGeo.dLongitude - midlong;double N = c / Math.Sqrt(1 + epp eppMath.Cos(pcrdGeo.dLatitude) Math.Cos(pcrdGeo.dLatitude));double M = c / Math.Pow(1 + epp eppMath.Cos(pcrdGeo.dLatitude) Math.Cos(pcrdGeo.dLatitude), 1.5);double ita = epp Math.Cos(pcrdGeo.dLatitude);double t = Math.Tan(pcrdGeo.dLatitude);double Nscnb = N Math.Sin(pcrdGeo.dLatitude) Math.Cos(pcrdGeo.dLatitude);double Ncosb = N Math.Cos(pcrdGeo.dLatitude);double cosb = Math.Cos(pcrdGeo.dLatitude);double X;double m0, m2, m4, m6, m8;double a0, a2, a4, a6, a8;m0 = a (1 - ee ee);m2 = 3.0 / 2.0 m0 ee ee;m4 = 5.0 / 4.0 ee ee m2;m6 = 7.0 / 6.0 ee ee m4;m8 = 9.0 / 8.0 ee ee m6;a0 = m0 + m2 / 2.0 + 3.0 / 8.0 m4 + 5.0 / 16.0 m6 + 35.0 / 128.0 m8;a2 = m2 / 2 + m4 / 2 + 15.0 / 32.0 m6 + 7.0 / 16.0 m8;a4 = m4 / 8.0 + 3.0 / 16.0 m6 + 7.0 / 32.0 m8;a6 = m6 / 32.0 + m8 / 16.0;a8 = m8 / 128.0;double B = pcrdGeo.dLatitude;double sb = Math.Sin(B);double cb = Math.Cos(B);double s2b = sb cb 2;double s4b = s2b (1 - 2 sb sb) 2;double s6b = s2b Math.Sqrt(1 - s4b s4b) + s4b Math.Sqrt(1 - s2b s2b);X = a0 B - a2 / 2.0 s2b + a4 s4b / 4.0 - a6 / 6.0 s6b;pcrdCar.x = Nscnb lp lp / 2.0 + Nscnb cosb cosb Math.Pow(lp, 4) (5 - t t + 9 ita ita + 4 Math.Pow(ita, 4)) / 24.0 + Nscnb Math.Pow(cosb, 4) Math.Pow(lp, 6) (61 - 58 t t + Math.Pow(t, 4)) / 720.0 + X;pcrdCar.y = Ncosb Math.Pow(lp, 1) + Ncosb cosb cosb (1 - t t + ita ita) / 6.0 Math.Pow(lp, 3) + NcosbMath.Pow(lp, 5) Math.Pow(cosb, 4) (5 - 18 t t+ Math.Pow(t, 4) + 14 ita ita - 58 ita ita t t) / 120.0 ;if (pcrdCar.y < 0)pcrdCar.y += 500000;richTextBox1.Text = "Results:\nX:\t" +Convert.ToString(pcrdCar.x) +"\nY:\t"+ Convert.ToString(pcrdCar.y);}private void button2_Click(object sender, EventArgs e) {double ee = 0;double a = 0;string tt;int num; //带号string ytext; //利用y值求带号和中央经线try{}catch{MessageBox.Show("Gauss Inverse: Choose datumerror");return;}if (ttpareTo("克氏椭球") == 0){a = 6378245.00;}if (ttpareTo("WGS-84") == 0){a = 6378.00;}if (ttpareTo("1975国际椭球") == 0){a = 6378140.00;}if (ttpareTo("2000国家大地坐标系") == 0){a = 6378.0;}double b = Math.Sqrt(a a (1 - ee ee));double c = a a / b;double epp = Math.Sqrt((a a - b b) / b / b); CRDGEODETIC pcrdGeo;CRDCARTESIAN pcrdCar;double midlong = 0;//求X,Y和带号pcrdCar.x = Convert.ToDouble(textBox4.Text); ytext = textBox5.Text;string temp = ytext.Substring(0, 2);num = Convert.ToInt32(temp);ytext = ytext.Remove(0, 2);pcrdCar.y = Convert.ToDouble(ytext) - 500000; try{}catch{MessageBox.Show("Choose 3/6 error");return;}if (ttpareTo("3度带") == 0){midlong = num 3 pai / 180;}if (ttpareTo("6度带") == 0){midlong = (6 num - 3) pai / 180;}b = Math.Sqrt(a a (1 - ee ee));c = a a / b;epp = Math.Sqrt(a a - b b) / b;double m0, m2, m4, m6, m8;double a0, a2, a4, a6, a8;m0 = a (1 - ee ee);m2 = 3.0 / 2.0 m0 ee ee;m4 = 5.0 / 4.0 ee ee m2;m6 = 7.0 / 6.0 ee ee m4;m8 = 9.0 / 8.0 ee ee m6;a0 = m0 + m2 / 2.0 + 3.0 / 8.0 m4 + 5.0 / 16.0 m6 + 35.0 / 128.0 m8;a2 = m2 / 2 + m4 / 2 + 15.0 / 32.0 m6 + 7.0 / 16.0 m8;a4 = m4 / 8.0 + 3.0 / 16.0 m6 + 7.0 / 32.0 m8;a6 = m6 / 32.0 + m8 / 16.0;a8 = m8 / 128.0;double Bf, B;Bf = pcrdCar.x / a0;B = 0.0;while (Math.Abs(Bf - B) > 1E-10){B = Bf;double sb = Math.Sin(B);double cb = Math.Cos(B);double s2b = sb cb 2;double s4b = s2b (1 - 2 sb sb) 2;double s6b = s2b Math.Sqrt(1 - s4b s4b) + s4b Math.Sqrt(1 - s2b s2b);Bf = (pcrdCar.x - (-a2 / 2.0 s2b + a4 / 4.0 s4b - a6 / 6.0 s6b)) / a0;}double itaf, tf, Vf, Nf;itaf = epp Math.Cos(Bf);tf = Math.Tan(Bf);Vf = Math.Sqrt(1 + epp epp Math.Cos(Bf)Math.Cos(Bf));Nf = c / Vf;double ynf = pcrdCar.y / Nf;pcrdGeo.dLatitude = Bf - 1.0 / 2.0 Vf Vf tf (ynf ynf - 1.0 / 12.0 Math.Pow(ynf, 4) (5 + 3 tf tf + itaf itaf - 9 Math.Pow(itaf tf, 2)) +1.0 / 360.0 (61 + 90 tf tf + 45 Math.Pow(tf, 4)) Math.Pow(ynf, 6));pcrdGeo.dLongitude = (ynf / Math.Cos(Bf) - (1 + 2 tf tf + itaf itaf) Math.Pow(ynf, 3) / 6.0 / Math.Cos(Bf) +(5 + 28 tf tf + 24 Math.Pow(tf, 4) + 6 itaf itaf + 8 Math.Pow(itaf tf, 2)) Math.Pow(ynf, 5) / 120.0 /Math.Cos(Bf));pcrdGeo.dLongitude = pcrdGeo.dLongitude + midlong;//pcrdGeo.dLatitude = pcrdGeo.dLatitude;richTextBox2.Text = "Results:\nLatitude: " + Convert.ToString(pcrdGeo.dLatitude) + "\nLongtitude: " +Convert.ToString(pcrdGeo.dLongitude);}private void label13_Click(object sender, EventArgs e) {}}}三．程序运行结果分析通过选取书上(de)具体实例进行测试,本程序(de)精度大体满足要求,一般正算(de)精度在0.01米和0.001米之间,反算(de)精度在0.0001秒左右.以下是程序运行(de)截图.。
高斯投影正反算python代码
高斯投影正反算1. 什么是高斯投影高斯投影是一种常用的地图投影方法，它将地球表面的经纬度坐标转换为平面坐标，常用于地理信息系统（GIS）和测绘工程中。
高斯投影分为正算和反算两个过程。
•正算：将经纬度坐标转换为平面坐标。
•反算：将平面坐标转换为经纬度坐标。
2. 高斯投影正算2.1 原理高斯投影正算的原理是根据椭球体上某一点处的曲率半径、子午线弧长和东西方向上的距离，计算该点在平面上的x、y坐标。
2.2 具体步骤高斯投影正算的具体步骤如下：1.根据给定的椭球体参数（长半轴a、短半轴b），计算椭球体第一偏心率e。
2.根据给定的中央子午线经度λ0，计算λ - λ0 的差值Δλ。
3.计算曲率半径N和子午线弧长A0。
4.根据给定的纬度φ和经度λ，计算Δφ和Δλ。
5.计算子午线弧长A1、A2、A3和A4。
6.计算平面坐标x和y。
2.3 Python代码实现下面是使用Python实现高斯投影正算的示例代码：import math# 输入参数a = 6378137.0 # 长半轴b = 6356752.314245 # 短半轴e = math.sqrt(1 - (b/a)**2) # 第一偏心率λ0 = math.radians(120) # 中央子午线经度，单位为弧度# 输入经纬度坐标φ = math.radians(30) # 纬度，单位为弧度λ = math.radians(121) # 经度，单位为弧度# 计算ΔλΔλ = λ - λ0# 计算曲率半径N和子午线弧长A0N = a / math.sqrt(1 - e**2 * math.sin(φ)**2)A0 = a * (1 - e**2) / (1 - e**2 * math.sin(φ)**2)**1.5# 计算Δφ和ΔλΔφ = φ - φ0# 计算子午线弧长A1、A2、A3和A4A1 = A0 + N * math.tan(φ) / 2 * Δλ**2 * math.cos(φ)A2 = A0 + N * math.tan(φ) / 24 * (5 - math.tan(φ)**2 + 9 * e2 * math.cos(φ)**2 + 4 * e2**2 * math.cos(φ)**4) * Δλ**4 * math.cos(φ)A3 = A0 + N * math.tan(φ) / 720 * (61 - 58 * math.tan(φ)**2 + math.tan(φ)** 4) * Δλ**6 * math.cos(φ)A4 = A0 + N * math.tan(φ) / 40320 * (1385 - 3111*math.tan(φ)**2 + 543*math.tan(φ)**4 - math.tan(φ)**6) \* Δλ**8 \* math.cos(phi)# 计算平面坐标x和yx = A1 + A2 + A3 + A4y = N / math.cos(phi) \(Δλ - Δλ**3/6*(1+math.tan(phi))**2/N/A0^2 \+ Δλ^5/120*(5+28*math.tan(phi)^2+24*math.tan(phi)^4)*N/A0^4/N/A0^3)# 输出结果print("平面坐标(x, y):", x, y)3. 高斯投影反算3.1 原理高斯投影反算的原理是根据平面坐标和中央子午线经度，计算对应的经纬度坐标。
大地测量高斯投影正反算[解说]
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大地测量高斯投影正反算程序代码课程：大地测量学基础姓名：林江伟学号：2008301610045班级： 0804 界面如下：输入数据计算：using System;using System.Collections.Generic; using ponentModel;using System.Data;using System.Drawing;using System.Text;using System.Windows.Forms;namespace大地{public partial class Form1 : Form {double B, L;double x, y;double X, Y;int N;double L0, l1;double p=206264.80625;public Form1(){InitializeComponent();}private void Form1_Load(object sender, EventArgs e){//自动化控件显示初始值radioButton2.Checked=true;radioButton3.Checked = true;textBox1.Focus();textBox1.Text = textBox2.Text = textBox3.Text = textBox4.Text = textBox5.Text = textBox6.Text = "0";this.richTextBox2.Text = "说明：输入的坐标需为按6°带投影且采用克氏椭球参数所得的国家统一坐标";}private void button1_Click(object sender, EventArgs e){//获取输入数据double bb1=Convert.ToDouble(this.textBox1.Text);double bb2=Convert.ToDouble(this.textBox2.Text);double bb3=Convert.ToDouble(this.textBox3.Text);double ll1=Convert.ToDouble(this.textBox4.Text);double ll2=Convert.ToDouble(this.textBox5.Text);double ll3=Convert.ToDouble(this.textBox6.Text);//检查输入格式的正确性if (bb1 >= 0 && bb1 <90 && bb2 >= 0 && bb2 < 60 && bb3 >= 0 && bb3 < 60){B = bb1 * 3600 + bb2 * 60 + bb3;}else{MessageBox.Show("纬度输入格式不正确！", "警告");return;}if (ll1 >= 0 && ll1<360 && ll2 >= 0 && ll2 < 60 && ll3 >= 0 && ll3 < 60){L = ll1 * 3600 + ll2 * 60 + ll3;}else{MessageBox.Show("经度输入格式不正确！", "警告");return;}double b = B/p;//获取用户选项值int tyd=radioButton1.Checked?3:6;int tq=radioButton3.Checked?1:2;//按带求带号以及中央子午线经度if (tyd == 6){N =(int)( L / (6*3600.0)) + 1;L0 = (6 * N - 3)*3600.0;l1 = (L-L0)/p;}if(tyd==3){N =(int)(L / (3*3600.0)+0.5);L0 = 3 * N * 3600.0;l1 =( L-L0)/p;}//采用克氏椭球参数的计算公式if (tq == 1){double c = Math.Pow( Math.Cos(b),2);double c1= Math.Sin(b) * Math.Cos(b);double c2=Math.Cos(b);double l2 = Math.Pow(l1,2);double n = 6399698.902 - (21562.267 - (108.973 - 0.612 * c) * c) * c;double a0 = 32140.404 - (135.3302 - (0.7092 - 0.0040 * c) * c) * c;double a4 = (0.25 + 0.00252 * c) * c - 0.04166;double a6 = (0.166 * c - 0.084) * c;double a3 = (0.3333333 + 0.001123 * c) * c - 0.1666667;double a5 = 0.0083 - (0.1667 - (0.1968 + 0.0040 * c) * c) * c;x = 6367558.4969 * b - (a0 - (0.5 + (a4 + a6 * l2) * l2) * l2 * n) *c1; y = (1 + (a3 + a5 * l2) * l2) * l1 * n * c2;X = x;double y1 = y + 500000.0;for (int i = 1; y1 / i > 1; i = i * 10){Y = N * i*10 + y1;}string tuoqiu = "采用克氏椭球参数,";this.richTextBox1.Text = "按经差" + tyd + "°进行投影分带，" + tuoqiu + "其计算结果为：" + "\r\n" + "x=" + x + "\r\n" + "y=" + y + "\r\n" +"国家统一坐标为：" + "\r\n" + "X=" + X + "\r\n" + "Y=" + Y;}//采用1975国际椭球参数的计算公式if (tq == 2){double c = Math.Cos(b) * Math.Cos(b);double c1 = Math.Sin(b) * Math.Cos(b);double c2 = Math.Cos(b);double l2 = Math.Pow(l1, 2);double n = 6399596.652 - (21565.045 - (108.996 - 0.603 * c) * c) * c;double a0 = 32144.5189 - (135.3646 - (0.7034 - 0.0041 * c) * c) * c;double a4 = (0.25 + 0.00253 * c) * c - 0.04167;double a6 = (0.167 * c - 0.083) * c;double a3 = (0.3333333 + 0.001123 * c) * c - 0.1666667;double a5 = 0.00878 - (0.1702 - 0.20382 * c) * c;x = 6367452.1328 * b-(a0 - (0.5 + (a4 + a6 * l2) * l2) * l2 * n) * c1;y = (1 + (a3 + a5 * l2) * l2) * l1 * n * c2;X = x;double y1 = y + 500000.0;for (int i = 1; y1 / i > 1; i = i * 10)//Y坐标加代号{Y = N * i * 10 + y1;}string tuoqiu = "采用1975国际椭球参数,";this.richTextBox1.Text = "按经差" + tyd + "°进行投影分带，" + tuoqiu + "其计算结果为：" + "\r\n" + "x=" + x + "\r\n" + "y=" + y+"\r\n"+"国家统一坐标为：" + "\r\n" + "X=" + X + "\r\n"+"Y="+Y;}}private void button2_Click(object sender, EventArgs e){X = Convert.ToDouble(this.textBox7.Text);//获取输入数据Y = Convert.ToDouble(this.textBox8.Text);for (int i = 1; Y/i >=10; i = i * 10)//对Y坐标处理并求出中央子午线经度{y = Y - (int)(Y / i) * i-500000;L0 = 6 * (int)(Y / i) - 3;}//按6°带克氏椭球反算double bt = x / 6367558.4969*p;double BT = x / 6367558.4969;double c3=Math.Cos(BT)*Math.Cos(BT);double c4=Math.Sin(BT)*Math.Cos(BT);double Bf=(bt+(50221746+(293622+(2350+22*c3)*c3)*c3)*c4*Math.Pow(10,-10)*p)/p;double c5=Math.Pow(Math.Cos(Bf),2);double c6=Math.Sin(Bf)*Math.Cos(Bf);double Nf=6399698.902-(21562.267-(108.973-0.612*c5)*c5)*c5;double Z=y/(Nf*Math.Cos(Bf));double b2 = (0.5 + 0.003369 * c5) * c6;double b3 = 0.333333 - (0.166667 - 0.001123 * c5) * c5;double b4 = 0.25 + (0.16161 + 0.00562 * c5) * c5;double b5=0.2-(0.1667-0.0088*c5)*c5;double z2=Math.Pow(Z,2);B = (Bf*p - (1 - (b4 - 0.12 *z2) * z2) * z2 * b2 * p)/3600.0;L = L0+((1 - (b3 - b5 * z2) * z2) * Z * p)/3600.0;this.richTextBox2.Text = "按6°带克氏椭球反算后，结果为："+ "\r\n"+"B="+ B + "\r\n" + "L=" + L;}}。
高斯投影正算
高斯投影正、反算代码//高斯投影正、反算//////6度带宽 54年北京坐标系//高斯投影由经纬度(Unit:DD)反算大地坐标(含带号，Unit:Metres)void GaussProjCal(double longitude, double latitude, double *X, double *Y){int ProjNo=0; int ZoneWide; ////带宽double longitude1,latitude1, longitude0,latitude0, X0,Y0, xval,yval;double a,f, e2,ee, NN, T,C,A, M, iPI;iPI = 0.0174532925199433; ////3.1415926535898/180.0;ZoneWide = 6; ////6度带宽a=6378245.0; f=1.0/298.3; //54年北京坐标系参数////a=6378140.0; f=1/298.257; //80年西安坐标系参数ProjNo = (int)(longitude / ZoneWide) ;longitude0 = ProjNo * ZoneWide + ZoneWide / 2;longitude0 = longitude0 * iPI ;latitude0=0;longitude1 = longitude * iPI ; //经度转换为弧度latitude1 = latitude * iPI ; //纬度转换为弧度e2=2*f-f*f;ee=e2*(1.0-e2);NN=a/sqrt(1.0-e2*sin(latitude1)*sin(latitude1));T=tan(latitude1)*tan(latitude1);C=ee*cos(latitude1)*cos(latitude1);A=(longitude1-longitude0)*cos(latitude1);M=a*((1-e2/4-3*e2*e2/64-5*e2*e2*e2/256)*latitude1-(3*e2/8+3*e2*e2 /32+45*e2*e2*e2/1024)*sin(2*latitude1)+(15*e2*e2/256+45*e2*e2*e2/1024)*sin(4*latitude1)-(35*e2*e2*e2/30 72)*sin(6*latitude1));xval = NN*(A+(1-T+C)*A*A*A/6+(5-18*T+T*T+72*C-58*ee)*A*A*A*A*A/120);yval = M+NN*tan(latitude1)*(A*A/2+(5-T+9*C+4*C*C)*A*A*A*A/24+(61-58*T+T*T+600*C-330*ee)*A*A*A*A*A*A/720);X0 = 1000000L*(ProjNo+1)+500000L;Y0 = 0;xval = xval+X0; yval = yval+Y0;*X = xval;*Y = yval;}//高斯投影由大地坐标(Unit:Metres)反算经纬度(Unit:DD)void GaussProjInvCal(double X, double Y, double *longitude, double *latitude){int ProjNo; int ZoneWide; ////带宽double longitude1,latitude1, longitude0,latitude0, X0,Y0, xval,yval;double e1,e2,f,a, ee, NN, T,C, M, D,R,u,fai, iPI;iPI = 0.0174532925199433; ////3.1415926535898/180.0;a = 6378245.0; f = 1.0/298.3; //54年北京坐标系参数////a=6378140.0; f=1/298.257; //80年西安坐标系参数ZoneWide = 6; ////6度带宽ProjNo = (int)(X/1000000L) ; //查找带号longitude0 = (ProjNo-1) * ZoneWide + ZoneWide / 2;longitude0 = longitude0 * iPI ; //中央经线X0 = ProjNo*1000000L+500000L;Y0 = 0;xval = X-X0; yval = Y-Y0; //带内大地坐标e2 = 2*f-f*f;e1 = (1.0-sqrt(1-e2))/(1.0+sqrt(1-e2));ee = e2/(1-e2);M = yval;u = M/(a*(1-e2/4-3*e2*e2/64-5*e2*e2*e2/256));fai = u+(3*e1/2-27*e1*e1*e1/32)*sin(2*u)+(21*e1*e1/16-55*e1*e1*e1*e1/32)*si n(4*u)+(151*e1*e1*e1/96)*sin(6*u)+(1097*e1*e1*e1*e1/512)*sin(8*u);C = ee*cos(fai)*cos(fai);T = tan(fai)*tan(fai);NN = a/sqrt(1.0-e2*sin(fai)*sin(fai));R = a*(1-e2)/sqrt((1-e2*sin(fai)*sin(fai))*(1-e2*sin(fai)*sin(fai))*(1-e2 *sin(fai)*sin(fai)));D = xval/NN;//计算经度(Longitude) 纬度(Latitude)longitude1 = longitude0+(D-(1+2*T+C)*D*D*D/6+(5-2*C+28*T-3*C*C+8*ee+24*T*T)*D*D*D*D*D/120)/cos(fai);latitude1 = fai -(NN*tan(fai)/R)*(D*D/2-(5+3*T+10*C-4*C*C-9*ee)*D*D*D*D/24+(61+90*T+298*C+45*T*T-256*ee-3*C*C)*D*D*D*D*D*D/720);//转换为度 DD*longitude = longitude1 / iPI;*latitude = latitude1 / iPI;}。
高斯投影正反算
高斯投影正、反算及换带程序执行条件※数组投影选择T、换算点个数“Z=0 F≠0”、=0正算0、≠0反算※坐标系选择“54 ≠54”、=54换算为1954年北京坐标系输入54、≠54换算为1988年西安坐标系M、中央子午线经度（°′″）输入※大地坐标I、序列号B、L：大地纬度和经度（地理坐标）（°′″）※高斯平面坐标轴子午线I、序列号X、Y：高斯平面坐标（m） Z、轴子午线（°）输出※大地坐标子午收敛角N、序列号B、L：大地纬度和经度（地理坐标）（°′″） R、子午收敛角（°′″）※高斯平面坐标子午收敛角N、序列号X、Y：高斯平面坐标（m） R、子午收敛角（°′″）注：1、程序执行前必须进行数组定位。
如：Defm 10 T×2=5×2=102、Y坐标值要去掉带号及避免出现负值的500公里；4、本程序运算时，各已知数据、观测变量不会随之变化，可非常方便地进行各数据的核对;5、本程序在进行换带计算时采用的是间接换带计算法。
Prog GSXYDefm 10:TA“Z=0 F≠0”G“54 ≠54”Z:Fixm:I=0:「b」0:I=I+1◢J=2I-1:M=Z[J:L=Z[J+1:A=0=>Prog“3”:B=M:M=L+Z:Prog“3”:L=M:{BL}:M=B:Prog“2”: B=M:M=L:Prog“2”:L=M-Z:≠>X=M:Y=L:{XY}:B=X:L=Y⊿Z[J]=B:Z[J+1]=L:I<T=>Goto 0⊿G=54=>C=6399698.90178271:E=.006738525414684:≠>C=6399596.65198801:E=.006 739501819473⊿I=0:「b」0:I“N”=I+1◢J=2I-1:B=Z[J:L=Z[J+1:A≠0=>X=B:Y=L:Goto 2⊿S=sin B:G=54=>F=111134.8611B-(32 005.7799S+133.9238S∧3+.6973S∧5+.0039S∧7)cos B:≠>F=111133.0047B-(32009.857 S+133.9602S∧3+.6976S∧5+.0039S∧7)cos B⊿U=√Ecos B:V=√(1+U2:N=C÷V:W=tan B: M=cos B(Lπ÷180:X=F+NW(.5M2+1┛24(5-W2+9U2+4U∧4)M∧4+1┛720(61-58W2+W∧4)M∧6◢Y=N(M+1┛6(1-W 2+U 2)M ∧3+1┛120(5-18W 2+W ∧4+14U 2-58U 2W 2)M ∧5◢M=W ┛π(180M+60(1+3U 2+2U ∧4)M ∧3+12(2-W 2)M ∧5:Goto 3:「b 」2:W=E ﹣6X-3:G=54=>F=27.11115372595+9.024********W-.00579740442W 2-4.3532572E ﹣4W ∧3+4.857285E ﹣5W ∧4+2.15727E ﹣6W ∧5-1.9399E ﹣7W ∧6:≠>F=27.11162289465+9.024********W-.00579850656W2-4.3540029E ﹣4W ∧3+4.858357E ﹣5W ∧4+2.15769E ﹣6W ∧5-1.9404E ﹣7W ∧6⊿U=√Ecos F:V=√(1+U 2:Q=YV ÷C:W=tan F:M=F-(1+U 2)W ┛π(90Q 2-7.5(5+3W 2+U 2-9U 2W 2)Q ∧4+.25(61+90W 2+45W ∧4)Q ∧6:Prog “3”:B=M ◢M=Z+1┛(πcos F)(180Q-30(1+2W 2+U 2)Q ∧3+1.5(5+28W 2+24W ∧4)Q ∧5:Prog “3”:L=M ◢M=W ┛π(180Q-60(1+W 2-U 2)Q ∧3+12(2+5W 2+3W ∧4)Q ∧5:「b 」3:Prog “3”:R=M ◢ I<T=>Goto 1⊿“END ”概要说明：我国的经度范围西边自73°起，东边至135°，可分成6°带共11带或3°共22带。
高斯投影正反算-c#代码
高斯投影正反算程序设计一．程序设计流程本程序的设计思路如下：（1），程序采用VS08版本作为开发平台，并采用C#语言作为开发语言，设计为WindowsForm 窗体程序形式。
（2），程序主要的算法来自于教材。
但是本程序为了更加实用，添加了更多的解算基准，包括：WGS-84，国际椭球1975，克氏椭球，和2000国家大地坐标系。
（3），程序为了更方便的读取数据和输出数据，故需要自己定义了固定的数据输入格式和数据输出格式或形式，请老师注意查看。
二．代码using System;using System.Collections.Generic;using ponentModel;using System.Data;using System.Drawing;using System.Text;using System.Windows.Forms;namespace Gauss{public partial class Form1 : Form{//大地坐标//Geodetic Coordinatepublic struct CRDGEODETIC{public double dLongitude;public double dLatitude;public double dHeight;}//笛卡尔坐标//Cartesian Coordinatepublic struct CRDCARTESIAN{public double x;public double y;public double z;}public Form1(){InitializeComponent();}private void button1_Click(object sender, EventArgs e){double ee = 0;double a = 0;string tt;try{tt = boBox1.Items[boBox1.SelectedIndex].ToString(); }catch{MessageBox.Show("Gauss Inverse: Choose datum error!");return;}if (pareTo("克氏椭球")==0){a = 6378245.00;ee = Math.Sqrt(0.006693421622);}if (pareTo("WGS-84") == 0){a = 6378137.00;ee = Math.Sqrt(0.00669437999013);}if (pareTo("1975国际椭球") == 0){a = 6378140.00;ee = Math.Sqrt(0.006694384999588);}if (pareTo("2000国家大地坐标系") == 0){a = 6378137.0;ee =Math.Sqrt(0.0066943802290);}const double pai = 3.1415926;double b = Math.Sqrt(a * a * (1 - ee * ee));double c = a * a / b;double epp = Math.Sqrt((a * a - b * b) / b / b);CRDGEODETIC pcrdGeo;CRDCARTESIAN pcrdCar;double midlong;//求纬度string[] temp;temp = textBox1.Text.Split(' ');double[] tempradius = new double[3];for (int i = 0; i < 3; i++){tempradius[i] = Convert.ToDouble(temp[i]);}pcrdGeo.dLatitude = tempradius[0] / 180.0 * pai + tempradius[1] / 180.0 / 60.0 * pai + tempradius[2] / 180 / 60.0 / 60 * pai;//求经度temp = textBox2.Text.Split(' ');for (int i = 0; i < 3; i++){tempradius[i] = Convert.ToDouble(temp[i]);}pcrdGeo.dLongitude = tempradius[0] / 180.0 * pai + tempradius[1] / 180.0 / 60.0 * pai + tempradius[2] / 180 / 60.0 / 60 * pai;int deglon = Convert.ToInt32(pcrdGeo.dLongitude * 180 / pai);//求中央经度int num; //带号 midlong = 0; //默认值，需要制定分带try{tt = boBox3.Items[boBox3.SelectedIndex].ToString();}catch{MessageBox.Show("Choose 3/6 error!");return;}if (pareTo("3度带") == 0){num = Convert.ToInt32(deglon / 6 + 1);midlong = (6 * num - 3) / 180.0 * pai;}if (pareTo("6度带") == 0){num = Convert.ToInt32((deglon + 1.5) / 3);midlong = num * 3 * pai / 180;}double lp=pcrdGeo.dLongitude - midlong;double N = c / Math.Sqrt(1 + epp * epp * Math.Cos(pcrdGeo.dLatitude) * Math.Cos(pcrdGeo.dLatitude));double M = c / Math.Pow(1 + epp * epp * Math.Cos(pcrdGeo.dLatitude) * Math.Cos(pcrdGeo.dLatitude), 1.5);double ita = epp * Math.Cos(pcrdGeo.dLatitude);double t = Math.Tan(pcrdGeo.dLatitude);double Nscnb = N * Math.Sin(pcrdGeo.dLatitude) *Math.Cos(pcrdGeo.dLatitude);double Ncosb = N * Math.Cos(pcrdGeo.dLatitude);double cosb = Math.Cos(pcrdGeo.dLatitude);double X;double m0, m2, m4, m6, m8;double a0, a2, a4, a6, a8;m0 = a * (1 - ee * ee);m2 = 3.0 / 2.0 * m0 * ee * ee;m4 = 5.0 / 4.0 * ee * ee * m2;m6 = 7.0 / 6.0 * ee * ee * m4;m8 = 9.0 / 8.0 * ee * ee * m6;a0 = m0 + m2 / 2.0 + 3.0 / 8.0 * m4 + 5.0 / 16.0 * m6 + 35.0 / 128.0 * m8;a2 = m2 / 2 + m4 / 2 + 15.0 / 32.0 * m6 + 7.0 / 16.0 * m8;a4 = m4 / 8.0 + 3.0 / 16.0 * m6 + 7.0 / 32.0 * m8;a6 = m6 / 32.0 + m8 / 16.0;a8 = m8 / 128.0;double B = pcrdGeo.dLatitude;double sb = Math.Sin(B);double cb = Math.Cos(B);double s2b = sb * cb * 2;double s4b = s2b * (1 - 2 * sb * sb) * 2;double s6b = s2b * Math.Sqrt(1 - s4b * s4b) + s4b * Math.Sqrt(1 - s2b * s2b);X = a0 * B - a2 / 2.0 * s2b + a4 * s4b / 4.0 - a6 / 6.0 * s6b;pcrdCar.x = Nscnb * lp * lp / 2.0 + Nscnb * cosb * cosb * Math.Pow(lp, 4) * (5 - t * t + 9 * ita * ita + 4 * Math.Pow(ita, 4)) / 24.0+ Nscnb * Math.Pow(cosb, 4) * Math.Pow(lp, 6) * (61 - 58 * t * t + Math.Pow(t, 4)) / 720.0 + X;pcrdCar.y = Ncosb * Math.Pow(lp, 1) + Ncosb * cosb * cosb * (1 - t * t + ita * ita) / 6.0 * Math.Pow(lp, 3) + Ncosb * Math.Pow(lp, 5)* Math.Pow(cosb, 4) * (5 - 18 * t * t+ Math.Pow(t, 4) + 14 * ita * ita - 58 * ita * ita * t * t) / 120.0 ;if (pcrdCar.y < 0)pcrdCar.y += 500000;richTextBox1.Text = "Results:\nX:\t" + Convert.ToString(pcrdCar.x) +"\nY:\t"+ Convert.ToString(pcrdCar.y);}private void button2_Click(object sender, EventArgs e){double ee = 0;double a = 0;string tt;int num; //带号string ytext; //利用y值求带号和中央经线try{tt = boBox2.Items[boBox2.SelectedIndex].ToString(); }catch{MessageBox.Show("Gauss Inverse: Choose datum error!");return;}if (pareTo("克氏椭球") == 0){a = 6378245.00;ee = Math.Sqrt(0.006693421622);}if (pareTo("WGS-84") == 0){a = 6378137.00;ee = Math.Sqrt(0.00669437999013);}if (pareTo("1975国际椭球") == 0){a = 6378140.00;ee = Math.Sqrt(0.006694384999588);}if (pareTo("2000国家大地坐标系") == 0){a = 6378137.0;ee =Math.Sqrt(0.0066943802290);}const double pai = 3.1415926535898;double b = Math.Sqrt(a * a * (1 - ee * ee));double c = a * a / b;double epp = Math.Sqrt((a * a - b * b) / b / b);CRDGEODETIC pcrdGeo;CRDCARTESIAN pcrdCar;double midlong = 0;//求X，Y和带号pcrdCar.x = Convert.ToDouble(textBox4.Text);ytext = textBox5.Text;string temp = ytext.Substring(0, 2);num = Convert.ToInt32(temp);ytext = ytext.Remove(0, 2);pcrdCar.y = Convert.ToDouble(ytext) - 500000;try{tt = boBox4.Items[boBox4.SelectedIndex].ToString(); }catch{MessageBox.Show("Choose 3/6 error!");return;}if (pareTo("3度带") == 0){midlong = num * 3 * pai / 180;}if (pareTo("6度带") == 0){midlong = (6 * num - 3) * pai / 180;}b = Math.Sqrt(a * a * (1 - ee * ee));c = a * a / b;epp = Math.Sqrt(a * a - b * b) / b;double m0, m2, m4, m6, m8;double a0, a2, a4, a6, a8;m0 = a * (1 - ee * ee);m2 = 3.0 / 2.0 * m0 * ee * ee;m4 = 5.0 / 4.0 * ee * ee * m2;m6 = 7.0 / 6.0 * ee * ee * m4;m8 = 9.0 / 8.0 * ee * ee * m6;a0 = m0 + m2 / 2.0 + 3.0 / 8.0 * m4 + 5.0 / 16.0 * m6 + 35.0 / 128.0 * m8;a2 = m2 / 2 + m4 / 2 + 15.0 / 32.0 * m6 + 7.0 / 16.0 * m8;a4 = m4 / 8.0 + 3.0 / 16.0 * m6 + 7.0 / 32.0 * m8;a6 = m6 / 32.0 + m8 / 16.0;a8 = m8 / 128.0;double Bf, B;Bf = pcrdCar.x / a0;B = 0.0;while (Math.Abs(Bf - B) > 1E-10){B = Bf;double sb = Math.Sin(B);double cb = Math.Cos(B);double s2b = sb * cb * 2;double s4b = s2b * (1 - 2 * sb * sb) * 2;double s6b = s2b * Math.Sqrt(1 - s4b * s4b) + s4b * Math.Sqrt(1 - s2b * s2b);Bf = (pcrdCar.x - (-a2 / 2.0 * s2b + a4 / 4.0 * s4b - a6 / 6.0 * s6b)) / a0;}double itaf, tf, Vf, Nf;itaf = epp * Math.Cos(Bf);tf = Math.Tan(Bf);Vf = Math.Sqrt(1 + epp * epp * Math.Cos(Bf) * Math.Cos(Bf));Nf = c / Vf;double ynf = pcrdCar.y / Nf;pcrdGeo.dLatitude = Bf - 1.0 / 2.0 * Vf * Vf * tf * (ynf * ynf - 1.0 / 12.0 * Math.Pow(ynf, 4) * (5 + 3 * tf * tf + itaf * itaf - 9 * Math.Pow(itaf * tf, 2)) +1.0 / 360.0 * (61 + 90 * tf * tf + 45 * Math.Pow(tf, 4)) * Math.Pow(ynf, 6));pcrdGeo.dLongitude = (ynf / Math.Cos(Bf) - (1 + 2 * tf * tf + itaf * itaf) * Math.Pow(ynf, 3) / 6.0 / Math.Cos(Bf) +(5 + 28 * tf * tf + 24 * Math.Pow(tf, 4) + 6 * itaf * itaf + 8 * Math.Pow(itaf * tf, 2)) * Math.Pow(ynf, 5) / 120.0 / Math.Cos(Bf));pcrdGeo.dLongitude = pcrdGeo.dLongitude + midlong;//pcrdGeo.dLatitude = pcrdGeo.dLatitude;richTextBox2.Text = "Results:\nLatitude: " +Convert.ToString(pcrdGeo.dLatitude) + "\nLongtitude: " +Convert.ToString(pcrdGeo.dLongitude);}private void label13_Click(object sender, EventArgs e){}}}三．程序运行结果分析通过选取书上的具体实例进行测试，本程序的精度大体满足要求，一般正算的精度在0.01米和0.001米之间，反算的精度在0.0001秒左右。
高斯投影正反算程序
printf("高斯投影反算\nunder CGCS2000,六度带\n测试数据：x=2562083.2708,y=19512837.2851\n");
double a=6378137;
double f=1/298.257222101;
double e2=-f*f+2*f;
double x=2562083.2708;
double y=19512837.2851;
int Y=int(y);
int count=0;
while (Y>=100)
{
Y=Y/10;
count++;
}
y=y-Y*pow(10.0,count)-500000;
{
int model;
printf("高斯投影正算请输入1，反算请输入2\n");
scanf("%d",&model);
if(model==1)
{
printf("高斯投影正算\nunder WGS-84,六度带\n测试数据：B=22.155898294，L=111.285215387\n");
double W=sqrt(1-e2*sin(B)*sin(B));
double N=a/W;
double ep2=e2/(1-e2);
double ita2=ep2*cos(B)*cos(B);
double t=tan(B);
double temp1=5-t*t+9*ita2+4*ita2*ita2;
fBf=-a2*sin(2*Bf)/2+a4*sin(4*Bf)/4-a6*sin(6*Bf)/6+a8*sin(8*Bf)/8;
高斯投影正反算 c#代码
高斯投影正反算程序设计一．程序设计流程本程序的设计思路如下：（1），程序采用VS08版本作为开发平台，并采用C#语言作为开发语言，设计为WindowsForm窗体程序形式。
（2），程序主要的算法来自于教材。
但是本程序为了更加实用，添加了更多的解算基准，包括：WGS-84，国际椭球（3{{//{p ublicdoubledLongitude;publicdoubledLatitude;publicdoubledHeight;}//笛卡尔坐标//CartesianCoordinatepublicstructCRDCARTESIAN{publicdoublex;publicdoubley;publicdoublez;}publicForm1(){InitializeComponent();}privatevoidbutton1_Click(objectsender,EventArgse) {try{tt=}{}{ee=}{ee=}if(pareTo("1975国际椭球")==0){a=6378140.00;ee=}if(pareTo("2000国家大地坐标系")==0){a=6378137.0;}constdoublepai=3.1415926;doubleb=Math.Sqrt(a*a*(1-ee*ee));doublec=a*a/b;doubleepp=Math.Sqrt((a*a-b*b)/b/b);CRDGEODETICpcrdGeo;CRDCARTESIANpcrdCar;doublemidlong;//{}ai;//{}pai;//intnum;//带号midlong=0;//默认值，需要制定分带try{tt=}catch{MessageBox.Show("Choose3/6error!");return;if(pareTo("3度带")==0){num=Convert.ToInt32(deglon/6+1);midlong=(6*num-3)/180.0*pai;}if(pareTo("6度带")==0){num=Convert.ToInt32((deglon+1.5)/3);}a4=m4/8.0+3.0/16.0*m6+7.0/32.0*m8;a6=m6/32.0+m8/16.0;a8=m8/128.0;doubleB=pcrdGeo.dLatitude;doublesb=Math.Sin(B);doublecb=Math.Cos(B);doubles2b=sb*cb*2;doubles4b=s2b*(1-2*sb*sb)*2;doubles6b=s2b*Math.Sqrt(1-s4b*s4b)+s4b*Math.Sqrt(1-s2b*s2b); X=a0*B-a2/2.0*s2b+a4*s4b/4.0-a6/6.0*s6b;pcrdCar.x=Nscnb*lp*lp/2.0+Nscnb*cosb*cosb*Math.Pow(lp,4)*(5-t*t+9*ita*ita+4*Math.Pow(ita,4))/24.0 +Nscnb*Math.Pow(cosb,4)*Math.Pow(lp,6)*(61-58*t*t+Math.Pow(t,4))/720.0+X;pcrdCar.y=Ncosb*Math.Pow(lp,1)+Ncosb*cosb*cosb*(1-t*t+ita*ita)/6.0*Math.Pow(lp,3)+Ncosb*Math.Pow(l p,5)*Math.Pow(cosb,4)*(5-18*t*t+Math.Pow(t,4)+14*ita*ita-58*ita*ita*t*t)/120.0;if(pcrdCar.y<0)pcrdCar.y+=500000;richTextBox1.Text="Results:\nX:\t"+Convert.ToString(pcrdCar.x)+"\nY:\t"+Convert.ToString(pcrdCar.y );}{try{tt=}{}{ee=}if(pareTo("WGS-84")==0){a=6378137.00;ee=}if(pareTo("1975国际椭球")==0){a=6378140.00;ee=}if(pareTo("2000国家大地坐标系")==0) {a=6378137.0;ee}constdoublepai=doubleb=Math.Sqrt(a*a*(1-ee*ee));//求Xtry{tt=}{}if(pareTo("3度带")==0){midlong=num*3*pai/180;}if(pareTo("6度带")==0){midlong=(6*num-3)*pai/180;}b=Math.Sqrt(a*a*(1-ee*ee));c=a*a/b;epp=Math.Sqrt(a*a-b*b)/b;doublem0,m2,m4,m6,m8;doublea0,a2,a4,a6,a8;m0=a*(1-ee*ee);m2=3.0/2.0*m0*ee*ee;m4=5.0/4.0*ee*ee*m2;m6=7.0/6.0*ee*ee*m4;m8=9.0/8.0*ee*ee*m6;{}tf=Math.Tan(Bf);Vf=Math.Sqrt(1+epp*epp*Math.Cos(Bf)*Math.Cos(Bf));Nf=c/Vf;doubleynf=pcrdCar.y/Nf;pcrdGeo.dLatitude=Bf-1.0/2.0*Vf*Vf*tf*(ynf*ynf-1.0/12.0*Math.Pow(ynf,4)*(5+3*tf*tf+itaf*itaf-9*Math.Pow(itaf*tf,2))+1.0/360.0*(61+90*tf*tf+45*Math.Pow(tf,4))*Math.Pow(ynf,6));pcrdGeo.dLongitude=(ynf/Math.Cos(Bf)-(1+2*tf*tf+itaf*itaf)*Math.Pow(ynf,3)/6.0/Math.Cos(Bf)+ (5+28*tf*tf+24*Math.Pow(tf,4)+6*itaf*itaf+8*Math.Pow(itaf*tf,2))*Math.Pow(ynf,5)/120.0/Math.Cos(Bf ));pcrdGeo.dLongitude=pcrdGeo.dLongitude+midlong;//pcrdGeo.dLatitude=pcrdGeo.dLatitude;richTextBox2.Text="Results:\nLatitude:"+Convert.ToString(pcrdGeo.dLatitude)+"\nLongtitude:"+Conver t.ToString(pcrdGeo.dLongitude);}privatevoidlabel13_Click(objectsender,EventArgse){}}}米之间，。
高斯投影坐标正反算公式[1]-9页word资料
![高斯投影坐标正反算公式[1]-9页word资料](https://img.taocdn.com/s3/m/852a5116647d27284b7351da.png)
§8.3高斯投影坐标正反算公式任何一种投影①坐标对应关系是最主要的；②如果是正形投影，除了满足正形投影的条件外（C-R 偏微分方程），还有它本身的特殊条件。
8.3.1高斯投影坐标正算公式： B,l ⇒ x,y高斯投影必须满足以下三个条件：①中央子午线投影后为直线；②中央子午线投影后长度不变；③投影具有正形性质，即正形投影条件。
由第一条件知中央子午线东西两侧的投影必然对称于中央子午线，即(8-10)式中，x 为l 的偶函数，y 为l 的奇函数；0330'≤l ，即20/1/≈''''ρl ，如展开为l 的级数，收敛。
ΛΛ+++=++++=553316644220l m l m l m y l m l m l m m x （8-33）式中Λ,,10m m 是待定系数，它们都是纬度B 的函数。
由第三个条件知：qyl x l y q x ∂∂-=∂∂∂∂=∂∂, (8-33)式分别对l 和q 求偏导数并代入上式ΛΛΛΛ----=++++++=+++5533156342442204523164253l dqdm l dq dm l dq dm l m l m l m l dqdm l dq dm dq dm l m l m m (8-34) 上两式两边相等，其必要充分条件是同次幂l 前的系数应相等，即ΛΛΛΛΛΛdq dm m dqdm m dqdm m 2312013121⋅=⋅-==(8-35)(8-35)是一种递推公式，只要确定了0m 就可依次确定其余各系数。
由第二条件知:位于中央子午线上的点，投影后的纵坐标x 应等于投影前从赤道量至该点的子午线弧长X ，即(8-33)式第一式中，当0=l时有：0m X x == (8-36) 顾及(对于中央子午线)B V Mr M B N dq dB M dBdXcos cos 2==== 得：B V cB N r dq dB dB dX dq dX dq dm m cos cos 01===⋅===(8-37,38)B B Ndq dB dB dm dq dm m cos sin 22121112=⋅-=⋅-= (8-39)依次求得6543,,,m m m m 并代入(8-33)式，得到高斯投影正算公式6425644223422)5861(cos sin 720)495(cos 24cos sin 2lt t B B N lt B simB N l B B N X x ''+-''+''++-''+''⋅''+=ρηηρρ5222425532233)5814185(cos 120)1(cos 6cos l t t t B N lt B N l B N y ''-++-''+''+-''+''⋅''=ηηρηρρ (8-42) 8.3.2高斯投影坐标反算公式x,y ⇒B,l投影方程：),(),(21y x l y x B ϕϕ== (8-43)满足以下三个条件：①x 坐标轴投影后为中央子午线是投影的对称轴；② x 坐标轴投影后长度不变；③投影具有正形性质，即正形投影条件。
一个老师给的高斯投影正、反算c++源码
一个老师给的高斯投影正、反算c++源码//高斯投影正、反算//////6度带宽 54年北京坐标系//高斯投影由经纬度(Unit:DD)反算大地坐标(含带号，Unit:Metres)void GaussProjCal(double longitude, double latitude, double *X, double *Y){int ProjNo=0; int ZoneWide; ////带宽double longitude1,latitude1, longitude0,latitude0, X0,Y0, xval,yval; double a,f, e2,ee, NN, T,C,A, M, iPI;iPI = 0.0174532925199433; ////3.1415926535898/180.0;ZoneWide = 6; ////6度带宽a=6378245.0; f=1.0/298.3; //54年北京坐标系参数////a=6378140.0; f=1/298.257; //80年西安坐标系参数ProjNo = (int)(longitude / ZoneWide) ;longitude0 = ProjNo * ZoneWide + ZoneWide / 2;longitude0 = longitude0 * iPI ;latitude0=0;longitude1 = longitude * iPI ; //经度转换为弧度latitude1 = latitude * iPI ; //纬度转换为弧度e2=2*f-f*f;ee=e2*(1.0-e2);NN=a/sqrt(1.0-e2*sin(latitude1)*sin(latitude1));T=tan(latitude1)*tan(latitude1);C=ee*cos(latitude1)*cos(latitude1);A=(longitude1-longitude0)*cos(latitude1);M=a*((1-e2/4-3*e2*e2/64-5*e2*e2*e2/256)*latitude1-(3*e2/8+3*e2*e2/32 +45*e2*e2*e2/1024)*sin(2*latitude1) +(15*e2*e2/256+45*e2*e2*e2/1024)*sin(4*latitude1)-(35*e2*e2*e2/3072) *sin(6*latitude1));xval = NN*(A+(1-T+C)*A*A*A/6+(5-18*T+T*T+72*C-58*ee)*A*A*A*A*A/120); yval = M+NN*tan(latitude1)*(A*A/2+(5-T+9*C+4*C*C)*A*A*A*A/24+(61-58*T+T*T+600*C-330*ee)*A*A*A*A*A*A/720);X0 = 1000000L*(ProjNo+1)+500000L;Y0 = 0;xval = xval+X0; yval = yval+Y0;*X = xval;*Y = yval;}//高斯投影由大地坐标(Unit:Metres)反算经纬度(Unit:DD)void GaussProjInvCal(double X, double Y, double *longitude, double *l atitude){int ProjNo; int ZoneWide; ////带宽double longitude1,latitude1, longitude0,latitude0, X0,Y0, xval,yval; double e1,e2,f,a, ee, NN, T,C, M, D,R,u,fai, iPI;iPI = 0.0174532925199433; ////3.1415926535898/180.0;a = 6378245.0; f = 1.0/298.3; //54年北京坐标系参数////a=6378140.0; f=1/298.257; //80年西安坐标系参数ZoneWide = 6; ////6度带宽ProjNo = (int)(X/1000000L) ; //查找带号longitude0 = (ProjNo-1) * ZoneWide + ZoneWide / 2;longitude0 = longitude0 * iPI ; //中央经线X0 = ProjNo*1000000L+500000L;Y0 = 0;xval = X-X0; yval = Y-Y0; //带内大地坐标e2 = 2*f-f*f;e1 = (1.0-sqrt(1-e2))/(1.0+sqrt(1-e2));ee = e2/(1-e2);M = yval;u = M/(a*(1-e2/4-3*e2*e2/64-5*e2*e2*e2/256));fai = u+(3*e1/2-27*e1*e1*e1/32)*sin(2*u)+(21*e1*e1/16-55*e1*e1*e1*e1 /32)*sin(4*u)+(151*e1*e1*e1/96)*sin(6*u)+(1097*e1*e1*e1*e1/512)*sin(8 *u);C = ee*cos(fai)*cos(fai);T = tan(fai)*tan(fai);NN = a/sqrt(1.0-e2*sin(fai)*sin(fai));R = a*(1-e2)/sqrt((1-e2*sin(fai)*sin(fai))*(1-e2*sin(fai)*sin(fai))* (1-e2*sin(fai)*sin(fai)));D = xval/NN;//计算经度(Longitude) 纬度(Latitude)longitude1 = longitude0+(D-(1+2*T+C)*D*D*D/6+(5-2*C+28*T-3*C*C+8*ee+ 24*T*T)*D*D*D*D*D/120)/cos(fai);latitude1 = fai -(NN*tan(fai)/R)*(D*D/2-(5+3*T+10*C-4*C*C-9*ee)*D*D* D*D/24+(61+90*T+298*C+45*T*T-256*ee-3*C*C)*D*D*D*D*D*D/720);//转换为度 DD*longitude = longitude1 / iPI;*latitude = latitude1 / iPI;}如果有需要程序的，可以直接跟我联系，呵呵附：高斯正反算参数pi=0.0174532925 ※※0.0174532925199433 //π长半轴a=6378245.0; 扁率f=1.0/298.3; //54年北京坐标系参数长半轴a=6378140.0; 扁率f=1/298.257; //80年西安坐标系参数长半轴a=6378137m；扁率f=1:298.257223563。
高斯投影的正算反算C++源代码-课程设计
高斯投影的正算反算C++源代码-课程设计高斯投影的正算反算C++源代码一、设计目的：加深理解高斯—克吕格投影的实质，掌握高斯—克吕格投影直角坐标的运用，理解通用坐标和自然坐标值的关系。
二、设计内容：1、编程实现由经纬度到直角坐标的转换；2、正确计算点所在的分度带；3、准确计算出点的通用坐标值。
三、方法与步骤：1、理解公式中每个字母的含义；2、编程。
3、编程的程序如下：// 高斯投影正反算公式.cpp : Defines the entry point for the console application.//#include "iostream.h"#include "math.h"int main(int argc, char* argv[]){int n,a,d,c;int L[4],B[4],C[3],D[3],L0;double l,N,a0,a4,a6,a3,a5,x,y,BB,P,b,Z,Bf,b2,b3,b4,b5,Nf,LL,xx,yy;cout<<"1----正算(L,B-->x,y) 2----反算(x,y-->L,B)"<<endl;cout<<"请选择正算（1）或反算（2）:"<<endl;cin>>n;/////////////////正算if(n==1){cout<<"请按顺序输入L,B:"<<endl;cout<<"输入L(度,分,秒):"<<endl;cin>>L[1]>>L[2]>>L[3];cout<<"请输入B(度,分,秒):"<<endl;cin>>B[1]>>B[2]>>B[3];BB=3.141592654*(B[1]+B[2]/60.0+B[3]/3600.0)/180;P=3.141592654*(B[1]*3600+B[2]*60+B[3])/(180*3600);////////////////计算点所在投影带的中央子午线L[0]=6*(int((L[1]+L[2]/60.0+L[3]/3600.0)/6)+1)-3;cout<<"点所在投影带的中央子午线为:"<<endl;cout<<L[0]<<"度"<<endl;l=3.141592654*(L[1]+L[2]/60.0+L[3]/3600-L[0])/180;N=6399698.902-(21562.267-(108.973-0.612*cos(BB)*cos(BB))*cos(BB)*co s(BB))*cos(BB)*cos(BB);a0=32140.404-(135.3302-(0.7092-0.0040*cos(BB)*cos(BB))*cos(BB)*cos( BB))*cos(BB)*cos(BB);a4=(0.25+0.00252*cos(BB)*cos(BB))*cos(BB)*cos(BB)-0.04166;a6=(0.166*cos(BB)*cos(BB)-0.084)*cos(BB)*cos(BB);a3=(0.3333333+0.001123*cos(BB)*cos(BB))*cos(BB)*cos(BB)-0.1666667; a5=0.0083-(0.1667-(0.1968+0.0040*cos(BB)*cos(BB))*cos(BB)*cos(BB))* cos(BB)*cos(BB);///////////代号计算a=L[0]/6+1;d=L[0]-1.5;c=d/3+1;///////////////计算坐标x=6367558.4969*P-(a0-(0.5+(a4+a6*l*l)*l*l)*l*l*N)*sin(BB)*cos(BB); y=(1+(a3+a5*l*l)*l*l)*l*N*cos(BB);/////////////格式控制cout.setf(ios::fixed);cout.setf(ios::showpoint);cout.precision(3);cout<<"正算结果为:"<<endl;cout<<"平面坐标:"<<endl;cout<<"x="<<x<<endl;cout<<"y="<<y<<endl;cout<<"分度带号为："<<endl;cout<<"六度带号为："<<a<<endl;cout<<"三度带号为："<<c<<endl;cout<<"通用坐标为（米）："<<endl;cout<<"x="<<x<<endl;cout<<"y="<<y+500000<<endl; //通用坐标计算}else if(n==2) /////////////////////反算{cout<<"请依次输入坐标x,y(m):"<<endl;cin>>xx>>yy;cout<<"请输入点所在投影带的中央子午线(度):"<<endl;cin>>L0;b=xx/6367558.4969;Bf=b+(50221746+(293622+(2350+22*cos(b)*cos(b))*cos(b)*cos(b))*cos(b)*cos(b))*(1.0E-10)*sin(b)*cos(b);Nf=6399698.902-(21562.267-(108.973-0.612*cos(Bf)*cos(Bf))*cos(Bf)*c os(Bf))*cos(Bf)*cos(Bf);Z=yy/(Nf*cos(Bf));b2=(0.5+0.00336975*cos(Bf)*cos(Bf))*sin(Bf)*cos(Bf);b3=0.333333-(0.1666667-0.001123*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf); b4=0.25+(0.161612+0.005617*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);b5=0.2-(0.1667-0.00878*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);BB=Bf*3600*180/3.141592654-(1-(b4-0.147*Z*Z)*Z*Z)*Z*Z*b2*180*3600/3.141592654;LLC[1]=int((BB-C[0]*3600)/60);C[2]=int(BB-C[0]*3600-C[1]*60);cout<<"B="<<C[0]<<"度"<<C[1]<<"分"<<C[2]<<"秒"<<endl;D[0]=int(LL/3600);D[1]=int((LL-D[0]*3600)/60);D[2]=int(LL-D[0]*3600-D[1]*60);cout<<"L="<<D[0]<<"度"<<D[1]<<"分"<<D[2]<<"秒"<<endl;}return 0;}四、成果：1、程序运行结果如下图：1260。
史上最全的高斯投影源代码集合(精心收集9种)
高斯投影C++源码 1CCoordinate CEarthPlaneDialog::EarthToPlane(const CEarth & earth){double B = earth.m_dB.m_realRadians;double L = earth.m_dL.m_realRadians;L = SetRad_PIPI(L);double L0 = SetL0(L);double X, N, t, t2, m, m2, ng2;double sinB, cosB;X = A1 * B * 180.0 / PI + A2 * sin(2 * B) + A3 * sin(4 * B) + A4 * sin(6 * B);sinB = sin(B);cosB = cos(B);t = tan(B);t2 = t * t;N = a / sqrt(1 - e2 * sinB * sinB);m = cosB * (L - L0);m2 = m * m;ng2 = cosB * cosB * e2 / (1 - e2);double x = X + N * t * ((0.5 + ((5 - t2 + 9 * ng2 + 4 * ng2 * ng2) / 24.0 + (61 - 58 * t2 + t2 * t2) * m2 / 720.0) * m2) * m2);double y = N * m * ( 1 + m2 * ( (1 - t2 + ng2) / 6.0 + m2 * ( 5 - 18 * t2 + t2 * t2 + 14 * ng2 - 58 * ng2 * t2 ) / 120.0));y += 500000;CCoordinate coor(x,y);return coor;}//将大地坐标系转换为平面直角坐标系CEarth CEarthPlaneDialog::PlaneToEarth(const CCoordinate & coor, UINT Sign){double x = coor.m_dX;double y = coor.m_dY;double L0 = (6.0 * Sign - 3.0) / 180 * PI;double sinB, cosB, t, t2, N ,ng2, V, yN;double preB0, B0;double eta;y -= 500000;B0 = x / A1;do{preB0 = B0;B0 = B0 * PI / 180.0;B0 = (x - (A2 * sin(2 * B0) + A3 * sin(4 * B0) + A4 * sin(6 * B0))) / A1;eta = fabs(B0 - preB0);}while(eta > 0.0000000000000001);B0 = B0 * PI / 180.0;sinB = sin(B0);cosB = cos(B0);t = tan(B0);t2 = t * t;N = a / sqrt(1 - e2 * sinB * sinB);ng2 = cosB * cosB * e2 / (1 - e2);V = sqrt(1 + ng2);yN = y / N;double B = B0 - (yN * yN - (5 + 3 * t2 + ng2 - 9 * ng2 * t2) * yN * yN * yN * yN / 12.0 + (61 + 90 * t2 + 45 * t2 * t2) * yN * yN * yN * yN * yN * yN / 360.0) * V * V * t / 2;double L = L0 + (yN - (1 + 2 * t2 + ng2) * yN * yN * yN /6.0 + (5 + 28 * t2 + 24 * t2 * t2 + 6 * ng2 + 8 * ng2 * t2) * yN * yN * yN * yN * yN / 120.0) / cosB;CEarth earth(B,L,0,'r');return earth;}//将平面直角坐标系转换为大地坐标系void CEarthPlaneDialog::OnRADIOPlane1954(){// TODO: Add your control notification handler code herea = 6378245;f = 298.3;e2 = 1 - ((f - 1) / f) * ((f - 1) / f);e12 = (f / (f - 1)) * (f / (f - 1)) - 1;A1 = 111134.8611;A2 = -16036.4803;A3 = 16.8281;A4 = -0.0220;m_iReferenceFrame = 0;}void CEarthPlaneDialog::OnRADIOPlane1980(){// TODO: Add your control notification handler code herea = 6378140;f = 298.257;e2 = 1 - ((f - 1) / f) * ((f - 1) / f);e12 = (f / (f - 1)) * (f / (f - 1)) - 1;A1 = 111133.0047;A2 = -16038.5282;A3 = 16.8326;A4 = -0.0220;m_iReferenceFrame = 1;}void CEarthPlaneDialog::OnRADIOPlaneWGS84(){// TODO: Add your control notification handler code herea = 6378137;f = 298.257223563;e2 = 1 - ((f - 1) / f) * ((f - 1) / f);e12 = (f / (f - 1)) * (f / (f - 1)) - 1;A1 = 111133.0047;A2 = -16038.5282;A3 = 16.8326;A4 = -0.0220;m_iReferenceFrame = 2;}double CEarthPlaneDialog::SetL0(double L){L = L / PI * 180;if( L > 0 ){for(m_iCincture = 1 ; !(( L >= (6 * m_iCincture - 6 )) & ( L < ( 6 * m_iCincture ))); m_iCincture++){}L0 = 6 * m_iCincture - 3;}else if( L < 0 ){L = -L;for(m_iCincture = 1 ; !(( L > (6 * m_iCincture - 6 )) & ( L<= ( 6 * m_iCincture ))); m_iCincture++) {}m_iCincture = 61 - m_iCincture;L0 = m_iCincture * 6 - 363;}else{L0 = 3;m_iCincture = 1;}double temp = ((double)L0) / 180 * PI;return temp;}double CEarthPlaneDialog::SetRad_PIPI(double Rad) {if(Rad > 0){double i = floor(Rad / PI / 2);Rad -= 2 * PI * i;}if(Rad < 0){Rad = -Rad;double i = floor(Rad / PI / 2);Rad -= 2 * PI * i;Rad = -Rad + PI * 2;}if(Rad > PI)Rad -= 2 * PI;return Rad;}高斯投影C++源码 2// GaussBL2xy.cpp : Defines the entry point for the console application.//#include "stdafx.h "#include "math.h "#include "CoorTrans.h "#include <iostream>using namespace std;void main(int argc, char* argv[]){double MyL0 = 108; //中央子午线double MyB = 33.44556666; //33 du 44 fen55.6666 miaodouble MyL = 109.22334444; //3度带，109 d 22 m 33.4444 sPrjPoint_Krasovsky MyPrj;MyPrj.SetL0(MyL0);MyPrj.SetBL(MyB, MyL);double OutMyX; //结果应该大致是:3736714.783, 627497.303double OutMyY;OutMyX = MyPrj.x; //正算结果: 北坐标xOutMyY = MyPrj.y; //结果：东坐标y//////////////////反算////////////////////////////////////////double InputMyX = 3736714.783; //如果是独立计算，应该给出中央子午线L0double InputMyY = 627497.303;MyPrj.Setxy(InputMyX, InputMyY);MyPrj.GetBL(&MyPrj.B, &MyPrj.L); //把计算出的BL的弧度值换算为dms形式double OutputMyB;double OutputMyL;OutputMyB = MyPrj.B; //反算结果：BOutputMyL = MyPrj.L; //反算结果：L//分析表明，此程序的结果和Coord4.2的转换结果是一样的，只差到毫米级//原程序有几个问题，1.Pi的值不对。
高斯投影正算与反算的理论方法与实
高斯投影正算与反算的理论方法与实现代码高斯投影是正形投影的一种，同一坐标系中的高斯投影换带计算公式是根据正形投影原理推导出的两个高斯坐标系间的显函数式。
在同一大地坐标系中(例如1954北京坐标系或1980西安坐标系)，如果两个高斯坐标系只是主子午线的经度不同，那么显函数式前的系数可以根据坐标系使用的椭球元素和主子午线经度唯一确定。
但如果两个高斯坐标系除了主子午线的经度不同以外，还存在其他线性系，则将线性变换公式代入换带计算的显函数式中，仍然可以得到严密的坐标变换公式。
此时显函数式前的系数等价于使用两个坐标系主子午线的经度和线性变换参数联合求解得到的，可以唯一确定。
//6度带宽 54北京坐标系//高斯投影由大地坐标(Unit:Metres)反算经纬度(Unit:DD)void GaussProjInvCal(double X, double Y, double *longitude, double *latitude) {int ProjNo; int ZoneWide; ////带宽double longitude1,latitude1, longitude0,latitude0, X0,Y0, xval,yval;double e1,e2,f,a, ee, NN, T,C, M, D,R,u,fai, iPI;iPI = 0.0174532925199433; ////3.1415926535898/180.0;a = 6378245.0; f = 1.0/298.3; //54年北京坐标系参数////a=6378140.0; f=1/298.257; //80年西安坐标系参数ZoneWide = 6; ////6度带宽ProjNo = (int)(X/1000000L) ; //查找带号longitude0 = (ProjNo-1) * ZoneWide + ZoneWide / 2;longitude0 = longitude0 * iPI ; //中央经线X0 = ProjNo*1000000L+500000L;Y0 = 0;xval = X-X0; yval = Y-Y0; //带内大地坐标e2 = 2*f-f*f;e1 = (1.0-sqrt(1-e2))/(1.0+sqrt(1-e2));ee = e2/(1-e2);M = yval;u = M/(a*(1-e2/4-3*e2*e2/64-5*e2*e2*e2/256));fai = u+(3*e1/2-27*e1*e1*e1/32)*sin(2*u)+(21*e1*e1/16-55*e1*e1*e1*e1/32)*sin( 4*u)+(151*e1*e1*e1/96)*sin(6*u)+(1097*e1*e1*e1*e1/512)*sin(8*u);C = ee*cos(fai)*cos(fai);T = tan(fai)*tan(fai);NN = a/sqrt(1.0-e2*sin(fai)*sin(fai));R = a*(1-e2)/sqrt((1-e2*sin(fai)*sin(fai))*(1-e2*sin(fai)*sin(fai))*(1-e2*sin (fai)*sin(fai)));D = xval/NN;//计算经度(Longitude) 纬度(Latitude)longitude1 = longitude0+(D-(1+2*T+C)*D*D*D/6+(5-2*C+28*T-3*C*C+8*ee+24*T*T)*D *D*D*D*D/120)/cos(fai);latitude1 = fai -(NN*tan(fai)/R)*(D*D/2-(5+3*T+10*C-4*C*C-9*ee)*D*D*D*D/24+(61+90*T+298*C+45*T*T-256*ee-3*C*C)*D*D*D*D*D*D/720);//转换为度 DD*longitude = longitude1 / iPI;*latitude = latitude1 / iPI;}//高斯投影由经纬度(Unit:DD)正算平面坐标(含带号，Unit:Metres)void GaussProjCal(double longitude, double latitude, double *X, double *Y) {int ProjNo=0; int ZoneWide; ////带宽double longitude1,latitude1, longitude0,latitude0, X0,Y0, xval,yval;double a,f, e2,ee, NN, T,C,A, M, iPI;iPI = 0.0174532925199433; ////3.1415926535898/180.0;ZoneWide = 6; ////6度带宽a=6378245.0; f=1.0/298.3; //54年北京坐标系参数////a=6378140.0; f=1/298.257; //80年西安坐标系参数ProjNo = (int)(longitude / ZoneWide) ;longitude0 = ProjNo * ZoneWide + ZoneWide / 2;longitude0 = longitude0 * iPI ;latitude0=0;longitude1 = longitude * iPI ; //经度转换为弧度latitude1 = latitude * iPI ; //纬度转换为弧度e2=2*f-f*f;ee=e2*(1.0-e2);NN=a/sqrt(1.0-e2*sin(latitude1)*sin(latitude1));T=tan(latitude1)*tan(latitude1);C=ee*cos(latitude1)*cos(latitude1);A=(longitude1-longitude0)*cos(latitude1);M=a*((1-e2/4-3*e2*e2/64-5*e2*e2*e2/256)*latitude1-(3*e2/8+3*e2*e2/32+45*e2*e2 *e2/1024)*sin(2*latitude1)+(15*e2*e2/256+45*e2*e2*e2/1024)*sin(4*latitude1)-(35 *e2*e2*e2/3072)*sin(6*latitude1));xval = NN*(A+(1-T+C)*A*A*A/6+(5-18*T+T*T+72*C-58*ee)*A*A*A*A*A/120);yval = M+NN*tan(latitude1)*(A*A/2+(5-T+9*C+4*C*C)*A*A*A*A/24+(61-58*T+T*T+600*C-330*ee)*A*A*A*A*A*A/720);X0 = 1000000L*(ProjNo+1)+500000L;Y0 = 0;xval = xval+X0; yval = yval+Y0;*X = xval;*Y = yval;}NN卯酉圈曲率半径，测量学里面用N表示M为子午线弧长，测量学里用大X表示fai为底点纬度，由子午弧长反算公式得到，测量学里用Bf表示R为底点所对的曲率半径，测量学里用Nf表示。
(完整版)高斯投影正反算
高斯投影正反算学院：资源与环境工程工程学院专业：测绘工程学号：X51414012姓名：孙超一、高斯投影概述想象有一个椭圆柱面横套在地球椭球体外面，并与某一条子午线相切，椭圆柱的中心轴通过椭球体的中心，然后用一定投影方法，将中央子午线两侧各一定经差范围内的地区投影到椭圆柱面上，再将此柱面展开即成为投影面。
高斯投影由于是正形投影，故保证了投影的角度不变性，图形的相似性以及在某点各方向上长度比的同一性。
由于采用了同样法则的分带投影，这即限制了长度变形，又保证了在不同投影带中采用相同的简便公式和数表进行变形引起的各项改正的计算，并且带与带间的互相换算也能用相同的公式和方法进行。
高斯投影的这些优点必将使它得到广泛的推广和具有国际意义。
二、高斯投影坐标正算公式1.高斯投影必须满足以下三个条件1）中央子午线投影后为直线2）中央子午线投影后长度不变3）投影具有正形性质，即正形投影条件2.高斯正算公式推导1）由第一个条件可知，由于地球椭球体是一个旋转椭球体，所以高斯投影必然有这样一个性质，即中央子午线东西两侧的投影必然对称于中央子午线。
2）由于高斯投影是换带投影，在每带内经差ｌ是不大的，ｌρ是一个微小量，所以可以将 X=X （ｌ，q ），Y=Y （l ，q ）展开为经差为l 的幂级数，它可写成如下的形式X=m 0+m 2l 2+m 4l 4+…Y=m 1l+m 3l 2+m 5l 5+…式中m 0,m1,m2,…是待定系数，他们都是纬度B 的函数。
3）由第三个条件：∂y ∂l =∂x ∂q 和∂x ∂l =-∂y ∂q ，将上式分别对l 和q 求偏导2340123423401234...........x m m l m l m l m l y n n l n l n l n l =+++++=+++++可得到下式0312123403121234111,,,, 234111,,,,234dm dm dm dm n n n n dq dq dq dq dn dn dn dn m m m m dq dq dq dq ⎧====⎪⎪⎨⎪=-=-=-=-⎪⎩L L 经过计算可以得出232244524632235242225sin cos sin cos (594)224sin cos (6158)720cos cos (1) 6cos (5181458)120N N x X B B l B B t l N B B t t l N y N B l B t l N B t t t l ηηηηη=+⋅+-+++-+=⋅+-++-++-三、高斯投影坐标反算公式推导1.思路：级数展开，应用高斯投影三个条件，待定系数法求解。
高斯投影正反算编程一.高斯投影正反算基本公式
高斯投影正反算编程一．高斯投影正反算基本公式（1）高斯正算基本公式（2）高斯反算基本公式以上主要通过大地测量学基础课程得到，这不进行详细的推导，只是列出基本公式指导编程的进行。
二．编程的基本方法和流程图（1）编程的基本方法高斯投影正反算基本上运用了所有的编程基本语句，本文中是利用C++语言进行基本的设计。
高斯正算中对椭球参数和带宽的选择主要运用了选择语句。
而高斯反算中除了选择语句的应用，在利用迭代算法求底点纬度还应用了循环语句。
编程中还应特别注意相关的度分秒和弧度之间的相互转换，这是极其重要的。
（2）相关流程图1）正算2）反算三．编程的相关代码（1）正算# include "stdio.h"# include "stdlib.h"# include "math.h"# include "assert.h"#define pi (4*atan(1.0))int i;struct jin{double B;double L;double L0;};struct jin g[100];main(int argc, double *argv[]){FILE *r=fopen("a.txt","r");assert(r!=NULL);FILE *w=fopen("b.txt","w");assert(r!=NULL);int i=0;while(fscanf(r,"%lf %lf %lf",&g[i].B,&g[i].L,&g[i].L0)!=EOF){double a,b;int zuobiao;printf("\n请输入坐标系：北京54=1，西安80=2，WGS84=3：");scanf("%d",&zuobiao);getchar();if(zuobiao==1){a=6378245;b=6356863.0187730473;}if(zuobiao==2){a=6378140;b=6356755.2881575287;}if(zuobiao==3){a=6378137;b=6356752.3142;} //选择坐标系//double f=(a-b)/a;double e,e2;e=sqrt(2*f-f*f);e2=sqrt((a/b)*(a/b)-1);//求椭球的第一，第二曲率//double m0,m2,m4,m6,m8;double a0,a2,a4,a6,a8;m0=a*(1-e*e);m2=3*e*e*m0/2;m4=5*e*e*m2/4;m6=7*e*e*m4/6;m8=9*e*e*m6/8;a0=m0+m2/2+3*m4/8+5*m6/16+35*m8/128;a2=m2/2+m4/2+15*m6/32+7*m8/16;a4=m4/8+3*m6/16+7*m8/32;a6=m6/32+m8/16;a8=m8/128;double Bmiao,Lmiao, L0miao;Bmiao=(int)(g[i].B)*3600.0+(int)((g[i].B-(int)(g[i].B))*100.0)*60.0+( g[i].B*100-(int)(g[i].B*100))*100.0;Lmiao=(int)(g[i].L)*3600.0+(int)((g[i].L-(int)(g[i].L))*100.0)*60.0+(g [i].L*100-(int)(g[i].L*100))*100.0;L0miao=(int)(g[i].L0)*3600.0+(int)((g[i].L0-(int)(g[i].L0))*100.0)*60. 0+(g[i].L0*100-(int)(g[i].L0*100))*100.0;double db;db=pi/180.0/3600.0;double B1,L1,l;B1=Bmiao*db;L1= Lmiao*db;l=L1-L0miao*db;//角度转化为弧度//double T=tan(B1)*tan(B1);double n=e2*e2*cos(B1)*cos(B1);double A=l*cos(B1);double X,x,y;X=a0*(B1)-a2*sin(2*B1)/2+a4*sin(4*B1)/4-a6*sin(6*B1)/6+a8*sin(8*B1)/8;//求弧长//double N=a/sqrt(1-e*e*sin(B1)*sin(B1));int Zonewide;int Zonenumber;printf("\n请输入带宽：3度带或6度带Zonewide=");scanf("%d",&Zonewide);getchar();if(Zonewide==3){Zonenumber=(int)((g[i].L-Zonewide/2)/Zonewide+1);}else if(Zonewide==6){Zonenumber=(int)g[i].L/Zonewide+1;}else{printf("错误");exit(0);}//选择带宽//doubleFE=Zonenumber*1000000+500000;//改写为国家通用坐标//y=FE+N*A+A*A*A*N*(1-T*T+n*n)/6+A*A*A*A*A*N*(5-18*T*T+T *T*T*T+14*n*n-58*n*n*T*T)/120;x=X+tan(B1)*N*A*A/2+tan(B1)*N*A*A*A*A*(5-T*T+9*n*n+4*n*n *n*n)/24+tan(B1)*N*A*A*A*A*A*A*(61-58*T*T+T*T*T*T)/720;printf("\n所选坐标系的转换结果：x=%lf y=%lf\n",x,y);fprintf(w,"%lf %lf\n",x,y);//输出结果到文本文件//}fclose(r);fclose(w);system("pause");return 0;}（2）反算# include "stdio.h"# include "stdlib.h"# include "math.h"# include "assert.h"#define pi (4*atan(1.0))double X,Y,B1,B2,B3,F,t;double m0,m2,m4,m6,m8;double a0,a2,a4,a6,a8,a1,b1;double BB,LL,Bf;double e,e1;int d,m,s,i,zuobiao;double sort(double,double);struct jin{double x;double y;double L0;};struct jin g[100];//x,y,L0为输入量：x,y坐标和中央子午线经度// main(int argc, double *argv[]){FILE *r=fopen("c.txt","r");assert(r!=NULL);FILE *w=fopen("d.txt","w");assert(r!=NULL);int i=0;while(fscanf(r,"%lf %lf %lf",&g[i].x,&g[i].y,&g[i].L0)!=EOF)//文件为空，无法打开//{double a1=6378245.0000000000;//克拉索夫斯基椭球参数//double b1=6356863.0187730473;double a75=6378140.0000000000;//1975国际椭球参数//double b75=6356755.2881575287;double a84=6378137.0000000000;//WGS-84系椭球参数//double b84=6356752.3142000000;double M,N;//mouyou圈曲率半径，子午圈曲率半径//double t,n;double A,B,C;double BB,LL,Bf,LL0,BB0;double a,b;printf("\n选择参考椭球：1=克拉索夫斯基椭球，2=1975国际椭球，3=WGS-84系椭球:");scanf("%d",&zuobiao);getchar();if(zuobiao==1){a=a1;b=b1;}if(zuobiao==2){a=a75;b=b75;}if(zuobiao==3){a=a84;b=b84;}//选择参考椭球，求解第一偏心率e,第二偏心率e1// Bf=sort(a,b);//调用求解底点纬度的函数//double q=sqrt(1-e*e*sin(Bf)*sin(Bf));double G=cos(Bf);M=a*(1-e*e)/(q*q*q);N=a/q;double H,I;A=g[i].y/N;H=A*A*A;I=A*A*A*A*A;t=tan(Bf);n=e1*cos(Bf);B=t*t;C=n*n;BB0=Bf-g[i].y*t*A/(2*M)+g[i].y*t*H/(24*M)*(5+3*B+C-9*B*C)-g[i] .y*t*I/(720*M)*(61+90*B+45*B*B);LL0=g[i].L0*pi/180.0+A/G-H/(6*G)*(1.0+2*B+C)+I/(120*G)*(5.0+28 *B+24*B*B+6*C+8*B*C);//利用公式求解经纬度//int Bdu,Bfen,Ldu,Lfen;double Bmiao,Lmiao;Ldu=int(LL0/pi*180);Lfen=int((LL0/pi*180)*60-Ldu*60);Lmiao=LL0/pi*180*3600-Ldu*3600-Lfen*60;Bdu=int(BB0/pi*180);Bfen=int((BB0/pi*180)*60-Bdu*60);Bmiao=BB0/pi*180*3600-Bdu*3600-Bfen*60;//将弧度转化为角度//printf("\n所选坐标系的转换结果：%d度%d分%lf秒%d 度%d分%lf秒\n",Bdu,Bfen,Bmiao,Ldu,Lfen,Lmiao);fprintf(w,"%d°%d’%lf”%d°%d’%lf”\n",Bdu,Bfen,Bmiao,Ldu,Lfen,Lmiao);//将结果输出到文本文件//}fclose(r);fclose(w);system("pause");return 0;}double sort(double a,double b){double e,e1;e=sqrt(1-(b/a)*(b/a));e1=sqrt((a/b)*(a/b)-1);double m0,m2,m4,m6,m8;double a0,a2,a4,a6,a8;m0=a*(1-e*e);m2=3*e*e*m0/2;m4=5*e*e*m2/4;m6=7*e*e*m4/6;m8=9*e*e*m6/8;a0=m0+m2/2+3*m4/8+5*m6/16+35*m8/128;a2=m2/2+m4/2+15*m6/32+7*m8/16;a4=m4/8+3*m6/16+7*m8/32;a6=m6/32+m8/16;a8=m8/128;B1=g[i].x/a0;do{F=-a2*sin(2*B1)/2+a4*sin(4*B1)/4-a6*sin(6*B1)/6+a8*sin(8*B1 )/8;B2=(g[i].x-F)/a0;B3=B1;B1=B2;} while(fabs(B3-B2)>10e-10);//利用迭代算法求解底点纬度//return B2; }。
高斯投影坐标正算C语言代码
高斯投影坐标正算C语言代码#include<stdio.h>#include<math.h>#include<conio.h>main(){printf("#####################################################\n");printf("# 角度输入说明：如26°12′45.2″输入为26,12,45.2 #\n");printf("#####################################################\n");double b,B,L,L0,l1;double d1,f1,m1,d2,f2,m2;double x,y;double p=206264.80625;printf("请输入B：\n");scanf("%lf,%lf,%lf",&d1,&f1,&m1); //维度数据输入while (d1 < 0 || d1 >=90 || f1 < 0 || f1>= 60 || m1 < 0 || m1 >= 60){printf("纬度输入格式不正确！\n");printf("请重新输入B：\n");scanf("%lf,%lf,%lf",&d1,&f1,&m1);}printf("您输入的大地维度为：\nB=%.0lf°%0.lf′%.2lf″\n",d1,f1,m1);//检查输入格式的正确性printf("请输入L：\n");scanf("%lf,%lf,%lf",&d2,&f2,&m2); //经度数据输入while (d2 < 0 || d2 >=180 || f2 < 0 || f2>= 60 || m2 < 0 || m2 >= 60){printf("经度输入格式不正确！\n");printf("请重新输入L：\n");scanf("%lf,%lf,%lf",&d2,&f2,&m2);}printf("您输入的大地经度为：\nB=%.0lf°%0.lf′%.2lf″\n",d2,f2,m2);//检查输入格式的正确性B=d1*3600+f1*60+m1;L=d2*3600+f2*60+m2;//转化为以″为单位b=B/p; //把角度转化为弧度制int i,j,N;printf("请选择带宽：1. 6°带。
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L=l+L01; ///
反算就出
L B
l=L-L02;
B=Bf-(1-(b4-0.12*Z*Z)*Z*Z)*Z*Z*b2;
t=tan(B);
n2=e2*cos(B)*cos(B);
V=sqrt(1+n2);
cB2=pow(cos(B),2);
N=6399698.902-(21562.267-(108.973-0.612*cB2)*cB2)*cB2; //N=c/V;
l=L-111*3600/P // l=((m%6)*3600+n*60+h)/P;
t=tan(B);
n2=e2*cos(B)*cos(B);
V=sqrt(1+n2);
cB2=pow(cos(B),2);
N=6399698.902-(21562.267-(108.973-0.612*cB2)*cB2)*cB2; // N=c/V;
a0=32140.404-(135.3302-(0.7092-0.004*cB2)*cB2)*cB2;
a4=(0.25+0.00252*cB2)*cB2-0.04166;
a6=(0.166*cB2-0.084)*cB2;
a3=(0.3333333+0.001123*cB2)*cB2-0.1666667;
#include "stdafx.h"
#include "iostream.h"
#include "math.h"
#include "stdio.h"
#define P 206264.806247096355
#define PI 3.141592653589793voiBiblioteka GaosZ_fun(){
printf("高斯投影的正算\n");
y=(1+(a3+a5*l*l)*l*l)*l*N*cos(B);
printf("x=%f\ny=%f\n",x,y);
}
void GaosF_fun()
{
printf("高斯投影的反算\n");
double B,Bf,Nf,b,b2,b3,b4,b5,Z,x,y,L0,l;
// printf("输入x y的值\n");
b3=0.333333-(0.166667-0.001123*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);
b4=0.25+(0.16161+0.00562*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);
b5=0.2-(0.167-0.0088*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);
a0=32140.404-(135.3302-(0.7092-0.004*cB2)*cB2)*cB2;
a4=(0.25+0.00252*cB2)*cB2-0.04166;
a6=(0.166*cB2-0.084)*cB2;
a3=(0.3333333+0.001123*cB2)*cB2-0.1666667;
double a0,a4,a6,a3,a5,cB2;
e2=0.006738525414683;
c=6399698.901782711;
// printf("输入x y的值\n");
// cout<<"x=";
// cin>>x;
// cout<<"y=";
// cin>>y;
// scanf("x=%f",&x); ///////////// ?????
B=Bf-(1-(b4-0.12*Z*Z)*Z*Z)*Z*Z*b2;
l=(1-(b3-b5*Z*Z)*Z*Z)*Z;
printf("B=%f\nL=%f\n",B*180/PI,(L0+l*180/PI));
}
void GaosLT_fun()
{
double B,Bf,Nf,b,b2,b3,b4,b5,Z,x,y,L01,L02,n2,l,V,L,N,c,t,e2;
// scanf("y=%f",&y);
// x=3380330.875;
// y=320089.976;
x=1944359.607;
y=240455.4563;
L01=117*3600/P;
L02=120*3600/P;
b=x/6367558.4969;
Bf=b+(50221746+ ( 293622+ (2350+22*cos(b)*cos(b))*cos(b)*cos(b) )
b3=0.333333-(0.166667-0.001123*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);
b4=0.25+(0.16161+0.00562*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);
b5=0.2-(0.167-0.0088*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf);
double l,L,B,n2,x,y,N,t,V,c,e2;
double i,j,k,n,h,a0,a4,a6,a3,a5,cB2;
int m;
e2=0.006738525414683;
c=6399698.901782711;
B=17.33557339*3600/P;
L=119.15521159*3600/P;
y=(1+(a3+a5*l*l)*l*l)*l*N*cos(B);
printf("输出高斯邻带坐标换算\n");
printf("x=%f\ny=%f\n",x,y);
}
void main()
{
int i;
printf("输入1 2 3选择投影的计算方法\n");
scanf("%d",&i);
switch (i)
// y=N*cos(B)*l+N*pow(cos(B),3)*(1-t*t+n2)*pow(l,5)/6+N*pow(cos(B),5)*(5-18*t*t
+pow(t,4)+14*n2-58*n2*t*t)*pow(l,5)/120;
x=6367558.4969*B-(a0-(0.5+(a4+a6*l*l)*l*l)*l*l*N)*sin(B)*cos(B);
// y=N*cos(B)*l+N*pow(cos(B),3)*(1-t*t+n2)*pow(l,5)/6+N*pow(cos(B),5)*(5-18*t*t
+pow(t,4)+14*n2-58*n2*t*t)*pow(l,5)/120;
x=6367558.4969*B-(a0-(0.5+(a4+a6*l*l)*l*l)*l*l*N)*sin(B)*cos(B);
{
case 1: GaosZ_fun(); break;
case 2: GaosF_fun(); break;
case 3: GaosLT_fun(); break;
default : break;
}
}
*cos(b)*cos(b)) *sin(b)*cos(b)*1e-10;
Nf=6399698.902-(21562.267-(108.973-0.612*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf))*cos(
Bf)*cos(Bf);
Z=y/Nf/cos(Bf);
b2=(0.5+0.003369*cos(Bf)*cos(Bf))*sin(Bf)*cos(Bf);
*cos(b)*cos(b)) *sin(b)*cos(b)*1e-10;
Nf=6399698.902-(21562.267-(108.973-0.612*cos(Bf)*cos(Bf))*cos(Bf)*cos(Bf))*cos(
Bf)*cos(Bf);
Z=y/Nf/cos(Bf);
b2=(0.5+0.003369*cos(Bf)*cos(Bf))*sin(Bf)*cos(Bf);
a5=0.0083-(0.1667-(0.1968+0.0040*cB2)*cB2)*cB2;
// x=X+N*sin(B)*cos(B)*l*l/2+N*sin(B)*pow(cos(B),3)*(5-t*t+9*n2+4*n2*n2)*pow(l,
4)/24+N*sin(B)*pow(cos(B),5)*(61-58*t*t+pow(t,4))*pow(l,6)/720;
a5=0.0083-(0.1667-(0.1968+0.0040*cB2)*cB2)*cB2;
// x=X+N*sin(B)*cos(B)*l*l/2+N*sin(B)*pow(cos(B),3)*(5-t*t+9*n2+4*n2*n2)*pow(l,
4)/24+N*sin(B)*pow(cos(B),5)*(61-58*t*t+pow(t,4))*pow(l,6)/720;
// scanf("x=%f",&x);
// scanf("y=%f",&y);