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中国地图偏移算法

中国地图偏移算法

WGS-84 坐标系,是 GPS 系统所采用的坐标系。一切正常工作的 GPS 或 GPS 芯片所返回的坐标值都是这个坐标系下的数值。Google 地图采用的卫星图也是按照这个坐标系摆放的。

GCJ-02 坐标系,是我天朝政府搞出来的加密坐标系,也常常被称为“火星坐标系”。包括(但可能不限于)高德地图在内的国内地图服务商采用它来绘制地图。Apple、Google等国外公司在其道路地图中使用的也是高德的数据。BD-09 坐标系则是百度地图专用的坐标系。

在开发一些 LBS 应用时,如果不加处理,很容易出现几种形式的地图之间出现偏移的情况。因此在这几个坐标系之间进行转换非常重要。以下代码就是网络上泄露出的从 WGS-84 转 GCJ-02 的算法,以及 GCJ-02 与 BD-09 的互相转换算法。

另外,代码中的从 GCJ-02 到 WGS-84 的逆变换是我用迭代法实现的。实验证明,由于原变换的局部线性性非常好,只要迭代两次(调用原变换三次),经纬度就可以达到大约 1e-8 度的精度(相当于毫米级精度)。所以运行速度不会太慢,对于一般应用足矣。

全部代码也可以在 GitHub 下载:https://github.com/fengzee-me/ChinaMapShift(已404)。代码和其编译出的 libChinaMapShift.a 库文件直接适用于 iOS 环境下,需要在其他平台下运行时,可以自行编译(源代码完全是原生 C 代码,只需要 math.h 库)。

源文件C

//
//  ChinaMapShift.h
//  ChinaMapShift
//
//  Most code created by someone anonymous.
//  transformFromGCJToWGS() added by Fengzee (fengzee@fengzee.com).
//
 
#ifndef ChinaMapShift_ChinaMapShift_h
#define ChinaMapShift_ChinaMapShift_h
 
typedef struct {
    double lng;
    double lat;
} Location;
 
Location transformFromWGSToGCJ(Location wgLoc);
Location transformFromGCJToWGS(Location gcLoc);
Location bd_encrypt(Location gcLoc);
Location bd_decrypt(Location bdLoc);
 
#endif
//
//  ChinaMapShift.mm
//  ChinaMapShift
//
//  Most code created by someone anonymous.
//  transformFromGCJToWGS() added by Fengzee (fengzee@fengzee.com).
//
 
#include "ChinaMapShift.h"
#include <math.h>
 
inline Location
LocationMake(double lng, double lat) {
    Location loc; loc.lng = lng, loc.lat = lat; return loc;
}
 
///
///  Transform WGS-84 to GCJ-02 (Chinese encrypted coordination system)
///
 
const double pi = 3.14159265358979324;
 
//
// Krasovsky 1940
//
// a = 6378245.0, 1/f = 298.3
// b = a * (1 - f)
// ee = (a^2 - b^2) / a^2;
const double a = 6378245.0;
const double ee = 0.00669342162296594323;
 
int outOfChina(double lat, double lon)
{
    if (lon < 72.004 || lon > 137.8347)
        return 1;
    if (lat < 0.8293 || lat > 55.8271)
        return 1;
    return 0;
}
 
double transformLat(double x, double y)
{
    double ret = -100.0 + 2.0 * x + 3.0 * y + 0.2 * y * y + 0.1 * x * y + 0.2 * sqrt(x > 0 ? x:-x);
    ret += (20.0 * sin(6.0 * x * pi) + 20.0 *sin(2.0 * x * pi)) * 2.0 / 3.0;
    ret += (20.0 * sin(y * pi) + 40.0 * sin(y / 3.0 * pi)) * 2.0 / 3.0;
    ret += (160.0 * sin(y / 12.0 * pi) + 320 * sin(y * pi / 30.0)) * 2.0 / 3.0;
    return ret;
}
 
double transformLon(double x, double y)
{
    double ret = 300.0 + x + 2.0 * y + 0.1 * x * x + 0.1 * x * y + 0.1 * sqrt(x > 0 ? x:-x);
    ret += (20.0 * sin(6.0 * x * pi) + 20.0 * sin(2.0 * x * pi)) * 2.0 / 3.0;
    ret += (20.0 * sin(x * pi) + 40.0 * sin(x / 3.0 * pi)) * 2.0 / 3.0;
    ret += (150.0 * sin(x / 12.0 * pi) + 300.0 * sin(x / 30.0 * pi)) * 2.0 / 3.0;
    return ret;
}
 
Location transformFromWGSToGCJ(Location wgLoc)
{
    Location mgLoc;
    if (outOfChina(wgLoc.lat, wgLoc.lng))
    {
        mgLoc = wgLoc;
        return mgLoc;
    }
    double dLat = transformLat(wgLoc.lng - 105.0, wgLoc.lat - 35.0);
    double dLon = transformLon(wgLoc.lng - 105.0, wgLoc.lat - 35.0);
    double radLat = wgLoc.lat / 180.0 * pi;
    double magic = sin(radLat);
    magic = 1 - ee * magic * magic;
    double sqrtMagic = sqrt(magic);
    dLat = (dLat * 180.0) / ((a * (1 - ee)) / (magic * sqrtMagic) * pi);
    dLon = (dLon * 180.0) / (a / sqrtMagic * cos(radLat) * pi);
    mgLoc.lat = wgLoc.lat + dLat;
    mgLoc.lng = wgLoc.lng + dLon;
 
    return mgLoc;
}
 
///
///  Transform GCJ-02 to WGS-84
///  Reverse of transformFromWGSToGC() by iteration.
///
///  Created by Fengzee (fengzee@fengzee.com) on 13-11-9.
///
Location transformFromGCJToWGS(Location gcLoc)
{
    Location wgLoc = gcLoc;
    Location currGcLoc, dLoc;
    while (1) {
        currGcLoc = transformFromWGSToGCJ(wgLoc);
        dLoc.lat = gcLoc.lat - currGcLoc.lat;
        dLoc.lng = gcLoc.lng - currGcLoc.lng;
        if (fabs(dLoc.lat) < 1e-7 && fabs(dLoc.lng) < 1e-7) {  // 1e-7 ~ centimeter level accuracy
          // Result of experiment:
          //   Most of the time 2 iterations would be enough for an 1e-8 accuracy (milimeter level).
          //
            return wgLoc;
        }
        wgLoc.lat += dLoc.lat;
        wgLoc.lng += dLoc.lng;
    }
 
    return wgLoc;
}
 
///
///  Transform GCJ-02 to BD-09
///
const double x_pi = 3.14159265358979324 * 3000.0 / 180.0;
Location bd_encrypt(Location gcLoc)
{
    double x = gcLoc.lng, y = gcLoc.lat;
    double z = sqrt(x * x + y * y) + 0.00002 * sin(y * x_pi);
    double theta = atan2(y, x) + 0.000003 * cos(x * x_pi);
    return LocationMake(z * cos(theta) + 0.0065, z * sin(theta) + 0.006);
}
 
///
///  Transform BD-09 to GCJ-02
///
Location bd_decrypt(Location bdLoc)
{
    double x = bdLoc.lng - 0.0065, y = bdLoc.lat - 0.006;
    double z = sqrt(x * x + y * y) - 0.00002 * sin(y * x_pi);
    double theta = atan2(y, x) - 0.000003 * cos(x * x_pi);
    return LocationMake(z * cos(theta), z * sin(theta));
}
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