百度BD09坐标-行列计算

该文章参考网络资料百度地图根据经纬度计算瓦片行列号与百度地图根据经纬度计算瓦片行列号进行整理，感谢作者的睿智。本问仅作个人资料整理记录。
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根据百度经纬度坐标计算该点所在瓦片的行列号的算法好像并没有公开，网上相关资料很少。

通过研究百度地图JavaScript API源代码（经过混淆后的），大致了解计算过程，现将具体过程解释如下：

1.JavaScript API经过混淆后的代码中包含以下三个方法：

convertMC2LL: function(cC) {
	var cD, cF;
	cD = new b4(Math.abs(cC.lng), Math.abs(cC.lat));
	for (var cE = 0; cE < this.MCBAND.length; cE++) {
		if (cD.lat >= this.MCBAND[cE]) {
			cF = this.MC2LL[cE];
			break
		}
	}
	var T = this.convertor(cC, cF);
	var cC = new b4(T.lng.toFixed(6), T.lat.toFixed(6));
	return cC
}
convertLL2MC: function(T) {
	var cC, cE;
	T.lng = this.getLoop(T.lng, -180, 180);
	T.lat = this.getRange(T.lat, -74, 74);
	cC = new b4(T.lng, T.lat);
	for (var cD = 0; cD < this.LLBAND.length; cD++) {
		if (cC.lat >= this.LLBAND[cD]) {
			cE = this.LL2MC[cD];
			break
		}
	}
	if (!cE) {
		for (var cD = this.LLBAND.length - 1; cD >= 0; cD--) {
			if (cC.lat <= -this.LLBAND[cD]) {
				cE = this.LL2MC[cD];
				break
			}
		}
	}
	var cF = this.convertor(T, cE);
	var T = new b4(cF.lng.toFixed(2), cF.lat.toFixed(2));
	return T
}
convertor: function(cD, cE) {
	if (!cD || !cE) {
		return
	}
	var T = cE[0] + cE[1] * Math.abs(cD.lng);
	var cC = Math.abs(cD.lat) / cE[9];
	var cF = cE[2] + cE[3] * cC + cE[4] * cC * cC + cE[5] * cC * cC * cC + cE[6] * cC * cC * cC * cC + cE[7] * cC * cC * cC * cC * cC + cE[8] * cC * cC * cC * cC * cC * cC;
	T *= (cD.lng < 0 ? -1 : 1);
	cF *= (cD.lat < 0 ? -1 : 1);
	return new b4(T, cF)
}

前两个方法分别负责将 墨卡托坐标转换成百度坐标、百度坐标转换成墨卡托坐标。

2.仿照编写出C#版：

//以下是根据百度地图JavaScript API破解得到 百度坐标<->墨卡托坐标 转换算法
private static double[] array1 = { 75, 60, 45, 30, 15, 0 };
private static double[] array3 = { 12890594.86, 8362377.87, 5591021, 3481989.83, 1678043.12, 0 };
private static double[][] array2 = {new double[]{-0.0015702102444, 111320.7020616939, 1704480524535203, -10338987376042340, 26112667856603880, -35149669176653700, 26595700718403920, -10725012454188240, 1800819912950474, 82.5}
                                               ,new double[]{0.0008277824516172526, 111320.7020463578, 647795574.6671607, -4082003173.641316, 10774905663.51142, -15171875531.51559, 12053065338.62167, -5124939663.577472, 913311935.9512032, 67.5}
                                               ,new double[]{0.00337398766765, 111320.7020202162, 4481351.045890365, -23393751.19931662, 79682215.47186455, -115964993.2797253, 97236711.15602145, -43661946.33752821, 8477230.501135234, 52.5}
                                               ,new double[]{0.00220636496208, 111320.7020209128, 51751.86112841131, 3796837.749470245, 992013.7397791013, -1221952.21711287, 1340652.697009075, -620943.6990984312, 144416.9293806241, 37.5}
                                               ,new double[]{-0.0003441963504368392, 111320.7020576856, 278.2353980772752, 2485758.690035394, 6070.750963243378, 54821.18345352118, 9540.606633304236, -2710.55326746645, 1405.483844121726, 22.5}
                                               ,new double[]{-0.0003218135878613132, 111320.7020701615, 0.00369383431289, 823725.6402795718, 0.46104986909093, 2351.343141331292, 1.58060784298199, 8.77738589078284, 0.37238884252424, 7.45}};
private static double[][] array4 = {new double[]{1.410526172116255e-8, 0.00000898305509648872, -1.9939833816331, 200.9824383106796, -187.2403703815547, 91.6087516669843, -23.38765649603339, 2.57121317296198, -0.03801003308653, 17337981.2}
                                               ,new double[]{-7.435856389565537e-9, 0.000008983055097726239, -0.78625201886289, 96.32687599759846, -1.85204757529826, -59.36935905485877, 47.40033549296737, -16.50741931063887, 2.28786674699375, 10260144.86}
                                               ,new double[]{-3.030883460898826e-8, 0.00000898305509983578, 0.30071316287616, 59.74293618442277, 7.357984074871, -25.38371002664745, 13.45380521110908, -3.29883767235584, 0.32710905363475, 6856817.37}
                                               ,new double[]{-1.981981304930552e-8, 0.000008983055099779535, 0.03278182852591, 40.31678527705744, 0.65659298677277, -4.44255534477492, 0.85341911805263, 0.12923347998204, -0.04625736007561, 4482777.06}
                                               ,new double[]{3.09191371068437e-9, 0.000008983055096812155, 0.00006995724062, 23.10934304144901, -0.00023663490511, -0.6321817810242, -0.00663494467273, 0.03430082397953, -0.00466043876332, 2555164.4}
                                               ,new double[]{2.890871144776878e-9, 0.000008983055095805407, -3.068298e-8, 7.47137025468032, -0.00000353937994, -0.02145144861037, -0.00001234426596, 0.00010322952773, -0.00000323890364, 826088.5}};
//百度坐标转墨卡托
private static PointF LatLng2Mercator(LatLngPoint p)
{
    double[] arr = null;
    double n_lat = p.Lat > 74 ? 74 : p.Lat;
    n_lat = n_lat < -74 ? -74 : n_lat;
    for (var i = 0; i < array1.Length; i++) 
    {
        if (p.Lat >= array1[i]) 
        {
            arr = array2[i];
            break;
        }
    }
    if (arr == null)     {
        for (var i = array1.Length - 1; i >= 0; i--)         {
            if (p.Lat <= -array1[i]) 
            {
                arr = array2[i];
                break;
            }
        }
    }
    double[] res = Convertor(p.Lng, p.Lat, arr);
    return new PointF((float)res[0], (float)res[1]);
}//墨卡托坐标转百度
private static LatLngPoint Mercator2LatLng(PointF p)
{
    double[] arr = null;
    PointF np = new PointF(Math.Abs(p.X),Math.Abs(p.Y));
    for (var i = 0; i < array3.Length; i++)     {
        if (np.Y >= array3[i]) 
        {
            arr = array4[i];
            break;
        }
   }
   double[] res = Convertor(np.X, np.Y, arr);
   return new LatLngPoint(res[0],res[1]);
}
private static double[] Convertor(double x, double y, double[] param)
{
    var T = param[0] + param[1] * Math.Abs(x);
    var cC = Math.Abs(y) / param[9];
    var cF = param[2] + param[3] * cC + param[4] * cC * cC + param[5] * cC * cC * cC + param[6] * cC * cC * cC * cC + param[7] * cC * cC * cC * cC * cC + param[8] * cC * cC * cC * cC * cC * cC;
    T *= (x < 0 ? -1 : 1);
    cF *= (y < 0 ? -1 : 1);
    return new double[] { T, cF };
}

3.根据百度经纬度计算出来墨卡托坐标后，将结果除以地图分辨率Math.Pow(2,18-zoom)即可得到平面像素坐标，然后将像素坐标除以256分别得到瓦片的行列号。

经测试，误差为0。

注意：
一下附加java版本后台行列处理代码

		double lat = -34.7715d;
        double lon = -113.7276d;

        System.out.println("经纬度坐标x--->"+lon);
        System.out.println("经纬度坐标y--->"+lat);

        Map<String, Double> stringDoubleMap = BDMercatorToLonLatAll.convertLonLatToMC(lon, lat);
        //System.out.println("墨卡托坐标--->"+stringDoubleMap);

        Double xMC = stringDoubleMap.get("x");
        Double yMC = stringDoubleMap.get("y");
        System.out.println("墨卡托坐标x--->"+xMC);
        System.out.println("墨卡托坐标y--->"+yMC);

        //根据百度经纬度计算出来墨卡托坐标后，将结果除以地图分辨率Math.Pow(2,18-zoom)即可得到平面像素坐标，然后将像素坐标除以256分别得到瓦片的行列号。

        int zoom = 13;
        System.out.println("地图层级--->"+zoom);

        double dpi = Math.pow(2, 18 - zoom);
        System.out.println("地图分辨率--->"+dpi);

        double xPlanePixelCoordinates = xMC / dpi;
        double yPlanePixelCoordinates = yMC / dpi;
        System.out.println("平面像素坐标x--->"+xPlanePixelCoordinates);
        System.out.println("平面像素坐标y--->"+yPlanePixelCoordinates);

        int tileImgDpi = 256;
        System.out.println("瓦片大小--->"+tileImgDpi);

        double xTile = xPlanePixelCoordinates / tileImgDpi;
        double yTile = yPlanePixelCoordinates / tileImgDpi;
        //System.out.println("瓦片行列号x--->"+xTile);
        //System.out.println("瓦片行列号y--->"+yTile);

        int xTileI = (int) xTile;
        int yTileI = (int) yTile;
        System.out.println("瓦片行列号x--->"+xTileI);
        System.out.println("瓦片行列号y--->"+yTileI);

java版本验证代码（参照上面所描述的第三段）

		double lat = -34.7715d;
        double lon = -113.7276d;

        System.out.println("经纬度坐标x--->"+lon);
        System.out.println("经纬度坐标y--->"+lat);

        Map<String, Double> stringDoubleMap = BDMercatorToLonLatAll.convertLonLatToMC(lon, lat);
        //System.out.println("墨卡托坐标--->"+stringDoubleMap);

        Double xMC = stringDoubleMap.get("x");
        Double yMC = stringDoubleMap.get("y");
        System.out.println("墨卡托坐标x--->"+xMC);
        System.out.println("墨卡托坐标y--->"+yMC);

        //根据百度经纬度计算出来墨卡托坐标后，将结果除以地图分辨率Math.Pow(2,18-zoom)即可得到平面像素坐标，然后将像素坐标除以256分别得到瓦片的行列号。

        int zoom = 13;
        System.out.println("地图层级--->"+zoom);

        double dpi = Math.pow(2, 18 - zoom);
        System.out.println("地图分辨率--->"+dpi);

        double xPlanePixelCoordinates = xMC / dpi;
        double yPlanePixelCoordinates = yMC / dpi;
        System.out.println("平面像素坐标x--->"+xPlanePixelCoordinates);
        System.out.println("平面像素坐标y--->"+yPlanePixelCoordinates);

        int tileImgDpi = 256;
        System.out.println("瓦片大小--->"+tileImgDpi);

        double xTile = xPlanePixelCoordinates / tileImgDpi;
        double yTile = yPlanePixelCoordinates / tileImgDpi;
        //System.out.println("瓦片行列号x--->"+xTile);
        //System.out.println("瓦片行列号y--->"+yTile);

        int xTileI = (int) xTile;
        int yTileI = (int) yTile;
        System.out.println("瓦片行列号x--->"+xTileI);
        System.out.println("瓦片行列号y--->"+yTileI);