cn.mapway.common.geo.tools.GlobalMercator

public class GlobalMercator extends Object

GlobalMercator 墨卡托信息

Author:

zhangjianshe <zhangjianshe@gmail.com>

TMS Global Mercator Profile ---------------------------

Functions necessary for generation of tiles in Spherical Mercator projection, EPSG:3857.

Such tiles are compatible with Google Maps, Bing Maps, Yahoo Maps, UK Ordnance Survey OpenSpace API, ... and you can overlay them on top of base maps of those web mapping applications.

Pixel and tile coordinates are in TMS notation (origin [0,0] in bottom-left).

What coordinate conversions do we need for TMS Global Mercator tiles::

LatLon <-> Meters <-> Pixels <-> Tile

WGS84 coordinates Spherical Mercator Pixels in pyramid Tiles in pyramid lat/lon XY in meters XY pixels Z zoom XYZ from TMS EPSG:4326 EPSG:3875 .----. --------- -- TMS / \ <-> | | <-> /----/ <-> Google \ / | | /--------/ QuadTree ----- --------- /------------/ KML, public WebMapService Web Clients TileMapService

What is the coordinate extent of Earth in EPSG:3857?

[-20037508.342789244, -20037508.342789244, 20037508.342789244, 20037508.342789244] Constant 20037508.342789244 comes from the circumference of the Earth in meters, which is 40 thousand kilometers, the coordinate origin is in the middle of extent. In fact you can calculate the constant as: 2 * math.pi * 6378137 / 2.0 $ echo 180 85 | gdaltransform -s_srs EPSG:4326 -t_srs EPSG:3857 Polar areas with abs(latitude) bigger then 85.05112878 are clipped off.

What are zoom level constants (pixels/meter) for pyramid with EPSG:3857?

whole region is on top of pyramid (zoom=0) covered by 256x256 pixels tile, every lower zoom level resolution is always divided by two initialResolution = 20037508.342789244 * 2 / 256 = 156543.03392804062

What is the difference between TMS and Google Maps/QuadTree tile name convention?

The tile raster itself is the same (equal extent, projection, pixel size), there is just different identification of the same raster tile. Tiles in TMS are counted from [0,0] in the bottom-left corner, id is XYZ. Google placed the origin [0,0] to the top-left corner, reference is XYZ. Microsoft is referencing tiles by a QuadTree name, defined on the website: http://msdn2.microsoft.com/en-us/library/bb259689.aspx

The lat/lon coordinates are using WGS84 datum, yes?

Yes, all lat/lon we are mentioning should use WGS84 Geodetic Datum. Well, the web clients like Google Maps are projecting those coordinates by Spherical Mercator, so in fact lat/lon coordinates on sphere are treated as if the were on the WGS84 ellipsoid.

From MSDN documentation: To simplify the calculations, we use the spherical form of 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 percent scale distortion in the Y direction, which is not visually noticeable.

How do I create a raster in EPSG:3857 and convert coordinates with PROJ.4?

You can use standard GIS tools like gdalwarp, cs2cs or gdaltransform. All of the tools supports -t_srs 'epsg:3857'.

For other GIS programs check the exact definition of the projection: More info at http://spatialreference.org/ref/user/google-projection/ The same projection is designated as EPSG:3857. WKT definition is in the official EPSG database.

Proj4 Text: +proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +no_defs

Human readable WKT format of EPSG:3857: PROJCS["Google Maps Global Mercator", GEOGCS["WGS 84", DATUM["WGS_1984", SPHEROID["WGS 84",6378137,298.257223563, AUTHORITY["EPSG","7030"]], AUTHORITY["EPSG","6326"]], PRIMEM["Greenwich",0], UNIT["degree",0.0174532925199433], AUTHORITY["EPSG","4326"]], PROJECTION["Mercator_1SP"], PARAMETER["central_meridian",0], PARAMETER["scale_factor",1], PARAMETER["false_easting",0], PARAMETER["false_northing",0], UNIT["metre",1, AUTHORITY["EPSG","9001"]]]

Field Summary

Fields

Modifier and Type

Field

Description

final long

EARTH_RADIUS

final int

MAXZOOMLEVEL
Constructor Summary

Constructors

Constructor

Description

GlobalMercator(int tileSize)
Method Summary

Modifier and Type

Method

Description

cn.mapway.geo.shared.vector.Point

geoToTile(double lng, double lat, double tx, double ty, int zoom)

地理坐标转化为 tile内像素坐标 (256*256) 坐标系为左下角为坐标原点

static GlobalMercator

get()

全局获取墨卡托参数信息

byte[]

getWhiteBand()

获取一个波段数据

cn.mapway.geo.shared.vector.Box

lngLatBoxToTileBox(cn.mapway.geo.shared.vector.Box lngLat, int zoom)

给定一个经纬度坐标范围返回一个墨卡托坐标系下 zoom级别中对应的瓦片范围

cn.mapway.geo.shared.vector.Point

lngLatToMeter(double lng, double lat)

"Converts lon/lat to pixel coordinates in given zoom of the EPSG:4326 pyramid" 经纬度转化为以mi为单位的坐标

cn.mapway.geo.shared.vector.Point

lngLatToTile(double lng, double lat, int zoom)

经纬度所在的tile编号

static void

main(String[] args)

cn.mapway.geo.shared.vector.Box

meterToGeo(cn.mapway.geo.shared.vector.Box meter)

墨卡托坐标转化为经纬度

cn.mapway.geo.shared.vector.Point

meterTolngLat(double mx, double my)

"Maximal scaledown zoom of the pyramid closest to the pixelSize." 墨卡托以米为单位的坐标转化为WGS84经纬度坐标

cn.mapway.geo.shared.vector.Point

meterToPixels(double mx, double my, int zoom)

Converts EPSG:3857 to pyramid pixel coordinates in given zoom level"

cn.mapway.geo.shared.vector.Point

meterToTile(double mx, double my, long tileX, long tileY, int zoom)

墨卡托坐标在 tile下的像素坐标

cn.mapway.geo.shared.vector.Point

pixelsToMeters(double px, double py, int zoom)

"Converts pixel coordinates in given zoom level of pyramid to EPSG:3857" tile (tx,ty)对应的经纬度范围墨卡托 tile编码规则左上角为（0,0）向右向下生长墨卡托坐标单位为 mi 坐标原点为将中央子午线和赤道的交点 (0,0) 这个方法将像素坐标转化为以mi为单位的墨卡托坐标

cn.mapway.geo.shared.vector.Point

pixelsToRaster(double px, double py, int zoom)

"Move the origin of pixel coordinates to top-left corner"

cn.mapway.geo.shared.vector.Point

pixelToTile(double px, double py)

"Returns a tile covering region in given pixel coordinates"

double

resolution(int zoom)

"Resolution (meters/pixel) for given zoom level (measured at Equator)"

cn.mapway.geo.shared.vector.Box

tileBounds(double tx, double ty, int zoom)

"Returns bounds of the given tile in EPSG:3857 coordinates"

cn.mapway.geo.shared.vector.Box

tileBoundsWebMercator(double tx, double ty, int zoom)

某一个级别下的瓦片编号 tx ty ,计算其WEB墨卡托的像素坐标 (tx ty) 左上角为 (0,0) 向右向下增加 WEB墨卡托所坐标系定义（地图中心点为坐标原点） (tx*512 , ty*512)是一个世界坐标系第0级是一个 512*512图片对应一个地球表面赤道上每个像素对应的地面距离为 RES= 2*PI*r/512 第n级赤道上每个像素对应的地面距离为 RES/2^n

cn.mapway.geo.shared.vector.Box

tileBoundWgs84(double tx, double ty, int zoom)

tile (tx,ty)对应的经纬度范围墨卡托 tile编码规则左上角为（0,0）向右向下生长墨卡托坐标单位为 mi 坐标原点为将中央子午线和赤道的交点 (0,0)

cn.mapway.geo.shared.vector.Box

tileLngLatBounds(long tx, long ty, int zoom)

墨卡托坐标下 tile的编号规则左下角的编号为 (0,0) 向右向上增加 WGS坐标统一称做 gps坐标

cn.mapway.geo.shared.vector.Box

tileNoBoxToLngLatBox(cn.mapway.geo.shared.vector.Box tileNo, int zoom)

给定瓦片的范围范围其经纬度信息范围

static TileNo

tileNoFromWgs84(double lat, double lng, int zoom)

经纬度坐标所在的tile索引参考 https://wiki.openstreetmap.org/wiki/Slippy_map_tilenames

int

zoomForPixelSize(double pixelSize)

"Maximal scaledown zoom of the pyramid closest to the pixelSize."

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details
- MAXZOOMLEVEL
  
  public final int MAXZOOMLEVEL
  See Also:
  
  Constant Field Values
- EARTH_RADIUS
  
  public final long EARTH_RADIUS
  See Also:
  
  Constant Field Values
Constructor Details
- GlobalMercator
  
  public GlobalMercator(int tileSize)
Method Details
- main
  
  public static void main(String[] args)
- get
  
  public static GlobalMercator get()
  
  全局获取墨卡托参数信息
  
  Returns:
- getWhiteBand
  
  public byte[] getWhiteBand()
  
  获取一个波段数据
  
  Returns:
- meterTolngLat
  
  public cn.mapway.geo.shared.vector.Point meterTolngLat(double mx, double my)
  
  "Maximal scaledown zoom of the pyramid closest to the pixelSize." 墨卡托以米为单位的坐标转化为WGS84经纬度坐标
  
  Parameters:
  
  mx -
  
  my -
  
  Returns:
- lngLatToMeter
  
  public cn.mapway.geo.shared.vector.Point lngLatToMeter(double lng, double lat)
  
  "Converts lon/lat to pixel coordinates in given zoom of the EPSG:4326 pyramid" 经纬度转化为以mi为单位的坐标
  
  Parameters:
  
  lng -
  
  lat -
  
  Returns:
- lngLatToTile
  
  public cn.mapway.geo.shared.vector.Point lngLatToTile(double lng, double lat, int zoom)
  
  经纬度所在的tile编号
  
  Parameters:
  
  lng -
  
  lat -
  
  Returns:
- pixelsToMeters
  
  public cn.mapway.geo.shared.vector.Point pixelsToMeters(double px, double py, int zoom)
  
  "Converts pixel coordinates in given zoom level of pyramid to EPSG:3857" tile (tx,ty)对应的经纬度范围墨卡托 tile编码规则左上角为（0,0）向右向下生长墨卡托坐标单位为 mi 坐标原点为将中央子午线和赤道的交点 (0,0) 这个方法将像素坐标转化为以mi为单位的墨卡托坐标
  (0,0) +------------------------------- | | | | | | |---------------|(0,0)--------------- py*res | | | |
  
  Parameters:
  
  px -
  
  py -
  
  zoom -
- lngLatBoxToTileBox
  
  public cn.mapway.geo.shared.vector.Box lngLatBoxToTileBox(cn.mapway.geo.shared.vector.Box lngLat, int zoom)
  
  给定一个经纬度坐标范围返回一个墨卡托坐标系下 zoom级别中对应的瓦片范围
  
  Parameters:
  
  lngLat -
  
  zoom -
  
  Returns:
- tileNoBoxToLngLatBox
  
  public cn.mapway.geo.shared.vector.Box tileNoBoxToLngLatBox(cn.mapway.geo.shared.vector.Box tileNo, int zoom)
  
  给定瓦片的范围范围其经纬度信息范围
  
  Parameters:
  
  tileNo -
  
  zoom -
  
  Returns:
- meterToPixels
  
  public cn.mapway.geo.shared.vector.Point meterToPixels(double mx, double my, int zoom)
  
  Converts EPSG:3857 to pyramid pixel coordinates in given zoom level"
  
  Parameters:
  
  mx -
  
  my -
  
  zoom -
  
  Returns:
- pixelToTile
  
  public cn.mapway.geo.shared.vector.Point pixelToTile(double px, double py)
  
  "Returns a tile covering region in given pixel coordinates"
  
  Parameters:
  
  px -
  
  py -
  
  Returns:
- resolution
  
  public double resolution(int zoom)
  
  "Resolution (meters/pixel) for given zoom level (measured at Equator)"
  
  Parameters:
  
  zoom -
  
  Returns:
- pixelsToRaster
  
  public cn.mapway.geo.shared.vector.Point pixelsToRaster(double px, double py, int zoom)
  
  "Move the origin of pixel coordinates to top-left corner"
  
  Parameters:
  
  px -
  
  py -
  
  zoom -
  
  Returns:
- geoToTile
  
  public cn.mapway.geo.shared.vector.Point geoToTile(double lng, double lat, double tx, double ty, int zoom)
  
  地理坐标转化为 tile内像素坐标 (256*256) 坐标系为左下角为坐标原点
  
  Parameters:
  
  lng -
  
  lat -
  
  zoom -
  
  Returns:
- tileLngLatBounds
  
  public cn.mapway.geo.shared.vector.Box tileLngLatBounds(long tx, long ty, int zoom)
  
  墨卡托坐标下 tile的编号规则左下角的编号为 (0,0) 向右向上增加 WGS坐标统一称做 gps坐标
  
  Parameters:
  
  tx - 墨卡托坐标下的X方向瓦片编号
  
  ty - 墨卡托坐标下的Y方向瓦片编号
  
  zoom - 图像LEVEL
  
  Returns:
- tileBounds
  
  public cn.mapway.geo.shared.vector.Box tileBounds(double tx, double ty, int zoom)
  
  "Returns bounds of the given tile in EPSG:3857 coordinates"
  
  Parameters:
  
  tx -
  
  ty -
  
  zoom -
  
  Returns:
- tileNoFromWgs84
  
  public static TileNo tileNoFromWgs84(double lat, double lng, int zoom)
  
  经纬度坐标所在的tile索引参考 https://wiki.openstreetmap.org/wiki/Slippy_map_tilenames
  
  Parameters:
  
  lat -
  
  lng -
  
  zoom -
  
  Returns:
- tileBoundWgs84
  
  public cn.mapway.geo.shared.vector.Box tileBoundWgs84(double tx, double ty, int zoom)
  
  tile (tx,ty)对应的经纬度范围墨卡托 tile编码规则左上角为（0,0）向右向下生长墨卡托坐标单位为 mi 坐标原点为将中央子午线和赤道的交点 (0,0)
  
  Parameters:
  
  tx -
  
  ty -
  
  zoom -
  
  Returns:
- tileBoundsWebMercator
  
  public cn.mapway.geo.shared.vector.Box tileBoundsWebMercator(double tx, double ty, int zoom)
  
  某一个级别下的瓦片编号 tx ty ,计算其WEB墨卡托的像素坐标 (tx ty) 左上角为 (0,0) 向右向下增加 WEB墨卡托所坐标系定义（地图中心点为坐标原点） (tx*512 , ty*512)是一个世界坐标系第0级是一个 512*512图片对应一个地球表面赤道上每个像素对应的地面距离为 RES= 2*PI*r/512 第n级赤道上每个像素对应的地面距离为 RES/2^n
  
  Parameters:
  
  tx -
  
  ty -
  
  zoom -
  
  Returns:
- meterToGeo
  
  public cn.mapway.geo.shared.vector.Box meterToGeo(cn.mapway.geo.shared.vector.Box meter)
  
  墨卡托坐标转化为经纬度
  
  Parameters:
  
  meter -
  
  Returns:
- zoomForPixelSize
  
  public int zoomForPixelSize(double pixelSize)
  
  "Maximal scaledown zoom of the pyramid closest to the pixelSize."
  
  Parameters:
  
  pixelSize -
  
  Returns:
- meterToTile
  
  public cn.mapway.geo.shared.vector.Point meterToTile(double mx, double my, long tileX, long tileY, int zoom)
  
  墨卡托坐标在 tile下的像素坐标
  
  Parameters:
  
  mx -
  
  my -
  
  tileX -
  
  tileY -
  
  zoom -
  
  Returns:

Class GlobalMercator

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Details

MAXZOOMLEVEL

EARTH_RADIUS

Constructor Details

GlobalMercator

Method Details

main

get

getWhiteBand

meterTolngLat

lngLatToMeter

lngLatToTile

pixelsToMeters

lngLatBoxToTileBox

tileNoBoxToLngLatBox

meterToPixels

pixelToTile

resolution

pixelsToRaster

geoToTile

tileLngLatBounds

tileBounds

tileNoFromWgs84

tileBoundWgs84

tileBoundsWebMercator

meterToGeo

zoomForPixelSize

meterToTile