[GRASS-user] What distance is being measured and used for buffers ?

[Moritz Lennert]

Hello,

I have a fundamental question about distances in GRASS, also in relation 
to buffers, that I stumbled upon trying to help a student who tried to 
draw buffers around cities indicating the maximum distance airplanes 
could fly at different times in history.

To test, I used the World Mercator projection:

+proj=merc
+lon_0=0
+k=1
+x_0=0
+y_0=0
+no_defs
+a=6378137
+rf=298.257223563
+towgs84=0.000,0.000,0.000
+to_meter=1

This projection has obvious deformations the further you get from the 
equator, and thus distances are seriously distorted[1].

Using GRASS 6.5 to create a buffer of 6000km around Belgium gives a map 
which shows a circular buffer [2].

Using the distance measuring tool in the wxGUI confirms that the 
distance from Belgium to the buffer line in all directions is around 6000km.

However, the actual distance is very different, especially towards the 
North: According to CloudMade's routing website based on OSM data 
northern tip of Norway is only ~3500km by car from Brussels, so very far 
from 6000km.

I get exactly the same results using r.grow.distance and r.cost.

For comparison, I used a simple Plate Carree projection:

+proj=eqc
+lat_ts=0
+lat_0=0
+lon_0=0
+x_0=0
+y_0=0
+no_defs
+a=6371007
+b=6371007
+to_meter=1

Distortions are obviously different [3]. And the 6000km buffer is also 
positioned differently compared to the land masses [4]. Again, measuring 
the distances with the wxGUI distance tool gives me ~6000km in all 
directions.

So, my question: which "distance" is used for measurement and for buffer 
creation ? A distance based buffer in map units should lead to deformed 
buffers in most projection systems. Is there anyway to achieve such 
deformed buffers and correct distance measures ?

Moritz


[1] http://164.15.12.207/grass/distances/worldmercator.png
[2] http://164.15.12.207/grass/distances/buffer_worldmercator.png
[3] http://164.15.12.207/grass/distances/platecarree.png
[4] http://164.15.12.207/grass/distances/buffer_platecarree.png