翻译：Bing地图瓦片体系

Bing Maps Tile System Bing地图瓦片体系

原文链接：http://msdn.microsoft.com/en-us/library/bb259689.aspx

Bing Maps provides a world map that users can directly manipulate to pan and zoom. To make this interaction as fast and responsive as possible, we chose to pre-render the map at many different levels of detail, and to cut each map into tiles for quick retrieval and display. This document describes the projection, coordinate systems, and addressing scheme of the map tiles, which collectively are called the Bing Maps Tile System.

Bing地图提供了用户可以直接交互的世界地图。为了使地图的交互响应速度进可能的快，

我们选择预渲染不同等级的地图（Lod），并且为了快速检索和显示将地图切割到不同的瓦片

这篇文档描述了投影，坐标系统和地图瓦片的定位方法，这个地图瓦片被称作BMTS，Bing地图瓦片体系。

Map Projection地图投影

To make the map seamless, and to ensure that aerial images from different sources line up properly, we have to use a single projection for the entire world. We chose to use the Mercator projection, which looks like this:

为了实现地图的无缝，保证不同数据源的一系列影像正常的上线，我们不得不给整个世界选择一个统一的投影，这里选择墨卡托投影，形式如下：

Although the Mercator projection significantly distorts scale and area (particularly near the poles), it has two important properties that outweigh the scale distortion:

尽管墨卡托有显著的尺度形变和面积形变（尤其是近极地地区），它有两个比长度形变更重要的属性

1. It’s a conformal projection, which means that it preserves the shape of relatively small objects. This is especially important when showing aerial imagery, because we want to avoid distorting the shape of buildings. Square buildings should appear square, not rectangular.

它是一个正形投影（等角投影），具有保持形状。这在显示航空影像时是尤其重要的。因为我们想避免建筑物形状的形变。方形的建筑物应该看着是方形的，不是长方形的。

1. It’s a cylindrical projection, which means that north and south are always straight up and down, and west and east are always straight left and right.

它是圆柱投影，北极和南极总是指向上下。东西总是指向左右。

Since the Mercator projection goes to infinity at the poles, it doesn’t actually show the entire world. Using a square aspect ratio for the map, the maximum latitude shown is approximately 85.05 degrees.

To simplify the calculations, we use the spherical form of this projection, not the ellipsoidal form. Since the projection is used only for map display, and not for displaying numeric coordinates, we don’t need the extra precision of an ellipsoidal projection. The spherical projection causes approximately 0.33% scale distortion in the Y direction, which is not visually noticeable.

因为墨卡托投影在两极地区趋于无限，并不显示整个世界。为地图设定一个square比例，最大的显示纬度接近85.05度。为了简化计算，我们采用球进行投影，不是椭球。由于投影是为了地图的显示，不是为了展示坐标数值，我们没有必要采用高精度的椭球投影。球形投影产生大约0.33%的y方向的长度变形，这不会明显的可以察觉。

Ground Resolution and Map Scale地面分辨率和地图比例尺

In addition to the projection, the ground resolution or map scale must be specified in order to render a map. At the lowest level of detail (Level 1), the map is 512 x 512 pixels. At each successive level of detail, the map width and height grow by a factor of 2: Level 2 is 1024 x 1024 pixels, Level 3 is 2048 x 2048 pixels, Level 4 is 4096 x 4096 pixels, and so on. In general, the width and height of the map (in pixels) can be calculated as:

map width = map height = 256 * 2 ^level pixels

除了投影之外，为了展示地图，地面分辨率和地图比例尺必须被定义。在最低一级Level1，地图是512x512像素的。在每个Lod系列，地图的宽度和高度按照2倍比例增长：Level2是1024x1024像素，Level3是2048x2048像素，level4是4096x4096像素，依次…通常，宽度和高度的计算公式如下：

The ground resolution indicates the distance on the ground that’s represented by a single pixel in the map. For example, at a ground resolution of 10 meters/pixel, each pixel represents a ground distance of 10 meters. The ground resolution varies depending on the level of detail and the latitude at which it’s measured. Using an earth radius of 6378137 meters, the ground resolution (in meters per pixel) can be calculated as:

ground resolution = cos(latitude * pi/180) * earth circumference / map width

= (cos(latitude * pi/180) * 2 * pi * 6378137 meters) / (256 * 2 ^level pixels)

地面分辨率指示地图上一个象素代表地面距离。例如，地面分辨率10m/pixel，每个像素代表地面距离10m。地面分辨率变量依赖被量测的Lod和纬度。采用地球半径6378137米，地面分辨率（m/pixel）按如下公式计算：

The map scale indicates the ratio between map distance and ground distance, when measured in the same units. For instance, at a map scale of 1 : 100,000, each inch on the map represents a ground distance of 100,000 inches. Like the ground resolution, the map scale varies with the level of detail and the latitude of measurement. It can be calculated from the ground resolution as follows, given the screen resolution in dots per inch, typically 96 dpi:

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

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

地图比例尺是指图上距离和实际距离的比值，以同样的测量单位。

例如，地图比例尺1 : 100,000，每英寸的地图距离代表地面100,000英寸的距离。和地面分辨率一样，地图比例尺随Lod和纬度变化。可以根据地面分辨率计算，方法如下：已知屏幕分辨率每英寸像素点数，一般为96dpi：

This table shows each of these values at each level of detail, as measured at the Equator. (Note that the ground resolution and map scale also vary with the latitude, as shown in the equations above, but not shown in the table below.)

下表显示了不同Lod在地球赤道测量的地面分辨率和比例尺的值。（提醒：地面分辨率和地图比例尺还随纬度变化，如上面的方程那样，但没有在下面的表格中显示。）

Level of Detail	Map Width and Height (pixels)	Ground Resolution (meters / pixel)	Map Scale (at 96 dpi)
1	512	78,271.5170	1 : 295,829,355.45
2	1,024	39,135.7585	1 : 147,914,677.73
3	2,048	19,567.8792	1 : 73,957,338.86
4	4,096	9,783.9396	1 : 36,978,669.43
5	8,192	4,891.9698	1 : 18,489,334.72
6	16,384	2,445.9849	1 : 9,244,667.36
7	32,768	1,222.9925	1 : 4,622,333.68
8	65,536	611.4962	1 : 2,311,166.84
9	131,072	305.7481	1 : 1,155,583.42
10	262,144	152.8741	1 : 577,791.71
11	524,288	76.4370	1 : 288,895.85
12	1,048,576	38.2185	1 : 144,447.93
13	2,097,152	19.1093	1 : 72,223.96
14	4,194,304	9.5546	1 : 36,111.98
15	8,388,608	4.7773	1 : 18,055.99
16	16,777,216	2.3887	1 : 9,028.00
17	33,554,432	1.1943	1 : 4,514.00
18	67,108,864	0.5972	1 : 2,257.00
19	134,217,728	0.2986	1 : 1,128.50
20	268,435,456	0.1493	1 : 564.25
21	536,870,912	0.0746	1 : 282.12
22	1,073,741,824	0.0373	1 : 141.06
23	2,147,483,648	0.0187	1 : 70.53

Pixel Coordinates像素坐标

Having chosen the projection and scale to use at each level of detail, we can convert geographic coordinates into pixel coordinates. Since the map width and height is different at each level, so are the pixel coordinates. The pixel at the upper-left corner of the map always has pixel coordinates (0, 0). The pixel at the lower-right corner of the map has pixel coordinates (width-1, height-1), or referring to the equations in the previous section, (256 * 2^level–1, 256 * 2^level–1). For example, at level 3, the pixel coordinates range from (0, 0) to (2047, 2047), like this:

选择了投影和不同Lod的比例尺，我们可以将地理坐标转换到像素坐标。由于每级地图的宽度和高度不同，同样的像素坐标也不相同。左上角的像素坐标总是（0，0）。右下角的地图象素坐标为（width-1,heght-1）,或者参照上一节的方程， 。例如，在Level3，象素坐标的范围是(0.0)到(2047,2047)，如下：

Given latitude and longitude in degrees, and the level of detail, the pixel XY coordinates can be calculated as follows:

sinLatitude = sin(latitude * pi/180)

pixelX = ((longitude + 180) / 360) * 256 * 2 ^level

pixelY = (0.5 – log((1 + sinLatitude) / (1 – sinLatitude)) / (4 * pi)) * 256 * 2 ^level

给定经纬度和Lod等级，像素坐标可以按如下方式计算：

The latitude and longitude are assumed to be on the WGS 84 datum. Even though Bing Maps uses a spherical projection, it’s important to convert all geographic coordinates into a common datum, and WGS 84 was chosen to be that datum. The longitude is assumed to range from -180 to +180 degrees, and the latitude must be clipped to range from -85.05112878 to 85.05112878. This avoids a singularity at the poles, and it causes the projected map to be square.

经纬度假定在WGS84基准面。尽管Bing地图采用墨卡托投影，将地理坐标转换到通常的基准面是十分重要的，WGS84被作为基准面。经度范围-180到180，纬度范围必须被裁减在范围(-85.05112878 , 85.05112878)。这样可以避免极地的异常，它使投影的地图为方形的。

Tile Coordinates and Quadkeys瓦片坐标和四叉树键

To optimize the performance of map retrieval and display, the rendered map is cut into tiles of 256 x 256 pixels each. As the number of pixels differs at each level of detail, so does the number of tiles:

map width = map height = 2 ^level tiles

为了优化地图的检索和显示，渲染地图被切割成256x256像素。不同Lod等级的象素数目不同，同样瓦片数目也不相同：

Each tile is given XY coordinates ranging from (0, 0) in the upper left to (2^level–1, 2^level–1) in the lower right. For example, at level 3 the tile coordinates range from (0, 0) to (7, 7) as follows:

每个瓦片给定xy坐标范围左上角(0, 0)，右下角(2^level–1, 2^level–1)。例如Level3的瓦片坐标范围(0, 0)到(7, 7)

Given a pair of pixel XY coordinates, you can easily determine the tile XY coordinates of the tile containing that pixel:

tileX = floor(pixelX / 256)

tileY = floor(pixelY / 256)

给定一组像素坐标XY，可以容易的计算包含该像素的瓦片的xy坐标。

To optimize the indexing and storage of tiles, the two-dimensional tile XY coordinates are combined into one-dimensional strings called quadtree keys, or “quadkeys” for short. Each quadkey uniquely identifies a single tile at a particular level of detail, and it can be used as an key in common database B-tree indexes. To convert tile coordinates into a quadkey, the bits of the Y and X coordinates are interleaved, and the result is interpreted as a base-4 number (with leading zeros maintained) and converted into a string. For instance, given tile XY coordinates of (3, 5) at level 3, the quadkey is determined as follows:

tileX = 3 = 011 ₂

tileY = 5 = 101 ₂

quadkey = 100111 ₂ = 213 ₄ = “213”

为了优化瓦片存储的索引，二维的瓦片坐标被包含在一维的字符串中，称为“四叉树键”，或者简称“四叉键”。每个四叉键唯一的定义了在特定Lod级别的一个瓦片，可以被用来作为通用数据库的b-tree索引。为了将瓦片坐标转换到四叉键，y和x坐标的位是隔行读取的，结果形成了4进制数，转换成字符串。例如，给定xy坐标(3, 5) 等级level 3，四叉键为下值：

Quadkeys have several interesting properties. First, the length of a quadkey (the number of digits) equals the level of detail of the corresponding tile. Second, the quadkey of any tile starts with the quadkey of its parent tile (the containing tile at the previous level). As shown in the example below, tile 2 is the parent of tiles 20 through 23, and tile 13 is the parent of tiles 130 through 133:

四叉键有一些有趣的属性。

首先，四叉键的长度等于Lod对应的瓦片等级。

第二，任何瓦片的四叉键开始于其父亲瓦片的四叉键。如下所示，瓦片2是瓦片20到23的父节点，瓦片13是瓦片130到133的父节点。

Finally, quadkeys provide a one-dimensional index key that usually preserves the proximity of tiles in XY space. In other words, two tiles that have nearby XY coordinates usually have quadkeys that are relatively close together. This is important for optimizing database performance, because neighboring tiles are usually requested in groups, and it’s desirable to keep those tiles on the same disk blocks, in order to minimize the number of disk reads.

最后，四叉键提供了一维的索引键，通常保存了邻近瓦片的XY空间。换言之，两个瓦片具有相邻的xy坐标通常具有相邻的四叉键。这对于优化数据库性能十分重要，因为相邻的瓦片通常会作为组进行请求，这样的描述可以保证这些瓦片在相同的硬盘块，减少磁盘的读取次数。

Sample Code

The following sample C# code illustrates how to implement the functions described in this document. These functions can be easily translated into other programming languages as needed.

如下的C# 代码阐述了如何实现本文的方法，这些方法可以很容易的转换到其他语言。

 //------------------------------------------------------------------------------

 // <copyright company="Microsoft">

 //     Copyright (c) 2006-2009 Microsoft Corporation.  All rights reserved.

 // </copyright>

 //------------------------------------------------------------------------------

 using System;

 using System.Text;

 namespace Microsoft.MapPoint

 {

     static class TileSystem

     {

         private const double EarthRadius = ;

         private const double MinLatitude = -85.05112878;

         private const double MaxLatitude = 85.05112878;

         private const double MinLongitude = -;

         private const double MaxLongitude = ;

         /// <summary>

         /// Clips a number to the specified minimum and maximum values.

         /// </summary>

         /// <param name="n">The number to clip.</param>

         /// <param name="minValue">Minimum allowable value.</param>

         /// <param name="maxValue">Maximum allowable value.</param>

         /// <returns>The clipped value.</returns>

         private static double Clip(double n, double minValue, double maxValue)

         {

             return Math.Min(Math.Max(n, minValue), maxValue);

         }

         /// <summary>

         /// Determines the map width and height (in pixels) at a specified level

         /// of detail.

         /// </summary>

         /// <param name="levelOfDetail">Level of detail, from 1 (lowest detail)

         /// to 23 (highest detail).</param>

         /// <returns>The map width and height in pixels.</returns>

         public static uint MapSize(int levelOfDetail)

         {

             return (uint)  << levelOfDetail;

         }

         /// <summary>

         /// Determines the ground resolution (in meters per pixel) at a specified

         /// latitude and level of detail.

         /// </summary>

         /// <param name="latitude">Latitude (in degrees) at which to measure the

         /// ground resolution.</param>

         /// <param name="levelOfDetail">Level of detail, from 1 (lowest detail)

         /// to 23 (highest detail).</param>

         /// <returns>The ground resolution, in meters per pixel.</returns>

         public static double GroundResolution(double latitude, int levelOfDetail)

         {

             latitude = Clip(latitude, MinLatitude, MaxLatitude);

             return Math.Cos(latitude * Math.PI / ) *  * Math.PI * EarthRadius / MapSize(levelOfDetail);

         }

         /// <summary>

         /// Determines the map scale at a specified latitude, level of detail,

         /// and screen resolution.

         /// </summary>

         /// <param name="latitude">Latitude (in degrees) at which to measure the

         /// map scale.</param>

         /// <param name="levelOfDetail">Level of detail, from 1 (lowest detail)

         /// to 23 (highest detail).</param>

         /// <param name="screenDpi">Resolution of the screen, in dots per inch.</param>

         /// <returns>The map scale, expressed as the denominator N of the ratio 1 : N.</returns>

         public static double MapScale(double latitude, int levelOfDetail, int screenDpi)

         {

             return GroundResolution(latitude, levelOfDetail) * screenDpi / 0.0254;

         }

         /// <summary>

         /// Converts a point from latitude/longitude WGS-84 coordinates (in degrees)

         /// into pixel XY coordinates at a specified level of detail.

         /// </summary>

         /// <param name="latitude">Latitude of the point, in degrees.</param>

         /// <param name="longitude">Longitude of the point, in degrees.</param>

         /// <param name="levelOfDetail">Level of detail, from 1 (lowest detail)

         /// to 23 (highest detail).</param>

         /// <param name="pixelX">Output parameter receiving the X coordinate in pixels.</param>

         /// <param name="pixelY">Output parameter receiving the Y coordinate in pixels.</param>

         public static void LatLongToPixelXY(double latitude, double longitude, int levelOfDetail, out int pixelX, out int pixelY)

         {

             latitude = Clip(latitude, MinLatitude, MaxLatitude);

             longitude = Clip(longitude, MinLongitude, MaxLongitude);

             double x = (longitude + ) / ; 

             double sinLatitude = Math.Sin(latitude * Math.PI / );

             double y = 0.5 - Math.Log(( + sinLatitude) / ( - sinLatitude)) / ( * Math.PI);

             uint mapSize = MapSize(levelOfDetail);

             pixelX = (int) Clip(x * mapSize + 0.5, , mapSize - );

             pixelY = (int) Clip(y * mapSize + 0.5, , mapSize - );

         }

         /// <summary>

         /// Converts a pixel from pixel XY coordinates at a specified level of detail

         /// into latitude/longitude WGS-84 coordinates (in degrees).

         /// </summary>

         /// <param name="pixelX">X coordinate of the point, in pixels.</param>

         /// <param name="pixelY">Y coordinates of the point, in pixels.</param>

         /// <param name="levelOfDetail">Level of detail, from 1 (lowest detail)

         /// to 23 (highest detail).</param>

         /// <param name="latitude">Output parameter receiving the latitude in degrees.</param>

         /// <param name="longitude">Output parameter receiving the longitude in degrees.</param>

         public static void PixelXYToLatLong(int pixelX, int pixelY, int levelOfDetail, out double latitude, out double longitude)

         {

             double mapSize = MapSize(levelOfDetail);

             double x = (Clip(pixelX, , mapSize - ) / mapSize) - 0.5;

             double y = 0.5 - (Clip(pixelY, , mapSize - ) / mapSize);

             latitude =  -  * Math.Atan(Math.Exp(-y *  * Math.PI)) / Math.PI;

             longitude =  * x;

         }

         /// <summary>

         /// Converts pixel XY coordinates into tile XY coordinates of the tile containing

         /// the specified pixel.

         /// </summary>

         /// <param name="pixelX">Pixel X coordinate.</param>

         /// <param name="pixelY">Pixel Y coordinate.</param>

         /// <param name="tileX">Output parameter receiving the tile X coordinate.</param>

         /// <param name="tileY">Output parameter receiving the tile Y coordinate.</param>

         public static void PixelXYToTileXY(int pixelX, int pixelY, out int tileX, out int tileY)

         {

             tileX = pixelX / ;

             tileY = pixelY / ;

         }

         /// <summary>

         /// Converts tile XY coordinates into pixel XY coordinates of the upper-left pixel

         /// of the specified tile.

         /// </summary>

         /// <param name="tileX">Tile X coordinate.</param>

         /// <param name="tileY">Tile Y coordinate.</param>

         /// <param name="pixelX">Output parameter receiving the pixel X coordinate.</param>

         /// <param name="pixelY">Output parameter receiving the pixel Y coordinate.</param>

         public static void TileXYToPixelXY(int tileX, int tileY, out int pixelX, out int pixelY)

         {

             pixelX = tileX * ;

             pixelY = tileY * ;

         }

         /// <summary>

         /// Converts tile XY coordinates into a QuadKey at a specified level of detail.

         /// </summary>

         /// <param name="tileX">Tile X coordinate.</param>

         /// <param name="tileY">Tile Y coordinate.</param>

         /// <param name="levelOfDetail">Level of detail, from 1 (lowest detail)

         /// to 23 (highest detail).</param>

         /// <returns>A string containing the QuadKey.</returns>

         public static string TileXYToQuadKey(int tileX, int tileY, int levelOfDetail)

         {

             StringBuilder quadKey = new StringBuilder();

             for (int i = levelOfDetail; i > ; i--)

             {

                 char digit = '';

                 int mask =  << (i - );

                 if ((tileX & mask) != )

                 {

                     digit++;

                 }

                 if ((tileY & mask) != )

                 {

                     digit++;

                     digit++;

                 }

                 quadKey.Append(digit);

             }

             return quadKey.ToString();

         }

         /// <summary>

         /// Converts a QuadKey into tile XY coordinates.

         /// </summary>

         /// <param name="quadKey">QuadKey of the tile.</param>

         /// <param name="tileX">Output parameter receiving the tile X coordinate.</param>

         /// <param name="tileY">Output parameter receiving the tile Y coordinate.</param>

         /// <param name="levelOfDetail">Output parameter receiving the level of detail.</param>

         public static void QuadKeyToTileXY(string quadKey, out int tileX, out int tileY, out int levelOfDetail)

         {

             tileX = tileY = ;

             levelOfDetail = quadKey.Length;

             for (int i = levelOfDetail; i > ; i--)

             {

                 int mask =  << (i - );

                 switch (quadKey[levelOfDetail - i])

                 {

                     case '':

                         break;

                     case '':

                         tileX |= mask;

                         break;

                     case '':

                         tileY |= mask;

                         break;

                     case '':

                         tileX |= mask;

                         tileY |= mask;

                         break;

                     default:

                         throw new ArgumentException("Invalid QuadKey digit sequence.");

                 }

             }

         }

     }

 }