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Spain Cadastre WMS in Spherical Mercator

As far as I know, the Spanish Cadastre WMS server (run by the Ministry of Economy of Spain) is one of the first to provide its data in the Spherical Mercator projection EPSG:3857 (aka EPSG:3785 and EPSG:900913), so now we can switch between the great cadastre layer and the OSM layers for example. This is the Montjuic Palace in Barcelona:

As we know, the Spherical Mercator projection is conformal (keeps angles and shapes locally) and all parallels have the same length E:

R = 6378137 m
E = 2 * pi * R = 40075016.686 m

But we know that the true length of each parallel is approximately P = E * cos(lat), so if one wishes to measure distances, perimeters or paths directly on a map in EPSG:3857, it’s necessary to multiply the result by a factor f = cos(lat). For areas, f = [cos(lat)]^2. For Barcelona, for example, we have:

lat = 41.402634
f = 0.75008067 (distance)
f = 0.56262101 (area)

According to these results obtained with gvSIG, the perimeter p and area a of that block of buildings should be:

p = 0.75008067 * 571.444 = 428.6 m
a = 0.56262101 * 22935.684 = 12904.1 sq m

The expected values (from the official size of the block shown here) are:

p = 418 m
a = 12387 sq m

Oops, I think I didn’t choose a very standard block.

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