This page http://www.maptiler.org/google-maps-coordinates-tile-bounds-projection provides algorithms, written in python, to compute tile bounds in EPSG:900913 coordinates and in latutude/longitude using WGS84 datum.
The class GlobalMercator in this script http://www.maptiler.org/google-maps-coordinates-tile-bounds-projection/globalmaptiles.py contains two methods, TileBounds() and TileLatLonBounds() to do this.
A modified version of the script to show tile bounds coordinates:
#!/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.
###############################################################################
"""
tilebounds.py
Adapted from:
http://www.maptiler.org/google-maps-coordinates-tile-bounds-projection/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 GlobalMercatorLight(object):
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 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 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)
#---------------------
if __name__ == "__main__":
import sys, os
def Usage(s = ""):
print "Usage: tilebounds.py tx ty zoomlevel"
print
sys.exit(1)
profile = 'mercator'
zoomlevel = None
tx, ty = None, None
argv = sys.argv
i = 1
while i < len(argv):
arg = argv[i]
if tx is None:
tx = float(argv[i])
elif ty is None:
ty = float(argv[i])
elif zoomlevel is None:
zoomlevel = int(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 tx == None or ty == None:
Usage("ERROR: Specify at least 'lat', 'lon' and 'zoomlevel'.")
tz = zoomlevel
mercator = GlobalMercatorLight()
minx, miny, maxx, maxy = mercator.TileBounds( tx, ty, tz )
print "Bounds of the given tile in EPSG:900913 coordinates: "
print " upper-left corner: "
print (minx, miny)
print " bottom-right corner: "
print (maxx, maxy)
print
minLat, minLon, maxLat, maxLon = mercator.TileLatLonBounds( tx, ty, tz )
print "Bounds of the given tile in latitude/longitude using WGS84 datum: "
print " upper-left corner: "
print (minLat, minLon)
print " bottom-right corner: "
print (maxLat, maxLon)
print
Usage: tilebounds xTile yTile zoom.
For example, the output for the tile x=49, y=30, z=6 is as follows:
$./tilebounds.py 49 30 6
Bounds of the given tile in EPSG:900913 coordinates:
upper-left corner:
(10644926.307106785, -1252344.271424327)
bottom-right corner:
(11271098.44281895, -626172.1357121654)
Bounds of the given tile in latitude/longitude using WGS84 datum:
upper-left corner:
(-11.178401873711772, 95.625)
bottom-right corner:
(-5.61598581915534, 101.25000000000001)
A tile can be downloaded with the url http://mt.google.com/vt?x=xTile&y=yTile&z=zoom, but this is forbidden to access it directly.
The software was originally written by Klokan Petr Přidal.
I hope this could help!
Best Answer
As of Jan 2015, I'm not aware of any open source implementation that fully supports every possible option in geopackage. The spec is authoritative (but likely to be updated) for implementation, so if you want to (or really don't want to, but still have to) write your own map engine, work from that. Look for a sane subset/profile, rather than trying to do it all. For example, choose to only support power-of-two zoom.
If you're able to constrain the problem a bit, the GDAL and spatialite implementations might work for you - both can give back tiles or composite images for a given area. Given your comment about iOS support, spatialite may be difficult. I don't have experience with GDAL on iOS. Those are both open source and can provide examples for how you might do a similar implementation. Even Rouault's blog entry on GeoPackage might also prove useful to either use GDAL or implement something similar.
Given arbitrary SRID, you'd need some way to either reproject the data you want to overlay on the map, or reproject the geopackage rasters and vectors, or both. That is usually proj.4 (used within both GDAL and spatialite, as well as many other tools), which is workable on Android. I can't say how hard it is on iOS.
Correction: GeoPackage origin is still (0,0) but there is no promise that there is any data at that position at any zoom level. The spec says "The tile coordinate (0,0) always refers to the tile in the upper left corner of the tile matrix at any zoom level, regardless of the actual availability of that tile." Actually, there is no promise there is data at any other position - the matrix is allowed to be empty. The background to this decision is to be able to add tiles later. What is allowed to occur though is that the (potentially empty) nominal bounding box in
gpkg_tile_matrix_setdoesn't need to be the whole world - it is the exact bounds for what might ever be filled in. Consider that a SRID like a UTM zone doesn't make sense to have "whole world" extent.