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Google Maps Projection, and how to use it for clustering

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How Google presents the world with Google Maps, and what problems and opportunities that brings to developers. Offers an introduction to map projections and their consequences.

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Google Maps Projection, and how to use it for clustering

  1. 1. Google Maps Projection And how to use it for clustering
  2. 2. Me = Lode Blomme  Software Engineer @ RouteYou  Blog: http://blog.lodeblomme.be  Twitter: http://twitter.com/lodeblomme  LinkedIn: http://www.linkedin.com/in/lodeblomme
  3. 3. RouteYou  Products : • Community website: http://www.routeyou.com • Online recreational route planning • Maps for outdoor navigation for Garmin devices  Elevator Pitch : http://www.techcrunch.com/2008/10/24/elevator- pitch-friday-routeyou-makes-it-easy-to-find-the- perfect-driving-hiking-or-biking-route/
  4. 4. I presume everybody knows Google? GOOGLE
  5. 5. Any method of representing the surface of a sphere on a plane MAP PROJECTION
  6. 6. Map Projection  (pseudo)cylindrical  (pseudo)conical  azimuthal  hybrid
  7. 7. Map projections can preserve one or more of the earth's properties, though not all of them simultaneously AREA SHAPE DIRECTION BEARING DISTANCE SCALE
  8. 8. Lambert Conformal Conic Projection
  9. 9. Cylindrical Projection
  10. 10. Cylindrical Equal-Area Projection
  11. 11. Mercator Projection
  12. 12. Google Maps : Zoom Level 0 256 px 256 px
  13. 13. Google Maps : Zoom Level 1 512 px
  14. 14. Google Maps : Zoom Level 1
  15. 15. Google Maps : Zoom Levels • 1 tile (2(0*2)) 256 x 256 pixels = 65 536 pixels 0 • 4 tiles (2(1*2))  512 x 512 pixels = 262 144 pixels 1 • 16 tiles (2(2*2))  1024 x 1024 pixels = 1 megapixel 2 ... • 17 179 869 184 tiles (2(17*2))  33.5 x 33.5 megapixels = 1 122 megapixels 17 ... • 274 877 906 944 tiles (2(19*2))  134 x 134 megapixels = 18 000 megapixels 19
  16. 16. Assigning an n-tuple of numbers to each point in an n-dimensional space COORDINATE SYSTEMS
  17. 17. Spherical Coordinate System
  18. 18. Cartesian Coordinate System
  19. 19. Everybody knows WGS 84 and pixels WGS 84  PIXELS
  20. 20. Mercator Projection : The Math $x = ($radius * deg2rad($lon)) - $falseEasting $y = (($radius / 2.0 * log((1.0 + sin(deg2rad($lat))) / (1.0 - sin(deg2rad($lat))))) - $falseNorthing) * -1
  21. 21. Radius 256 px 256 px $tiles = pow(2, $zoom); $circumference = 256 * $tiles; $radius = $circumference / (2 * pi());
  22. 22. Radius 512 px
  23. 23. False Easting & False Northing 256 px 256 px $falseEasting = -1.0 * $circumference / 2.0; $falseNorthing = $circumference / 2.0;
  24. 24. False Easting & False Northing X:0 X:1 Y:0 Y:0 X:0 X:1 Y:1 Y:1
  25. 25. Partitioning of a data set into subsets, in which the data share some common trait - often proximity according to some defined distance measure CLUSTERING
  26. 26. I thought we had a moment there HAPPY ENDING
  27. 27. Scale
  28. 28. Scale

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