[R] why variations in accuracy between R to ARCGIS for the same point reprojection?

[Prof Brian Ripley]

There is no 'reprojection' in R (which is upper case).  Please attribute 
blame correctly.

You seem to be talking about some contributed addon package, not 
specified.  But I think you should be asking this on R-sig-geo.

On 02/09/2012 19:24, Camilo Mora wrote:
> Hi everyone,
>
> I wonder if anyone knows the reason why the outputs of the same
> reprojection in r and arcgis are different?. The magnitude of the change
> can be up to 40 km in the poles.
> Basically, I have a database of points equally separated by one degree
> over the globe.
> In ARCGIS,  I am projecting the data in GCS-WGS-1984 and then
> reprojected it to Berhmann to ensure equal area distribution of the points.
> In R, I am using:
> spPoint <-
> SpatialPoints(coords=coordinates(Data),proj4string=CRS("+proj=longlat
> +datum=WGS84"))
> and then reprojecting it to Berhmann with:
> spPointReprj=spTransform(Data,CRS("+proj=cea +lon_0=0 +lat_ts=30 +x_0=0
> +y_0=0 +ellps=WGS84"))
>
> If I put the two outputs of the reprojections in the same map, they are
> off by few meters in the tropics by up to 40km in the poles.
>
> I decided to investigate how the reprojections are done and my
> calculations are different from both R and ArcGis:
>
> First, I calculated the radious of the Earth in two different ways:
> =Re * (1 - e^2)/ (1 - e^2 *SIN(RADIANS(Latitude))^2)^(3/2)
> =Re * SQRT(1 - e^2) / (1 - e^2 * (SIN(RADIANS(Latitude)))^2)
>
> where Re is the radius of the Earth at the tropics(6378km) and e is the
> eccentricity of the ellipsoid (0.081082).
>
> According to several books I used, the position of a point in the Y-axis
> in the Berhmann projection could be estimated as:
> =Re*(SIN(RADIANS(Latitude))/COS(RADIANS(Spll)))
> where Spll is the standard parallel, which in the Berhmann's projection
> is 30.
> Unfortunately, the resulting output, although similar in shape to the
> outputs in R and Arcgis, is still not quite the same. Any thoughts why
> these differences in supposedly the same calculations?
>
> Any input will be greatly appreciated,
>
> Thanks,
>
> Camilo
>
>
>
>
> Camilo Mora, Ph.D.
> Department of Geography, University of Hawaii
> Currently available in Colombia
> Phone:   Country code: 57
>           Provider code: 313
>           Phone 776 2282
>           From the USA or Canada you have to dial 011 57 313 776 2282
> http://www.soc.hawaii.edu/mora/
>
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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595