google maps projection, and how to use it for clustering
DESCRIPTION
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.TRANSCRIPT
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Google Maps Projection
And how to use it for clustering
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Me = Lode Blomme
Software Engineer @ RouteYou
Blog: http://blog.lodeblomme.be
Twitter: http://twitter.com/lodeblomme
LinkedIn: http://www.linkedin.com/in/lodeblomme
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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/
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I presume everybody knows Google?
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MAP PROJECTION
Any method of representing the surface of a sphere on a plane
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Map Projection
(pseudo)cylindrical
(pseudo)conical
azimuthal
hybrid
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AREASHAPEDIRECTIONBEARINGDISTANCE SCALE
Map projections can preserve one or more of the earth's properties, though not all of them simultaneously
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Lambert Conformal Conic Projection
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Cylindrical Projection
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Cylindrical Equal-Area Projection
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Mercator Projection
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Google Maps : Zoom Level 0
256 px
256 px
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Google Maps : Zoom Level 1
512 px
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Google Maps : Zoom Level 1
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Google Maps : Zoom Levels
0 • 1 tile (2(0*2)) 256 x 256 pixels = 65 536 pixels
1 • 4 tiles (2(1*2)) 512 x 512 pixels = 262 144 pixels
2 • 16 tiles (2(2*2)) 1024 x 1024 pixels = 1 megapixel
...
17 • 17 179 869 184 tiles (2(17*2)) 33.5 x 33.5 megapixels = 1 122 megapixels
...
19 • 274 877 906 944 tiles (2(19*2)) 134 x 134 megapixels = 18 000 megapixels
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COORDINATE SYSTEMS
Assigning an n-tuple of numbers to each point in an n-dimensional space
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Spherical Coordinate System
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Cartesian Coordinate System
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WGS 84 PIXELS
Everybody knows WGS 84 and pixels
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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
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Radius
256 px
256 px
$tiles = pow(2, $zoom); $circumference = 256 * $tiles;$radius = $circumference / (2 * pi());
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Radius
512 px
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False Easting & False Northing
256 px
256 px
$falseEasting = -1.0 * $circumference / 2.0;$falseNorthing = $circumference / 2.0;
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False Easting & False Northing
X : 0Y : 0
X : 1Y : 0
X : 0Y : 1
X : 1Y : 1
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CLUSTERING
Partitioning of a data set into subsets, in which the data share some common trait - often proximity according to some defined distance measure
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HAPPY ENDING
I thought we had a moment there
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Scale
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Scale