Package org.hortonmachine.gears.modules.r.tmsgenerator

Class GlobalMercator

  • public class GlobalMercator
extends Object
    TMS Global Mercator OmsProfile --------------------------- 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"]]]

    • Field Summary

      Fields 
      Modifier and Type Field Description
      static int TILE_SIZE  

    • Constructor Summary

      Constructors 
      Constructor Description
      GlobalMercator()  

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      int[] GoogleTile​(double lat, double lon, int zoom)
      Converts a lat long coordinates to Google Tile Coordinates
      int[] GoogleTile​(int tx, int ty, int zoom)
      Converts TMS tile coordinates to Google Tile coordinates
      double[] LatLonToMeters​(double lat, double lon)
      Converts given lat/lon in WGS84 Datum to XY in Spherical Mercator EPSG:900913
      static void main​(String[] args)  
      double[] MetersToLatLon​(double mx, double my)
      Converts XY point from Spherical Mercator EPSG:900913 to lat/lon in WGS84 Datum
      int[] MetersToPixels​(double mx, double my, int zoom)
      Converts EPSG:900913 to pyramid pixel coordinates in given zoom level
      int[] metersToPixelsDown​(double mx, double my, int zoom)  
      int[] metersToPixelsUp​(double mx, double my, int zoom)  
      int[] MetersToTile​(double mx, double my, int zoom)
      Returns tile for given mercator coordinates
      int[] metersToTileDown​(double mx, double my, int zoom)  
      int[] metersToTileUp​(double mx, double my, int zoom)  
      double[] PixelsToMeters​(double px, double py, int zoom)
      Converts pixel coordinates in given zoom level of pyramid to EPSG:900913
      int[] PixelsToRaster​(int px, int py, int zoom)
      Move the origin of pixel coordinates to top-left corner
      int[] PixelsToTile​(int px, int py)
      Returns a tile covering region in given pixel coordinates
      int[] pixelsToTileDown​(int px, int py)  
      int[] pixelsToTileUp​(int px, int py)  
      String QuadTree​(int tx, int ty, int zoom)
      Converts TMS tile coordinates to Microsoft QuadTree
      double Resolution​(int zoom)
      Resolution (meters/pixel) for given zoom level (measured at Equator)
      double[] TileBounds​(int tx, int ty, int zoom)
      Returns bounds of the given tile in EPSG:900913 coordinates
      org.locationtech.jts.geom.Envelope TileLatLonBounds​(int tx, int ty, int zoom)
      Returns bounds of the given tile in latitude/longitude using WGS84 datum return the array of [w, s, e, n]
      int[] TMSTileFromGoogleTile​(int tx, int ty, int zoom)  
      int ZoomForPixelSize​(int pixelSize)
      Maximal scaledown zoom of the pyramid closest to the pixelSize

    • Constructor Detail

      • GlobalMercator

        public GlobalMercator()

    • Method Detail

      • LatLonToMeters

        public double[] LatLonToMeters​(double lat,
                               double lon)
        Converts given lat/lon in WGS84 Datum to XY in Spherical Mercator EPSG:900913
        Parameters:
        lat -
        lon -
        Returns:

      • MetersToLatLon

        public double[] MetersToLatLon​(double mx,
                               double my)
        Converts XY point from Spherical Mercator EPSG:900913 to lat/lon in WGS84 Datum
        Returns:

      • PixelsToMeters

        public double[] PixelsToMeters​(double px,
                               double py,
                               int zoom)
        Converts pixel coordinates in given zoom level of pyramid to EPSG:900913
        Returns:

      • MetersToPixels

        public int[] MetersToPixels​(double mx,
                            double my,
                            int zoom)
        Converts EPSG:900913 to pyramid pixel coordinates in given zoom level
        Parameters:
        mx -
        my -
        zoom -
        Returns:

      • PixelsToTile

        public int[] PixelsToTile​(int px,
                          int py)
        Returns a tile covering region in given pixel coordinates
        Parameters:
        px -
        py -
        Returns:

      • PixelsToRaster

        public int[] PixelsToRaster​(int px,
                            int py,
                            int zoom)
        Move the origin of pixel coordinates to top-left corner
        Parameters:
        px -
        py -
        zoom -
        Returns:

      • MetersToTile

        public int[] MetersToTile​(double mx,
                          double my,
                          int zoom)
        Returns tile for given mercator coordinates
        Returns:

      • metersToTileUp

        public int[] metersToTileUp​(double mx,
                            double my,
                            int zoom)

      • metersToPixelsUp

        public int[] metersToPixelsUp​(double mx,
                              double my,
                              int zoom)

      • pixelsToTileUp

        public int[] pixelsToTileUp​(int px,
                            int py)

      • metersToTileDown

        public int[] metersToTileDown​(double mx,
                              double my,
                              int zoom)

      • metersToPixelsDown

        public int[] metersToPixelsDown​(double mx,
                                double my,
                                int zoom)

      • pixelsToTileDown

        public int[] pixelsToTileDown​(int px,
                              int py)

      • TileBounds

        public double[] TileBounds​(int tx,
                           int ty,
                           int zoom)
        Returns bounds of the given tile in EPSG:900913 coordinates
        Parameters:
        tx -
        ty -
        zoom -
        Returns:
        the array of [w, s, e, n]

      • TileLatLonBounds

        public org.locationtech.jts.geom.Envelope TileLatLonBounds​(int tx,
                                                           int ty,
                                                           int zoom)
        Returns bounds of the given tile in latitude/longitude using WGS84 datum return the array of [w, s, e, n]

      • Resolution

        public double Resolution​(int zoom)
        Resolution (meters/pixel) for given zoom level (measured at Equator)
        Returns:

      • ZoomForPixelSize

        public int ZoomForPixelSize​(int pixelSize)
        Maximal scaledown zoom of the pyramid closest to the pixelSize
        Parameters:
        pixelSize -
        Returns:

      • GoogleTile

        public int[] GoogleTile​(int tx,
                        int ty,
                        int zoom)
        Converts TMS tile coordinates to Google Tile coordinates
        Parameters:
        tx -
        ty -
        zoom -
        Returns:

      • TMSTileFromGoogleTile

        public int[] TMSTileFromGoogleTile​(int tx,
                                   int ty,
                                   int zoom)

      • GoogleTile

        public int[] GoogleTile​(double lat,
                        double lon,
                        int zoom)
        Converts a lat long coordinates to Google Tile Coordinates
        Parameters:
        lat -
        lon -
        zoom -
        Returns:

      • QuadTree

        public String QuadTree​(int tx,
                       int ty,
                       int zoom)
        Converts TMS tile coordinates to Microsoft QuadTree
        Returns:

      • main

        public static void main​(String[] args)