[Proj] Optimal Albers Standard parallels

[strebe]

Oscar:

>From the publication you cited (http://www.ec-gis.org/sdi/publist/pdfs/annoni-etal2003eur.pdf):

"A simple but useful way of appraising the location of the origin of an azimuthal projection is to plot a series of concentric circles of radii z representing the isograms of maximum Angular Deformation and those of Scale Error at the scale of a convenient atlas map and to shift this overlay about on the map until a good fit is obtained between some of the extreme points of the area of mapped."

While phrased in an unnecessarily complicated way, the recommendation in "Map Projections for Europe" is the equivalent of my recommendation. You have a bunch of points you know are within the area of interest. Whether manually (as described in that publication) or programmatically, you need to find the smallest small circle that circumscribes them all. I don't know of any non-iterative method for doing that, though possibly one could be devised. As an algorithmic process, it is not difficult, but unlike Albers, it is not just a matter of observing the most northerly and most southerly points.

I note that you talk about comparing Albers to LAEA. Once you know the optimal LAEA you can do that, since the distortion values at the extremes of the region of interest can be computed by known formulæ once the parameters for the projection are known.

Can I interpret your inquiry to mean that you want to know (presumably in complete detail) the algorithm for finding the projection center of the optimal LAEA for a region, given a list of points in that region? Or are you just wondering if one could be devised?

Regards,
— daan Strebe


On Feb 21, 2010, at 8:01:56 AM, OvV_HN <ovv at hetnet.nl> wrote:
In the article I was referring to, the angular deformation and the scale 
error of the Albers and the LAEA projections are compared for the whole of 
the European Union. The Albers has two standard parallels at 38 and 61 d N, 
with a CM at 9 E. The LAEA has its center at 9 E and 53 N.
I got the impression that the author just shifted the LAEA center up and 
down by trial and error until a reasonable comparison could be made with the 
Albers.
I wondered, could the center of the LAEA projection have been determined 
algorithmically?
Still an academic discussion, of course......


Oscar van Vlijmen

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