Google Maps Projection
And how to use it for clustering

Me = Lode Blomme
 Software Engineer @ RouteYou
 Blog: http://blog.lodeblomme.be
 Twitter: http://twitter.com/lodeblomme
 LinkedIn: http://www.linkedin.com/in/lodeblomme

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/

I presume everybody knows Google?
GOOGLE

Any method of representing the surface of a sphere on a plane
MAP PROJECTION

Map Projection
 (pseudo)cylindrical
 (pseudo)conical
 azimuthal
 hybrid

Map projections can preserve one or more of the earth's properties,
though not all of them simultaneously
AREA
SHAPE
DIRECTION
BEARING
DISTANCE
SCALE

Lambert Conformal Conic Projection

Cylindrical Projection

Cylindrical Equal-Area Projection

Mercator Projection

Google Maps : Zoom Level 0
256 px
256 px

Google Maps : Zoom Level 1
512 px

Google Maps : Zoom Level 1

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

Assigning an n-tuple of numbers to each point in an n-dimensional space
COORDINATE SYSTEMS

Spherical Coordinate System

Cartesian Coordinate System

Everybody knows WGS 84 and pixels
WGS 84  PIXELS

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

Radius
256 px
256 px
$tiles = pow(2, $zoom);
$circumference = 256 * $tiles;
$radius = $circumference / (2 * pi());

Radius
512 px

False Easting & False Northing
256 px
256 px
$falseEasting = -1.0 * $circumference / 2.0;
$falseNorthing = $circumference / 2.0;

False Easting & False Northing
X:0 X:1
Y:0 Y:0
X:0 X:1
Y:1 Y:1

Partitioning of a data set into subsets, in which the data share some
common trait - often proximity according to some defined distance
measure
CLUSTERING

I thought we had a moment there
HAPPY ENDING

Scale

Scale