GIS理论（墨卡托投影、地理坐标系、地面分辨率、地图比例尺、Bing Maps Tile System）

喜欢ヅ旅行 2022-09-24 12:21 325阅读 0赞

http://www.cnblogs.com/beniao/archive/2010/04/18/1714544.html

墨卡托投影（Mercator Projection），又名“等角正轴圆柱投影”，荷兰地图学家墨卡托（Mercator）在1569年拟定，假设地球被围在一个中空的圆柱里，其赤道与圆柱相接触，然后再假想地球中心有一盏灯，把球面上的图形投影到圆柱体上，再把圆柱体展开，这就是一幅标准纬线为零度（即赤道）的“墨卡托投影”绘制出的世界地图。

![A3a6Nr2.jpg_web][]

#### 一、墨卡托投影坐标系（Mercator Projection） ####

墨卡托投影以整个世界范围，赤道作为标准纬线，本初子午线作为中央经线，两者交点为坐标原点，向东向北为正，向西向南为负。南北极在地图的正下、上方，而东西方向处于地图的正右、左。

由于Mercator Projection在两极附近是趋于无限值得，因此它并没完整展现了整个世界，地图上最高纬度是85.05度。为了简化计算，我们采用球形映射，而不是椭球体形状。虽然采用Mercator Projection只是为了方便展示地图，需要知道的是，这种映射会给Y轴方向带来0.33%的误差。

![qYNBry.jpg_web][]

由于赤道半径为6378137米，则赤道周长为2\*PI\*r = 40075016.6855784（原文是20037508.3427892，应该是错误的），因此X轴的取值范围：\[-20037508.3427892,20037508.3427892\]。当纬度φ接近两极，即90°时，Y值趋向于无穷。因此通常把Y轴的取值范围也限定在\[-20037508.3427892,20037508.3427892\]之间。因此在墨卡托投影坐标系（米）下的坐标范围是：最小为(-20037508.3427892, -20037508.3427892 )到最大 坐标为(20037508.3427892, 20037508.3427892)。

#### 二、地理坐标系（Geographical coordinates） ####

地理经度的取值范围是\[-180,180\]，纬度不可能到达90°，通过纬度取值范围为\[-20037508.3427892, 20037508.3427892\]反计算可得到纬度值为85.05112877980659。因此纬度取值范围是\[-85.05112877980659, 85.05112877980659\]。因此，地理坐标系（经纬度）对应的范围是：最小地理坐标(-180, -85.05112877980659)，最大地理坐标(180, 85.05112877980659)。

三、地面分辨率（Ground Resolution）

地面分辨率是以一个像素(pixel)代表的地面尺寸(米)。以微软Bing Maps为例，当Level为1时，图片大小为512\*512（4个Tile），那么赤道空间分辨率为：赤道周长/512。其他纬度的空间分辨率则为 纬度圈长度/512，极端的北极则为0。Level为2时，赤道的空间分辨率为 赤道周长/1024，其他纬度为 纬度圈长度1024。很明显，Ground Resolution取决于两个参数，缩放级别Level和纬度latitude ，Level决定像素的多少，latitude决定地面距离的长短。

#### 地面分辨率的公式为，单位：米/像素： ####

ground resolution = (cos(latitude \* pi/180) \* 2 \* pi \* 6378137 meters) / (256 \* 2level pixels)

最低地图放大级别（1级），地图是512 x 512像素。每下一个放大级别，地图的高度和宽度分别乘于2：2级是1024 x 1024像素，3级是2048 x 2048像素，4级是4096 x 4096像素，等等。通常而言，地图的宽度和高度可以由以下式子计算得到： map width = map height = 256 \* 2^ level `pixels`

#### 四、地图比例尺（Map Scale） ####

地图比例尺是指测量相同目标时，地图上距离与实际距离的比例。通过地图分辨率在计算可知由Level可得到图片的像素大小，那么需要把其转换为以米为单位的距离，涉及到DPI（dot per inch），暂时可理解为类似的PPI（pixelper inch），即每英寸代表多少个像素。256 \* 2level / DPI 即得到相应的英寸inch，再把英寸inch除以0.0254转换为米。实地距离仍旧是：cos(latitude \* pi/180) \* 2 \* pi \* 6378137 meters; 因此比例尺的公式为：

map scale = 256 \* 2level / screen dpi / 0.0254 / (cos(latitude \* pi/180) \* 2 \* pi \* 6378137)

比例尺= 1 : (cos(latitude \* pi/180) \* 2 \* pi \* 6378137 \* screen dpi) / (256 \* 2level \* 0.0254)

地面分辨率和地图比例尺之间的关系：

map scale = 1 : ground resolution \* screen dpi / 0.0254 meters/inch

<table style="max-width:100%; border-spacing:0px; width:603px; margin-bottom:1.5em; border-width:1px 1px 1px 0px; border-top-style:solid; border-right-style:solid; border-bottom-style:solid; border-top-color:rgb(221,221,221); border-right-color:rgb(221,221,221); border-bottom-color:rgb(221,221,221); font-size:14px; line-height:1.3em; color:rgb(51,51,51); font-family:'Helvetica Neue',Helvetica,Tahoma,Arial,STXihei,'Microsoft YaHei',微软雅黑,sans-serif; background-color:rgb(254,254,254)"> 
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 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:0px; border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> <h4 style="margin:0px 0px 0.5em; font-family:inherit; line-height:1.7em; color:inherit; font-size:16px; text-indent:1em"> 缩放级别</h4> </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:0px; border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> <h4 style="margin:0px 0px 0.5em; font-family:inherit; line-height:1.7em; color:inherit; font-size:16px; text-indent:1em"> 地图宽度、高度(像素)</h4> </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:0px; border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> <h4 style="margin:0px 0px 0.5em; font-family:inherit; line-height:1.7em; color:inherit; font-size:16px; text-indent:1em"> 地面分辨率(米/像素)</h4> </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:0px; border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> <h4 style="margin:0px 0px 0.5em; font-family:inherit; line-height:1.7em; color:inherit; font-size:16px; text-indent:1em"> 地图比例尺(以96dpi为例)</h4> </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 512 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 78,271.5170 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 295,829,355.45 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 2 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1,024 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 39,135.7585 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 147,914,677.73 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 3 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 2,048 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 19,567.8792 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 73,957,338.86 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 4 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 4,096 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 9,783.9396 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 36,978,669.43 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 5 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 8,192 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 4,891.9698 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 18,489,334.72 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 6 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 16,384 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 2,445.9849 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 9,244,667.36 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 7 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 32,768 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1,222.9925 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 4,622,333.68 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 8 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 65,536 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 611.4962 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 2,311,166.84 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 9 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 131,072 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 305.7481 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 1,155,583.42 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 10 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 262,144 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 152.8741 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 577,791.71 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 11 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 524,288 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 76.4370 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 288,895.85 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 12 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1,048,576 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 38.2185 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 144,447.93 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 13 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 2,097,152 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 19.1093 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 72,223.96 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 14 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 4,194,304 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 9.5546 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 36,111.98 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 15 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 8,388,608 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 4.7773 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 18,055.99 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 16 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 16,777,216 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 2.3887 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 9,028.00 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 17 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 33,554,432 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1.1943 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 4,514.00 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 18 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 67,108,864 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 0.5972 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 2,257.00 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 19 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 134,217,728 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 0.2986 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 1,128.50 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 20 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 268,435,456 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 0.1493 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 564.25 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 21 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 536,870,912 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 0.0746 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 282.12 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 22 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1,073,741,824 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 0.0373 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 141.06 </td> 
 </tr> 
 <tr style="line-height:1.3em"> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 23 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 2,147,483,648 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 0.0187 </td> 
 <td style="padding:8px; line-height:1.3em; vertical-align:top; border-top-width:1px; border-top-style:solid; border-top-color:rgb(221,221,221); border-left-width:1px; border-left-style:solid; border-left-color:rgb(221,221,221); font-size:14px"> 1 : 70.53 </td> 
 </tr> 
 </tbody> 
</table>

#### 五、Bing Maps像素坐标系和地图图片编码 ####

为了优化地图系统性能，提高地图下载和显示速度，所有地图都被分割成256 x 256像素大小的正方形小块。由于在每个放大级别下的像素数量都不一样，因此地图图片（Tile）的数量也不一样。每个tile都有一个XY坐标值，从左上角的(0, 0)至右下角的(2^level–1, 2^level–1)。例如在3级放大级别下，所有tile的坐标值范围为(0, 0)至(7, 7)，如下图：

![VbUBZf.jpg_web][]

已知一个像素的XY坐标值时，我们很容易得到这个像素所在的Tile的XY坐标值：

`tileX = floor(pixelX / 256)` `tileY = floor(pixelY / 256)`

为了简化索引和存储地图图片，每个tile的二维XY值被转换成一维字串，即四叉树键值（quardtree key，简称quadkey）。每个quadkey独立对应某个放大级别下的一个tile，并且它可以被用作数据库中B-tree索引值。为了将坐标值转换成quadkey，需要将Y和X坐标二进制值交错组合，并转换成4进制值及对应的字符串。例如，假设在放大级别为3时，tile的XY坐标值为（3，5），quadkey计算如下:

tileX = 3 = 011（二进制）

tileY = 5 = 101（二进制）

`quadkey = 100111（二进制）` `= 213（四进制）` `= “213”`

Quadkey还有其他一些有意思的特性。第一，quadkey的长度等于该tile所对应的放大级别；第二，每个tile的quadkey的前几位和其父tile（上一放大级别所对应的tile）的quadkey相同，下图中，tile 2是tile 20至23的父tile，tile 13是tile 130至133的父级：

![nMVRn2.jpg_web][]

最后，quadkey提供的一维索引值通常显示了两个tile在XY坐标系中的相似性。换句话说，两个相邻的tile对应的quadkey非常接近。这对于优化数据库的性能非常重要，因为相邻的tile通常被同时请求显示，因此可以将这些tile存放在相同的磁盘区域中，以减少磁盘的读取次数。

下面是微软Bing Maps的TileSystem相关算法：

![jYN3ey.gif][]

using

System;

using

System.Text;

namespace

Microsoft.MapPoint

static class

TileSystem

private const double EarthRadius = 6378137

;

private const double MinLatitude = - 85.05112878 ;

[A3a6Nr2.jpg_web]: http://img1.tuicool.com/A3a6Nr2.jpg!web
[qYNBry.jpg_web]: http://img1.tuicool.com/qYNBry.jpg!web
[VbUBZf.jpg_web]: http://img1.tuicool.com/VbUBZf.jpg!web
[nMVRn2.jpg_web]: http://img0.tuicool.com/nMVRn2.jpg!web
[jYN3ey.gif]: http://img2.tuicool.com/jYN3ey.gif