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The Exponential Nature of Tiled Maps

 

Magnitude

The Tiled method of providing basemap images to an application has mountains of benefits to the user.  These benefits are not cheap or easy, however, for those involved in creating and providing those tiled images.  To cover a geographic area at increasing zoom levels (or increased resolution), nested sets of tiles must be created; each additional zoom-level consisting of 4 times the number of tiles from the previous zoom level.

For example, Virtual Earth requires four 256 x 256 tiles to represent the world at zoom-level 1.  At zoom-level 2, sixteen tiles are required to cover the same geographic extent.  Since there are more images, the level of detail increases (i.e., it looks like you are zooming in and things are getting bigger).  Here is a chart that illustrates how quadrupling the number of required tile images per zoom-level quickly requires an exponentially large set of tiles.  This is just for the first four zoom-levels…

Tiles Per Zoom-Level

Here is a series of images to illustrate resolution changes per zoom level and the number of tiles required at each to cover the same geographic extent (the yellow box in the corner is a preview area for the geographic area covered by one tile at the next zoom-level).  This first 256 x 256 tile image shows the region around New Orleans/Lake Pontchartrain.  At the next zoom-level, that same geographic area is split into four individual 256 x 256 tile images to provide greater detail.  Again, each additional zoom-level has quadruple the number of tiles as the previous zoom-level.

 Tile 1; the region around New Orleans/Lake Pontchartrain.

 4 tiles (to cover the same geographic extent as the image above).

 16 tiles.

 64 tiles.

 256 tiles.

 1,024 tiles.

 4,096 tiles.

 16,384 tiles.

 65,536 tiles.

 262,144 tiles.

 1,048,576 tiles.

 4,194,304 tiles.

 16,777,216 tiles (to cover the same geographic extent as that top image).

 

How Many Tiles??

That pool up there is at Virtual Earth’s zoom-level 20.  That’s pretty amazing.  If VE had individual tiles for the whole world at this resolution (which they don’t), they would need 366,503,875,924 tiles per map style!  Here’s how it breaks down per zoom-level…

4
16
64
256
1,024
4,096
16,384
65,536
262,144
1,048,576
4,194,304
16,777,216
67,108,864
268,435,456
1,073,741,824
4,294,967,296
17,179,869,184

John Nelson / IDV Solutions / john.nelson@idvsolutions.com

 

68,719,476,736
274,877,906,944

2 responses

  1. Unknown

    Thank you .
    31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

    August 31, 2008 at 8:28 am

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