引言
众所周知，近年来互联网地图发展迅猛，不同的大腕级公司也推出自己的互联网地图，但在技术上始终遵循着一个相同的规则，那就是地图瓦片技术。如Google Map、Microsoft Bing、甚至是开源地图的代表Openstreetmap，似乎也达成了一种默契，所有这些地图瓦片都采用Web墨卡托投影，虽然都采用了不同的索引算法，但其瓦片数据的范围是相同的，下文就是对地图瓦片的各种索引算法(包括Google XYZ、TMS、QuardTree)进行的详细分析和转换，并且提供了瓦片坐标、WGS84经纬度坐标、墨卡托投影坐标、瓦片像素坐标等之间的相互转换算法。
需要注意的是：国内的地图如百度、MapBar等的瓦片数据的范围不同，但其切片规则及索引则类似。
Addressing tiles: same tile bounds with different indexes
Click on a tile to display the numerical boundaries...
Google Maps, Microsoft Virtual Earth, Yahoo Maps, and other commercial API providers as well as OpenStreetMap and OpenAerialMap are using the same projection and tiling profile and tiles are therefore compatible. The extents of all tiles as well as the zoom levels (resolution in meters per pixel) are predefined for the whole Earth.
Difference is only in the way how the equivalent tiles are indexed. There are three main systems of tile adressing: Google XYZ, Microsoft QuadTree and from the open-source world comming TMS (Tile Map Service).
- Google - described in the Google Maps API documentation
- TMS an variant of Google tile addressing, which is used in open-source projects like OpenLayers or TileCache. This system is described in the OSGEO Tile Map Service (TMS) Specification
- QuadTree - with documentation in the Virtal Earth Tile System from Microsoft
MapTiler/GDAL2Tiles (the tile generator application) is following the TMS specification, because there is not any standard for tiling yet, OGC (Open Geospatial Consorcium) is working on the WMTS (Web Map Tiling Service) which is inspired by TMS.
Spherical Mercator EPSG:900913 (EPSG:3857) and WGS84 Datum
The coordinates you use in the Google Maps API and which are presented to the users is Latitude/Longitude in WGS84 Datum (when directly projected by Platte Carre then it is referenced as EPSG:4326).
But for map publishing in the form compatible with all the popular interactive maps and especially for ground tile overlays you need to use Mercator map projection. Interactive web maps are using "Spherical Mercator" system which uses Mercator projection on the sphere instead of WGS84 ellipsoid. It is defined as EPSG:900913 or EPSG:3857 (deprecated EPSG:3785). Details about this system are part of Virtual Earth documentation as well as OpenLayers documentation. Exact numeric definition for GIS systems (in formats like WKT or Proj4), is available in the SpatialReference.org on-line database.
Links ...
Spatial references, coordinate systems, projections, datums, ellipsoids – confusing?
Source code for utility calculating tile bounds
I wrote a class GlobalMercator implementing all necessary coordinate system conversions in Python. The class is documented and quite straightforward.
You can also download the source code globalmaptiles.py and run it as a command line utility. It prints the list of tiles for given WGS84 lat/lon coordinates (or bounding box). For each tile several information is printed including boundaries in EPSG:900913 and WGS84:
python globalmaptiles.py [zoom] [lat] [lon]
#!/usr/bin/env python
###############################################################################
# $Id$
#
# Project: GDAL2Tiles, Google Summer of Code 2007 & 2008
# Global Map Tiles Classes
# Purpose: Convert a raster into TMS tiles, create KML SuperOverlay EPSG:4326,
# generate a simple HTML viewers based on Google Maps and OpenLayers
# Author: Klokan Petr Pridal, klokan at klokan dot cz
# Web: http://www.klokan.cz/projects/gdal2tiles/
#
###############################################################################
# Copyright (c) 2008 Klokan Petr Pridal. All rights reserved.
#
# Permission is hereby granted, free of charge, to any person obtaining a
# copy of this software and associated documentation files (the "Software"),
# to deal in the Software without restriction, including without limitation
# the rights to use, copy, modify, merge, publish, distribute, sublicense,
# and/or sell copies of the Software, and to permit persons to whom the
# Software is furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included
# in all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
# DEALINGS IN THE SOFTWARE.
###############################################################################
"""
globalmaptiles.py
Global Map Tiles as defined in Tile Map Service (TMS) Profiles
==============================================================
Functions necessary for generation of global tiles used on the web.
It contains classes implementing coordinate conversions for:
- GlobalMercator (based on EPSG:900913 = EPSG:3785)
for Google Maps, Yahoo Maps, Microsoft Maps compatible tiles
- GlobalGeodetic (based on EPSG:4326)
for OpenLayers Base Map and Google Earth compatible tiles
More info at:
http://wiki.osgeo.org/wiki/Tile_Map_Service_Specification
http://wiki.osgeo.org/wiki/WMS_Tiling_Client_Recommendation
http://msdn.microsoft.com/en-us/library/bb259689.aspx
http://code.google.com/apis/maps/documentation/overlays.html#Google_Maps_Coordinates
Created by Klokan Petr Pridal on 2008-07-03.
Google Summer of Code 2008, project GDAL2Tiles for OSGEO.
In case you use this class in your product, translate it to another language
or find it usefull for your project please let me know.
My email: klokan at klokan dot cz.
I would like to know where it was used.
Class is available under the open-source GDAL license (www.gdal.org).
"""
import math
class GlobalMercator(object):
"""
TMS Global Mercator Profile
---------------------------
Functions necessary for generation of tiles in Spherical Mercator projection,
EPSG:900913 (EPSG:gOOglE, Google Maps Global Mercator), EPSG:3785, OSGEO:41001.
Such tiles are compatible with Google Maps, Microsoft Virtual Earth, 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 metres XY pixels Z zoom XYZ from TMS
EPSG:4326 EPSG:900913
.----. --------- -- TMS
/ \ <-> | | <-> /----/ <-> Google
\ / | | /--------/ QuadTree
----- --------- /------------/
KML, public WebMapService Web Clients TileMapService
What is the coordinate extent of Earth in EPSG:900913?
[-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:900913
Polar areas with abs(latitude) bigger then 85.05112878 are clipped off.
What are zoom level constants (pixels/meter) for pyramid with EPSG:900913?
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, yeh?
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 noticable.
How do I create a raster in EPSG:900913 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:900913'.
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 degined as EPSG:3785. 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 EPGS:900913:
PROJCS["Google Maps Global Mercator",
GEOGCS["WGS 84",
DATUM["WGS_1984",
SPHEROID["WGS 84",6378137,298.2572235630016,
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"]]]
"""
def __init__(self, tileSize=256):
"Initialize the TMS Global Mercator pyramid"
self.tileSize = tileSize
self.initialResolution = 2 * math.pi * 6378137 / self.tileSize
# 156543.03392804062 for tileSize 256 pixels
self.originShift = 2 * math.pi * 6378137 / 2.0
# 20037508.342789244
def LatLonToMeters(self, lat, lon ):
"Converts given lat/lon in WGS84 Datum to XY in Spherical Mercator EPSG:900913"
mx = lon * self.originShift / 180.0
my = math.log( math.tan((90 + lat) * math.pi / 360.0 )) / (math.pi / 180.0)
my = my * self.originShift / 180.0
return mx, my
def MetersToLatLon(self, mx, my ):
"Converts XY point from Spherical Mercator EPSG:900913 to lat/lon in WGS84 Datum"
lon = (mx / self.originShift) * 180.0
lat = (my / self.originShift) * 180.0
lat = 180 / math.pi * (2 * math.atan( math.exp( lat * math.pi / 180.0)) - math.pi / 2.0)
return lat, lon
def PixelsToMeters(self, px, py, zoom):
"Converts pixel coordinates in given zoom level of pyramid to EPSG:900913"
res = self.Resolution( zoom )
mx = px * res - self.originShift
my = py * res - self.originShift
return mx, my
def MetersToPixels(self, mx, my, zoom):
"Converts EPSG:900913 to pyramid pixel coordinates in given zoom level"
res = self.Resolution( zoom )
px = (mx + self.originShift) / res
py = (my + self.originShift) / res
return px, py
def PixelsToTile(self, px, py):
"Returns a tile covering region in given pixel coordinates"
tx = int( math.ceil( px / float(self.tileSize) ) - 1 )
ty = int( math.ceil( py / float(self.tileSize) ) - 1 )
return tx, ty
def PixelsToRaster(self, px, py, zoom):
"Move the origin of pixel coordinates to top-left corner"
mapSize = self.tileSize << zoom
return px, mapSize - py
def MetersToTile(self, mx, my, zoom):
"Returns tile for given mercator coordinates"
px, py = self.MetersToPixels( mx, my, zoom)
return self.PixelsToTile( px, py)
def TileBounds(self, tx, ty, zoom):
"Returns bounds of the given tile in EPSG:900913 coordinates"
minx, miny = self.PixelsToMeters( tx*self.tileSize, ty*self.tileSize, zoom )
maxx, maxy = self.PixelsToMeters( (tx+1)*self.tileSize, (ty+1)*self.tileSize, zoom )
return ( minx, miny, maxx, maxy )
def TileLatLonBounds(self, tx, ty, zoom ):
"Returns bounds of the given tile in latutude/longitude using WGS84 datum"
bounds = self.TileBounds( tx, ty, zoom)
minLat, minLon = self.MetersToLatLon(bounds[0], bounds[1])
maxLat, maxLon = self.MetersToLatLon(bounds[2], bounds[3])
return ( minLat, minLon, maxLat, maxLon )
def Resolution(self, zoom ):
"Resolution (meters/pixel) for given zoom level (measured at Equator)"
# return (2 * math.pi * 6378137) / (self.tileSize * 2**zoom)
return self.initialResolution / (2**zoom)
def ZoomForPixelSize(self, pixelSize ):
"Maximal scaledown zoom of the pyramid closest to the pixelSize."
for i in range(30):
if pixelSize > self.Resolution(i):
return i-1 if i!=0 else 0 # We don't want to scale up
def GoogleTile(self, tx, ty, zoom):
"Converts TMS tile coordinates to Google Tile coordinates"
# coordinate origin is moved from bottom-left to top-left corner of the extent
return tx, (2**zoom - 1) - ty
def QuadTree(self, tx, ty, zoom ):
"Converts TMS tile coordinates to Microsoft QuadTree"
quadKey = ""
ty = (2**zoom - 1) - ty
for i in range(zoom, 0, -1):
digit = 0
mask = 1 << (i-1)
if (tx & mask) != 0:
digit += 1
if (ty & mask) != 0:
digit += 2
quadKey += str(digit)
return quadKey
#---------------------
class GlobalGeodetic(object):
"""
TMS Global Geodetic Profile
---------------------------
Functions necessary for generation of global tiles in Plate Carre projection,
EPSG:4326, "unprojected profile".
Such tiles are compatible with Google Earth (as any other EPSG:4326 rasters)
and you can overlay the tiles on top of OpenLayers base map.
Pixel and tile coordinates are in TMS notation (origin [0,0] in bottom-left).
What coordinate conversions do we need for TMS Global Geodetic tiles?
Global Geodetic tiles are using geodetic coordinates (latitude,longitude)
directly as planar coordinates XY (it is also called Unprojected or Plate
Carre). We need only scaling to pixel pyramid and cutting to tiles.
Pyramid has on top level two tiles, so it is not square but rectangle.
Area [-180,-90,180,90] is scaled to 512x256 pixels.
TMS has coordinate origin (for pixels and tiles) in bottom-left corner.
Rasters are in EPSG:4326 and therefore are compatible with Google Earth.
LatLon <-> Pixels <-> Tiles
WGS84 coordinates Pixels in pyramid Tiles in pyramid
lat/lon XY pixels Z zoom XYZ from TMS
EPSG:4326
.----. ----
/ \ <-> /--------/ <-> TMS
\ / /--------------/
----- /--------------------/
WMS, KML Web Clients, Google Earth TileMapService
"""
def __init__(self, tileSize = 256):
self.tileSize = tileSize
def LatLonToPixels(self, lat, lon, zoom):
"Converts lat/lon to pixel coordinates in given zoom of the EPSG:4326 pyramid"
res = 180 / 256.0 / 2**zoom
px = (180 + lat) / res
py = (90 + lon) / res
return px, py
def PixelsToTile(self, px, py):
"Returns coordinates of the tile covering region in pixel coordinates"
tx = int( math.ceil( px / float(self.tileSize) ) - 1 )
ty = int( math.ceil( py / float(self.tileSize) ) - 1 )
return tx, ty
def Resolution(self, zoom ):
"Resolution (arc/pixel) for given zoom level (measured at Equator)"
return 180 / 256.0 / 2**zoom
#return 180 / float( 1 << (8+zoom) )
def TileBounds(tx, ty, zoom):
"Returns bounds of the given tile"
res = 180 / 256.0 / 2**zoom
return (
tx*256*res - 180,
ty*256*res - 90,
(tx+1)*256*res - 180,
(ty+1)*256*res - 90
)
if __name__ == "__main__":
import sys, os
def Usage(s = ""):
print "Usage: globalmaptiles.py [-profile 'mercator'|'geodetic'] zoomlevel lat lon [latmax lonmax]"
print
if s:
print s
print
print "This utility prints for given WGS84 lat/lon coordinates (or bounding box) the list of tiles"
print "covering specified area. Tiles are in the given 'profile' (default is Google Maps 'mercator')"
print "and in the given pyramid 'zoomlevel'."
print "For each tile several information is printed including bonding box in EPSG:900913 and WGS84."
sys.exit(1)
profile = 'mercator'
zoomlevel = None
lat, lon, latmax, lonmax = None, None, None, None
boundingbox = False
argv = sys.argv
i = 1
while i < len(argv):
arg = argv[i]
if arg == '-profile':
i = i + 1
profile = argv[i]
if zoomlevel is None:
zoomlevel = int(argv[i])
elif lat is None:
lat = float(argv[i])
elif lon is None:
lon = float(argv[i])
elif latmax is None:
latmax = float(argv[i])
elif lonmax is None:
lonmax = float(argv[i])
else:
Usage("ERROR: Too many parameters")
i = i + 1
if profile != 'mercator':
Usage("ERROR: Sorry, given profile is not implemented yet.")
if zoomlevel == None or lat == None or lon == None:
Usage("ERROR: Specify at least 'zoomlevel', 'lat' and 'lon'.")
if latmax is not None and lonmax is None:
Usage("ERROR: Both 'latmax' and 'lonmax' must be given.")
if latmax != None and lonmax != None:
if latmax < lat:
Usage("ERROR: 'latmax' must be bigger then 'lat'")
if lonmax < lon:
Usage("ERROR: 'lonmax' must be bigger then 'lon'")
boundingbox = (lon, lat, lonmax, latmax)
tz = zoomlevel
mercator = GlobalMercator()
mx, my = mercator.LatLonToMeters( lat, lon )
print "Spherical Mercator (ESPG:900913) coordinates for lat/lon: "
print (mx, my)
tminx, tminy = mercator.MetersToTile( mx, my, tz )
if boundingbox:
mx, my = mercator.LatLonToMeters( latmax, lonmax )
print "Spherical Mercator (ESPG:900913) cooridnate for maxlat/maxlon: "
print (mx, my)
tmaxx, tmaxy = mercator.MetersToTile( mx, my, tz )
else:
tmaxx, tmaxy = tminx, tminy
for ty in range(tminy, tmaxy+1):
for tx in range(tminx, tmaxx+1):
tilefilename = "%s/%s/%s" % (tz, tx, ty)
print tilefilename, "( TileMapService: z / x / y )"
gx, gy = mercator.GoogleTile(tx, ty, tz)
print "\tGoogle:", gx, gy
quadkey = mercator.QuadTree(tx, ty, tz)
print "\tQuadkey:", quadkey, '(',int(quadkey, 4),')'
bounds = mercator.TileBounds( tx, ty, tz)
print
print "\tEPSG:900913 Extent: ", bounds
wgsbounds = mercator.TileLatLonBounds( tx, ty, tz)
print "\tWGS84 Extent:", wgsbounds
print "\tgdalwarp -ts 256 256 -te %s %s %s %s %s %s_%s_%s.tif" % (
bounds[0], bounds[1], bounds[2], bounds[3], "<your-raster-file-in-epsg900913.ext>", tz, tx, ty)
print原文地址： http://www.maptiler.org/google-maps-coordinates-tile-bounds-projection/
（有时需要翻墙才能访问，故转载此处）。