经纬度坐标转换高斯-克吕格平面坐标

原作者链接：https://blog.csdn.net/jianyi7659/article/details/7583339

前言

支持将地理坐标（经纬度坐标）转换到高斯-克吕格投影下的平面坐标，如北京54平面坐标、西安80平面坐标、大地2000平面坐标。

主要代码

代码已经封装成了dojo模块(类)，方便在使用ArcGIS JS API时引用该坐标转换模块。

LatLong2GaussKruger.js

/**
 * WGS-84椭球经纬度坐标转高斯-克吕格平面坐标
 */
define(["dojo/_base/declare"], function (declare) {
    return declare(null, {
        //基本变量定义
        a: 0,//'椭球体长半轴
        b: 0,// '椭球体短半轴
        f: 0, //'扁率
        e: 0,// '第一偏心率
        e: 0, //'第二偏心率

        FE: 0,//'东偏移
        FN: 0,//'北偏移
        L0: 0,//'中央经度
        W0: 0,//'原点纬线
        k0: 0,//'比例因子
        // PI: 3.14159265358979,

        /**
         * 用于初始化椭球参数
         * @param {*} TuoqiuCanshu 枚举类型，提供北京54、西安80、WGS84、CGCS2000椭球参数
         * @param {*} CentralMeridian 中央经线
         * @param {*} OriginLatitude 原点纬度，如果是标准的分幅，则该参数是0
         * @param {*} EastOffset 东偏移
         * @param {*} NorthOffset 北偏移
         */
        constructor: function (TuoqiuCanshu, CentralMeridian, OriginLatitude, EastOffset, NorthOffset) {
            /*
             *  Canshu
             *  Beijing54 = 0;Krassovsky （北京54采用） 6378245 6356863.0188
                Xian80 = 1;IAG 75（西安80采用） 6378140 6356755.2882
                WGS84 = 2;WGS 84 6378137 6356752.3142
                CGCS2000 = 3
            */
           if (TuoqiuCanshu == 0)//北京五四
            {
                a = 6378245;
                b = 6356863.0188;
            }
            if (TuoqiuCanshu == 1)// '西安八零
            {
                a = 6378140;
                b = 6356755.2882;
            }
            if (TuoqiuCanshu == 2)//'WGS84
            {
                a = 6378137;
                b = 6356752.3142;
            }
            if (TuoqiuCanshu == 3)//'CGCS2000
            {
                a = 6378137;
                b = 6356752.314140356;
            }
            f = (a - b) / a;//扁率
            //e = Math.sqrt(1 - Math.pow((b / a) ,2));//'第一偏心率
            e = Math.sqrt(2 * f - Math.pow(f, 2));//'第一偏心率

            //eq = Math.sqrt(Math.pow((a / b) , 2) - 1);//'第二偏心率
            e1 = e / Math.sqrt(1 - Math.pow(e, 2));//'第二偏心率

            L0 = CentralMeridian;//中央经
            W0 = OriginLatitude;//原点纬线
            k0 = 1;//'比例因子
            FE = EastOffset;//东偏移
            FN = NorthOffset;//北偏移
        },
        /**
         * 经纬度转高斯-克吕格平面坐标
         * @param {*} J 经度
         * @param {*} W 维度
         */
        JWgetGK: function (J, W) {
            //'给出经纬度坐标，转换为高克投影坐标
            var resultP = {};
            var BR = (W - W0) * Math.PI / 180;//纬度弧长
            var lo = (J - L0) * Math.PI / 180; //经差弧度

            var N = a / Math.sqrt(1 - Math.pow((e * Math.sin(BR)), 2)) //卯酉圈曲率半径

            //求解参数s
            var B0;
            var B2;
            var B4;
            var B6;
            var B8;
            var C = Math.pow(a, 2) / b;
            B0 = 1 - 3 * Math.pow(e1, 2) / 4 + 45 * Math.pow(e1, 4) / 64 - 175 * Math.pow(e1, 6) / 256 + 11025 * Math.pow(e1, 8) / 16384;
            B2 = B0 - 1
            B4 = 15 / 32 * Math.pow(e1, 4) - 175 / 384 * Math.pow(e1, 6) + 3675 / 8192 * Math.pow(e1, 8);
            B6 = 0 - 35 / 96 * Math.pow(e1, 6) + 735 / 2048 * Math.pow(e1, 8);
            B8 = 315 / 1024 * Math.pow(e1, 8);
            s = C * (B0 * BR + Math.sin(BR) * (B2 * Math.cos(BR) + B4 * Math.pow((Math.cos(BR)), 3) + B6 * Math.pow((Math.cos(BR)), 5) + B8 * Math.pow((Math.cos(BR)), 7)));

            var t = Math.tan(BR);
            var g = e1 * Math.cos(BR);

            var XR = s + Math.pow(lo, 2) / 2 * N * Math.sin(BR) * Math.cos(BR) + Math.pow(lo, 4) * N * Math.sin(BR) * Math.pow((Math.cos(BR)), 3) / 24 * (5 - Math.pow(t, 2) + 9 * Math.pow(g, 2) + 4 * Math.pow(g, 4)) + Math.pow(lo, 6) * N * Math.sin(BR) * Math.pow((Math.cos(BR)), 5) * (61 - 58 * Math.pow(t, 2) + Math.pow(t, 4)) / 720;
            var YR = lo * N * Math.cos(BR) + Math.pow(lo, 3) * N / 6 * Math.pow((Math.cos(BR)), 3) * (1 - Math.pow(t, 2) + Math.pow(g, 2)) + Math.pow(lo, 5) * N / 120 * Math.pow((Math.cos(BR)), 5) * (5 - 18 * Math.pow(t, 2) + Math.pow(t, 4) + 14 * Math.pow(g, 2) - 58 * Math.pow(g, 2) * Math.pow(t, 2));

            resultP.x = YR + FE;
            resultP.y = XR + FN;
            return resultP;
        },
        /**
         * 高斯-克吕格平面转经纬度坐标
         * @param {*} X  
         * @param {*} Y 
         */
        GKgetJW: function (X, Y) {
            //'给出高克投影坐标，转换为经纬度坐标
            var resultP = {};
            var El1 = (1 - Math.sqrt(1 - Math.pow(e, 2))) / (1 + Math.sqrt(1 - Math.pow(e, 2)));

            var Mf = (Y - FN) / k0;//真实坐标值

            var Q = Mf / (a * (1 - Math.pow(e, 2) / 4 - 3 * Math.pow(e, 4) / 64 - 5 * Math.pow(e, 6) / 256));//角度

            Bf = Q + (3 * El1 / 2 - 27 * Math.pow(El1, 3) / 32) * Math.sin(2 * Q) + (21 * Math.pow(El1, 2) / 16 - 55 * Math.pow(El1, 4) / 32) * Math.sin(4 * Q) + (151 * Math.pow(El1, 3) / 96) * Math.sin(6 * Q) + 1097 / 512 * Math.pow(El1, 4) * Math.sin(8 * Q);
            Rf = a * (1 - Math.pow(e, 2)) / Math.sqrt(Math.pow((1 - Math.pow((e * Math.sin(Bf)), 2)), 3));
            Nf = a / Math.sqrt(1 - Math.pow((e * Math.sin(Bf)), 2));//卯酉圈曲率半径
            Tf = Math.pow((Math.tan(Bf)), 2);
            D = (X - FE) / (k0 * Nf);

            Cf = Math.pow(e1, 2) * Math.pow((Math.cos(Bf)), 2);

            var B = Bf - Nf * Math.tan(Bf) / Rf * (Math.pow(D, 2) / 2 - (5 + 3 * Tf + 10 * Cf - 9 * Tf * Cf - 4 * Math.pow(Cf, 2) - 9 * Math.pow(e1, 2)) * Math.pow(D, 4) / 24 + (61 + 90 * Tf + 45 * Math.pow(Tf, 2) - 256 * Math.pow(e1, 2) - 3 * Math.pow(Cf, 2)) * Math.pow(D, 6) / 720);
            var L = CentralMeridian * Math.PI / 180 + 1 / Math.cos(Bf) * (D - (1 + 2 * Tf + Cf) * Math.pow(D, 3) / 6 + (5 - 2 * Cf + 28 * Tf - 3 * Math.pow(Cf, 2) + 8 * Math.pow(e1, 2) + 24 * Math.pow(Tf, 2)) * Math.pow(D, 5) / 120);

            var Bangle = B * 180 / Math.PI;
            var Langle = L * 180 / Math.PI;

            resultP.x = Langle;//RW * 180 / Math.PI;
            resultP.y = Bangle + W0;//RJ * 180 / Math.PI;
            return resultP;
        }
    });
});

使用示例

<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <meta http-equiv="X-UA-Compatible" content="ie=edge">
    <title>坐标转换模块title>
    <link rel="stylesheet" href="https://js.arcgis.com/4.11/esri/themes/light/main.css" />
head>
<style>
    html,
    body,
    #viewDiv {
        height: 100%;
        width: 100%;
        margin: 0;
        padding: 0;
    }
    .horizontal-toolbar{
        position: absolute;
        top: 30px;
        right: 75px;
        /* width: 100px; */
        height: 50px;
        overflow: hidden;
        background-color: white;
        border-radius: 4px;
        z-index: 100;
    }
    .horizontal-toolbar>li{
        position: relative;
        margin: 5px;
        list-style: none; 
        float: left;
        width: 46px;
        height: 46px;
    }
style>
<script>
    var package_path = window.location.pathname.substring(0, window.location.pathname.lastIndexOf('/'));
    //var package_path = window.location.pathname.replace(/\/[^\/]*$/,"");
    var dojoConfig = {
        packages: [{
            name: "modules",
            location: package_path + '/modules'
        }]
    };
script>
<script src="https://js.arcgis.com/4.12/">script>
<script>
    var map,measureTool;
    require([
        "modules/LatLong2GaussKruger",
        "esri/Map",
        "esri/views/MapView",
        "esri/config"
    ], function (LatLong2GaussKruger, Map, MapView, esriConfig) {
        const map = new Map({
          basemap: "streets",
        });

        const view = new MapView({
          container: "viewDiv",
          map: map,
          zoom: 5,
          center: [90, 45]
        });

        convertTool = new LatLong2GaussKruger(3,114,0,500000,0);
    });
    function convert () {
        console.log("经纬度坐标：113.554688,22.25256")
        let coord = convertTool.JWgetGK(113.554688,22.25256);
        console.log("转换后：" + coord.x + "," + coord.y);
    }
script>
<body>
    <div id="viewDiv" style="position:relative;">
        <ul class="horizontal-toolbar">
            <li onclick="convert()">坐标转换
            li>
        ul>
    div>
body>
html>

经过与ArcGIS Server的几何服务投影功能的结果对比，结果 <0.0001

参考链接

https://blog.csdn.net/jianyi7659/article/details/7583339