Merkator Projection Issue

[merkator]

Hi,

I try to figure out something about Merkator projection and that it is being said it preserves angles.

I took a rectangular building from openstreetmap and took the lat/long values of its corners. openstreetmap uses Merkator. The lat/long values are

lon="7.2839266" lat="49.7198872"
lon="7.2844648" lat="49.7196165"
lon="7.2843206" lat="49.7194966"
lon="7.2837824" lat="49.7197673"

of course these are in degrees and not radiant, so I did a transformation to radiant:

0.1271285016436, 0.8677757353602
0.1271378950056, 0.8677710107539
0.1271353782408, 0.8677689181041
0.1271259848788, 0.8677736427104

I assume the earth radius to be 1 since I don't mind the size, only the shape (angles). So the x value to draw the shape is simply the longitude value, to get the y value I took the formula from http://en.wikipedia.org/wiki/Mercator_projection

y = ln (tan (pi/4 + lat/2))

The y values are now this:

1.003099466
1.003092159
1.003088922
1.003096229

If I now plot the x,y values the shape is not having right angles, it looks a bit distorted. Is there something I understood wrong about the projection? simple math mistake? Why is the shape on openstreetmap shown as rectangle?

Appreciate any ideas, thanks!

[daan]

I plotted those geographic coordinates on a Web maps Mercator and then rotated the result to be vertical. It looks quite rectangular to me.

Quite rectangular

Screen shot 2014-06-05 at 1.31.15 AM.png (7.85 KiB) Viewed 1824 times

— daab