update docs with section on tile sizes#

Author: Hagellach37

docs/source/_static/img/area-plot.png

@@ -55,6 +55,7 @@ Welcome to MapSwipe Back-End's documentation!
    contributing
    diagrams
    use_cases
+   tile_size
 
 
 Indices and tables

docs/source/_static/img/chad_area.png

@@ -0,0 +1,40 @@
+# Analysis of the Mapswipe Tiles – how ‘square’ are they?
+
+To generate VGI for humanitarian use, project areas are cut into tiles in order for users to search for buildings on aerial imagery. The Mapswipe tiles are created as described by [Bing](https://msdn.microsoft.com/en-us/library/bb259689.aspx "Bing Maps Tile System") using Level of Detail 18 (task_z = 18 for Mapswipe data). The users assign a ‘Yes’, ‘No’, ‘Maybe’ or ‘Bad Imagery’ to each tile. This information is used to select on positive tiles and create bigger geometries representing a settlement layer.  While these tiles look absolutely squared (e.g. in a web map or in mobile applications such as MapSwipe), they **DON'T** represent the same area.
+
+The web mercator projection distorts the image in a way that objects further away from the equator will continuously appear bigger than they are. So always keep in mind: **The area represented by a tile will be getting smaller the further north or south your tile is located.** Table 1 shows that the area of projects further away from the equator have smaller areas and smaller side length. Furthermore, the angles will deviate further from rectangular.
+
+
+|        | 10836 Chad           | 7605 Madagascar  |
+| ------------- |:-------------:| -----:|
+| Geographical Latitude      | 21 ° North | 25 ° South |
+| Average Tile X Length [m]      | 144.9570      |   138.3959 |
+| Average Tile Y Length [m] | 144.0854      | 137.6354 |
+| Area average [m²] | 20886.2967      | 19048.1169 |
+| Area min [m²] | 20791.6519      | 18921.4767 |
+| Area max [m²] | 20949.2044     | 19139.2674 |
+| Area range [m²] | 157.5525      | 217.7908 |
+| Deviation from 90° angle |  ~ 0.01171 °      |  ~ 0.0063 ° |
+
+*Table 1:  Measurements for Mapswipe Tiles.*
+
+Figure 1 shows the decrease in size from south to north in project 10836 (Chad) on the northern hemisphere.
+
+<img src="/_static/img/chad_area.png" width="800">
+<p><i>Figure 1: Area in m² of Mapswipe tiles in project 10836.  As it is located on the northern hemisphere, tiles further north are smaller.</i></p>
+
+In the Mapswipe App, each tile has a size of 256x256 pixels. The translation of pixels into meters is depending on geographical longitude and level of details (see Figure 2).
+
+<img src="/_static/img/length-plot.png" width="600">
+<p><i>Figure 2: Tile length from pixel to meters: f(latitude, level) =  (cos(latitude * pi/180) * 2 * pi * 6378137) / (256 * 2^level) * 256;  for level = 18. Values range from 152.8741 m (Equator) to close to 0 m (poles). </i></p>
+
+As a result of the change in sidelength and inner angles, the area of the tiles decreases with distance from equator as well. Have a look at Figure 3.
+
+<img src="/_static/img/area-plot.png" width="800">
+<p><i>Figure 3 shows the calculated area for the standart level 18 from 90 ° to 0 °.</i></p>
+
+## Summary
+-	Area and side length of a tile will continuously decrease with distance to the equator
+-	within one project the differences in size depend on the north-south extend of the project
+-	The tile shapes differ from rectangular form the further away they are from the equator
+- Find a [example geojson file](../../mapswipe_workers/sample_data/tiles.geojson) with calculated area and side length for given task_y or the Y-coordiantes of the tile center. You can use this file in QGIS or any other GIS software.