depending on the scale and the accurancy you need....
Lambert area is a good way for world wide [non polar] data, like 
Behrmann and maybe also Peters...to view Areas in the nearly real 
[scaled] size - but with a bit deformation for the well known shapes...
e.g. look at Behrmann
http://mapsof.net/map/behrmann-projection#.UlfIJhDGD5w
Standard-mercator:
http://www.math.ubc.ca/~israel/m103/mercator.png

for worldwide area-calculations it would be a good solution to get some 
approach formulas to correct the calculations from your data...but for 
worldwide data I don't beleive that theres a beter way to get results 
better than several/many square km's....from far away I would suggesting 
the usage of the spherical area formular - or reproject your data into 
any cylindric Projection for getting cartesian coordinates, so then you 
can use the much easier gaussian polygon area formular ....keep in mind 
that both results will finally differ

you should difference between the view of an areaconform projection and 
the calculation of the area itself...1st thing is madeable using such 
projection (s.a.) to get a graphical view over size-differences....2nd 
would be solvable much more easier - resulted accurancy depending 
primary on the data and then to the used correction formular
and of course commonly there's just the 2D projected Area :)....e.g. 
switzerland would have a bigger 3D area [natural area], then complete 
denmark [as a flat area] would have... in 2D it is swiched [I'd never 
never calulated...]...
also different projection will cause different deformations....
an calculated area in e.g.
WGS84[worldwide] <> UTM-Zone <> Gauss-Krüger [germany] <> Nature....

so also true nescessary for wich application you need the area of any 
worldwide polygon...and wich accurancie will be needed...the resulting 
work ranges from a few minutes upo to workload for following generations ...
regards
rolf gabler-mieck

> Hello,
>
> what I understood so far:
> for calculating the area of a polygon, a fitting equal area projection for 
> the region of the world is required to get good results.
> For different areas different projections are required.
> So when I plan to cover the whole world (lets say for an online application) 
> I have to find out which projection is good for this area, which might be a 
> complex requirement.
>
> Is this correct? Or is there one standard way which is working for the whole 
> world ?
>
> Or - Is there a different approach to calculate the area with geotools, for 
> example like the geodesic calculation of Open Layers?
>
> Regards,
> Peter


-- 
#-/\-#-/\-#-/\-#-/\-#-/\-#-/\-#-/\-#
Dipl. Ing. d. Geomatik Rolf Gabler-Mieck
Geographisches Institut der CAU-Kiel
LGI
Ludewig-Meyn Str. 14
24098 Kiel
Tel.: 0431-880 2955
#-/\-#-/\-#-/\-#-/\-#-/\-#-/\-#-/\-#


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