openlayers加载百度地图作为底图坐标偏移的解决办法

openlayers加载天地图作为底图，在网上找了公开的服务资源，要做到百度地图与天地图之间切换，同样也从网上找到百度地图的服务资源但是在地图上坐标总是有偏差，最初的代码是这样的：

var projection = ol.proj.get("EPSG:3857");       //加载百度地图采用3857坐标系
var resolutions = [];
for(var i=0; i<19; i++){
    resolutions[i] = Math.pow(2, 18-i);
}
var tilegrid  = new ol.tilegrid.TileGrid({
    origin: [2200,23],
    resolutions: resolutions
});
var baidu_source = new ol.source.TileImage({
    projection: "EPSG:3857",
    tileGrid: tilegrid,
    tileUrlFunction: function(tileCoord, pixelRatio, proj){
        if(!tileCoord){
            return "";
        }
        var z = tileCoord[0];
        var x = tileCoord[1];
        var y = tileCoord[2];
        console.log(x+" "+y+" "+z);
        if(x<0){
            x = "M"+(-x);
        }
        if(y<0){
            y = "M"+(-y);
        }
        return "http://online3.map.bdimg.com/onlinelabel/?qt=tile&x="+x+"&y="+y+"&z="+z+"&styles=pl&udt=20151021&scaler=1&p=1";
    }
});
var baidu = new ol.layer.Tile({
    title : "百度地图卫星服务",
    source : baidu_source
});
var map = new ol.Map({
    layers: [
       baidu
    ],
    // 设置显示地图的视图
    view: new ol.View({
        center: [120.65527228569908, 31.296768058299392],
        projection: 'EPSG:4326',                       //指定投影采用4326坐标系
        zoom: 13               // 并且定义地图显示层级为13
    }),
    target: 'map'
});

采用上面的方式加载，百度地图能够加载出来，但是与天地图总是会存在坐标上的偏移，原因是百度地图的坐标系很特殊，采用加密之后的BD-09坐标系，因此要想在地图上正常显示出来，必须转换成3857坐标系，但是转换之后还是有偏差；经过处理方法，转换成baiduMercator 投影后发现偏差比3857坐标系小了很多，经过处理后的代码是这样的：

var forEachPoint = function(func) {
  return function(input, opt_output, opt_dimension) {
    var len = input.length;
    var dimension = opt_dimension ? opt_dimension : 2;
    var output;
    if (opt_output) {
      output = opt_output;
    } else {
      if (dimension !== 2) {
        output = input.slice();
      } else {
        output = new Array(len);
      }
    }
    for (var offset = 0; offset < len; offset += dimension) {
      func(input, output, offset)
    }
    return output;
  };
};

var sphericalMercator = {}

var RADIUS = 6378137;
var MAX_LATITUDE = 85.0511287798;
var RAD_PER_DEG = Math.PI / 180;

sphericalMercator.forward = forEachPoint(function(input, output, offset) {
  var lat = Math.max(Math.min(MAX_LATITUDE, input[offset + 1]), -MAX_LATITUDE);
  var sin = Math.sin(lat * RAD_PER_DEG);

  output[offset] = RADIUS * input[offset] * RAD_PER_DEG;
  output[offset + 1] = RADIUS * Math.log((1 + sin) / (1 - sin)) / 2;
});

sphericalMercator.inverse = forEachPoint(function(input, output, offset) {
  output[offset] = input[offset] / RADIUS / RAD_PER_DEG;
  output[offset + 1] = (2 * Math.atan(Math.exp(input[offset + 1] / RADIUS)) - (Math.PI / 2)) / RAD_PER_DEG;
});


var baiduMercator = {}

var MCBAND = [12890594.86, 8362377.87,
    5591021, 3481989.83, 1678043.12, 0];

var LLBAND = [75, 60, 45, 30, 15, 0];

var MC2LL = [
    [1.410526172116255e-8, 0.00000898305509648872, -1.9939833816331,
        200.9824383106796, -187.2403703815547, 91.6087516669843,
        -23.38765649603339, 2.57121317296198, -0.03801003308653,
        17337981.2],
    [-7.435856389565537e-9, 0.000008983055097726239,
        -0.78625201886289, 96.32687599759846, -1.85204757529826,
        -59.36935905485877, 47.40033549296737, -16.50741931063887,
        2.28786674699375, 10260144.86],
    [-3.030883460898826e-8, 0.00000898305509983578, 0.30071316287616,
        59.74293618442277, 7.357984074871, -25.38371002664745,
        13.45380521110908, -3.29883767235584, 0.32710905363475,
        6856817.37],
    [-1.981981304930552e-8, 0.000008983055099779535, 0.03278182852591,
        40.31678527705744, 0.65659298677277, -4.44255534477492,
        0.85341911805263, 0.12923347998204, -0.04625736007561,
        4482777.06],
    [3.09191371068437e-9, 0.000008983055096812155, 0.00006995724062,
        23.10934304144901, -0.00023663490511, -0.6321817810242,
        -0.00663494467273, 0.03430082397953, -0.00466043876332,
        2555164.4],
    [2.890871144776878e-9, 0.000008983055095805407, -3.068298e-8,
        7.47137025468032, -0.00000353937994, -0.02145144861037,
        -0.00001234426596, 0.00010322952773, -0.00000323890364,
        826088.5]];

var LL2MC = [
    [-0.0015702102444, 111320.7020616939, 1704480524535203,
        -10338987376042340, 26112667856603880,
        -35149669176653700, 26595700718403920,
        -10725012454188240, 1800819912950474, 82.5],
    [0.0008277824516172526, 111320.7020463578, 647795574.6671607,
        -4082003173.641316, 10774905663.51142, -15171875531.51559,
        12053065338.62167, -5124939663.577472, 913311935.9512032,
        67.5],
    [0.00337398766765, 111320.7020202162, 4481351.045890365,
        -23393751.19931662, 79682215.47186455, -115964993.2797253,
        97236711.15602145, -43661946.33752821, 8477230.501135234,
        52.5],
    [0.00220636496208, 111320.7020209128, 51751.86112841131,
        3796837.749470245, 992013.7397791013, -1221952.21711287,
        1340652.697009075, -620943.6990984312, 144416.9293806241,
        37.5],
    [-0.0003441963504368392, 111320.7020576856, 278.2353980772752,
        2485758.690035394, 6070.750963243378, 54821.18345352118,
        9540.606633304236, -2710.55326746645, 1405.483844121726,
        22.5],
    [-0.0003218135878613132, 111320.7020701615, 0.00369383431289,
        823725.6402795718, 0.46104986909093, 2351.343141331292,
        1.58060784298199, 8.77738589078284, 0.37238884252424, 7.45]];


function getRange(v, min, max) {
  v = Math.max(v, min);
  v = Math.min(v, max);

  return v;
}

function getLoop(v, min, max) {
  var d = max - min;
  while (v > max) {
    v -= d;
  }
  while (v < min) {
    v += d;
  }

  return v;
}

function convertor(input, output, offset, table) {
  var px = input[offset];
  var py = input[offset + 1];
  var x = table[0] + table[1] * Math.abs(px);
  var d = Math.abs(py) / table[9];
  var y = table[2]
      + table[3]
      * d
      + table[4]
      * d
      * d
      + table[5]
      * d
      * d
      * d
      + table[6]
      * d
      * d
      * d
      * d
      + table[7]
      * d
      * d
      * d
      * d
      * d
      + table[8]
      * d
      * d
      * d
      * d
      * d
      * d;

  output[offset] = x * (px < 0 ? -1 : 1);
  output[offset + 1] = y * (py < 0 ? -1 : 1);
}

baiduMercator.forward = forEachPoint(function(input, output, offset) {
  var lng = getLoop(input[offset], -180, 180);
  var lat = getRange(input[offset + 1], -74, 74);

  var table = null;
  var j;
  for (j = 0; j < LLBAND.length; ++j) {
    if (lat >= LLBAND[j]) {
      table = LL2MC[j];
      break;
    }
  }
  if (table === null) {
    for (j = LLBAND.length - 1; j >= 0; --j) {
      if (lat <= -LLBAND[j]) {
        table = LL2MC[j];
        break;
      }
    }
  }
  output[offset] = lng;
  output[offset + 1] = lat;
  convertor(output, output, offset, table);
});

baiduMercator.inverse = forEachPoint(function(input, output, offset) {
  var y_abs = Math.abs(input[offset + 1]);

  var table = null;
  for (var j = 0; j < MCBAND.length; j++) {
    if (y_abs >= MCBAND[j]) {
      table = MC2LL[j];
      break;
    }
  }

  convertor(input, output, offset, table);
});

var gcj02 = {}

var PI = Math.PI;
var AXIS = 6378245.0;
var OFFSET = 0.00669342162296594323;  // (a^2 - b^2) / a^2

function delta(wgLon, wgLat) {
  var dLat = transformLat(wgLon - 105.0, wgLat - 35.0);
  var dLon = transformLon(wgLon - 105.0, wgLat - 35.0);
  var radLat = wgLat / 180.0 * PI;
  var magic = Math.sin(radLat);
  magic = 1 - OFFSET * magic * magic;
  var sqrtMagic = Math.sqrt(magic);
  dLat = (dLat * 180.0) / ((AXIS * (1 - OFFSET)) / (magic * sqrtMagic) * PI);
  dLon = (dLon * 180.0) / (AXIS / sqrtMagic * Math.cos(radLat) * PI);
  return [dLon, dLat];
}

function outOfChina(lon, lat) {
  if (lon < 72.004 || lon > 137.8347) {
    return true;
  }
  if (lat < 0.8293 || lat > 55.8271) {
    return true;
  }
  return false;
}

function transformLat(x, y) {
  var ret = -100.0 + 2.0 * x + 3.0 * y + 0.2 * y * y + 0.1 * x * y + 0.2 * Math.sqrt(Math.abs(x));
  ret += (20.0 * Math.sin(6.0 * x * PI) + 20.0 * Math.sin(2.0 * x * PI)) * 2.0 / 3.0;
  ret += (20.0 * Math.sin(y * PI) + 40.0 * Math.sin(y / 3.0 * PI)) * 2.0 / 3.0;
  ret += (160.0 * Math.sin(y / 12.0 * PI) + 320 * Math.sin(y * PI / 30.0)) * 2.0 / 3.0;
  return ret;
}

function transformLon(x, y) {
  var ret = 300.0 + x + 2.0 * y + 0.1 * x * x + 0.1 * x * y + 0.1 * Math.sqrt(Math.abs(x));
  ret += (20.0 * Math.sin(6.0 * x * PI) + 20.0 * Math.sin(2.0 * x * PI)) * 2.0 / 3.0;
  ret += (20.0 * Math.sin(x * PI) + 40.0 * Math.sin(x / 3.0 * PI)) * 2.0 / 3.0;
  ret += (150.0 * Math.sin(x / 12.0 * PI) + 300.0 * Math.sin(x / 30.0 * PI)) * 2.0 / 3.0;
  return ret;
}

gcj02.toWGS84 = forEachPoint(function(input, output, offset) {
  var lng = input[offset];
  var lat = input[offset + 1];
  if (!outOfChina(lng, lat)) {
    var deltaD = delta(lng, lat);
    lng = lng - deltaD[0];
    lat = lat - deltaD[1];
  }
  output[offset] = lng;
  output[offset + 1] = lat;
});

gcj02.fromWGS84 = forEachPoint(function(input, output, offset) {
  var lng = input[offset];
  var lat = input[offset + 1];
  if (!outOfChina(lng, lat)) {
    var deltaD = delta(lng, lat);
    lng = lng + deltaD[0];
    lat = lat + deltaD[1];
  }
  output[offset] = lng;
  output[offset + 1] = lat;
});

var bd09 = {}

var PI = Math.PI;
var X_PI = PI * 3000 / 180;

function toGCJ02(input, output, offset) {
  var x = input[offset] - 0.0065;
  var y = input[offset + 1] - 0.006;
  var z = Math.sqrt(x * x + y * y) - 0.00002 * Math.sin(y * X_PI);
  var theta = Math.atan2(y, x) - 0.000003 * Math.cos(x * X_PI);
  output[offset] = z * Math.cos(theta);
  output[offset + 1] = z * Math.sin(theta);
  return output;
}

function fromGCJ02(input, output, offset) {
  var x = input[offset];
  var y = input[offset + 1];
  var z = Math.sqrt(x * x + y * y) + 0.00002 * Math.sin(y * X_PI);
  var theta = Math.atan2(y, x) + 0.000003 * Math.cos(x * X_PI);
  output[offset] = z * Math.cos(theta) + 0.0065;
  output[offset + 1] = z * Math.sin(theta) + 0.006;
  return output;
}

bd09.toWGS84 = function(input, opt_output, opt_dimension) {
  var output = forEachPoint(toGCJ02)(input, opt_output, opt_dimension);
  return gcj02.toWGS84(output, output, opt_dimension);
};

bd09.fromWGS84 = function(input, opt_output, opt_dimension) {
  var output = gcj02.fromWGS84(input, opt_output, opt_dimension);
  return forEachPoint(fromGCJ02)(output, output, opt_dimension);
};


var projzh = {}

projzh.smerc2bmerc = function(input, opt_output, opt_dimension) {
  var output = sphericalMercator.inverse(input, opt_output, opt_dimension);
  output = bd09.fromWGS84(output, output, opt_dimension);
  return baiduMercator.forward(output, output, opt_dimension);
};

projzh.bmerc2smerc = function(input, opt_output, opt_dimension) {
  var output = baiduMercator.inverse(input, opt_output, opt_dimension);
  output = bd09.toWGS84(output, output, opt_dimension);
  return sphericalMercator.forward(output, output, opt_dimension);
};

projzh.bmerc2ll = function(input, opt_output, opt_dimension) {
  var output = baiduMercator.inverse(input, opt_output, opt_dimension);
  return bd09.toWGS84(output, output, opt_dimension);
};

projzh.ll2bmerc = function(input, opt_output, opt_dimension) {
  var output = bd09.fromWGS84(input, opt_output, opt_dimension);
  return baiduMercator.forward(output, output, opt_dimension);
};

projzh.ll2smerc = sphericalMercator.forward;
projzh.smerc2ll = sphericalMercator.inverse;



var extent = [72.004, 0.8293, 137.8347, 55.8271];

var baiduMercatorProj = new ol.proj.Projection({
  code: 'baidu',
  extent: ol.extent.applyTransform(extent, projzh.ll2bmerc),
  units: 'm'
});

ol.proj.addProjection(baiduMercatorProj);
ol.proj.addCoordinateTransforms('EPSG:4326', baiduMercatorProj, projzh.ll2bmerc, projzh.bmerc2ll);
ol.proj.addCoordinateTransforms('EPSG:3857', baiduMercatorProj, projzh.smerc2bmerc, projzh.bmerc2smerc);

var bmercResolutions = new Array(19);
for (var i = 0; i < 19; ++i) {
  bmercResolutions[i] = Math.pow(2, 18 - i);
}
var baidu = new ol.layer.Tile({
  source: new ol.source.XYZ({
    projection: 'baidu',
    maxZoom: 18,
    tileUrlFunction: function(tileCoord) {
      var x = tileCoord[1];
      var y = tileCoord[2];
      var z = tileCoord[0];
      return "http://api0.map.bdimg.com/customimage/tile?x=" + x
        + "&y=" + y + "&z=" + z
        + "&udt=20170908&scale=2&ak=ZUONbpqGBsYGXNIYHicvbAbM"
        + "&styles=t%3Awater%7Ce%3Aall%7Cc%3A%23044161%2Ct%3Aland%7Ce%3Aall%7Cc%3A%23004981%2Ct%3Aboundary%7Ce%3Ag%7Cc%3A%23064f85%2Ct%3Arailway%7Ce%3Aall%7Cv%3Aoff%2Ct%3Ahighway%7Ce%3Ag%7Cc%3A%23004981%2Ct%3Ahighway%7Ce%3Ag.f%7Cc%3A%23005b96%7Cl%3A1%2Ct%3Ahighway%7Ce%3Al%7Cv%3Aoff%2Ct%3Aarterial%7Ce%3Ag%7Cc%3A%23004981%2Ct%3Aarterial%7Ce%3Ag.f%7Cc%3A%2300508b%2Ct%3Apoi%7Ce%3Aall%7Cv%3Aoff%2Ct%3Agreen%7Ce%3Aall%7Cv%3Aoff%7Cc%3A%23056197%2Ct%3Asubway%7Ce%3Aall%7Cv%3Aoff%2Ct%3Amanmade%7Ce%3Aall%7Cv%3Aoff%2Ct%3Alocal%7Ce%3Aall%7Cv%3Aoff%2Ct%3Aarterial%7Ce%3Al%7Cv%3Aoff%2Ct%3Aboundary%7Ce%3Ag.f%7Cc%3A%23029fd4%2Ct%3Abuilding%7Ce%3Aall%7Cc%3A%231a5787%2Ct%3Alabel%7Ce%3Aall%7Cv%3Aoff&t = 1505487396397";;
    },
    tileGrid: new ol.tilegrid.TileGrid({
      resolutions: bmercResolutions,
      origin: [0, 0],
      extent: ol.extent.applyTransform(extent, projzh.ll2bmerc),
      tileSize: [256, 256]
    })
  })
});

参考网址：https://segmentfault.com/a/1190000011195549

把BD-09坐标转换成baiduMercator 投影后，发现坐标偏移真的减少了很多，这样百度地图终于可以加进来了。。
同时，我也总结出来一个问题，初始化地图使用的坐标系和定义图层的坐标系并不是一回事，初始化地图只是声明地图的加载方式采用什么方式，以及加载上地图上的要素采用什么坐标系显示。。。

github上面发现了一个添加百度地图的例子，具体网址请参考：
https://github.com/openlayers/openlayers/issues/3522