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| GeoCommunity Mailing List |
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| Subject: | RE: [gislist] US cities and counties |
| Date: |
03/23/2004 11:15:01 AM |
| From: |
Quantitative Decisions |
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Martin,
At 08:59 AM 3/23/2004 -0600, you wrote:
>One of the goals is to calculate a center of mass for production. The
>region of interest spans:
>
>Lat: 35N to 49N
>Lon: -104 to -80
>
>The question is how to choose a projection that will allow me to calculate
>a reasonable (yet to be determined what will be considered reasonable)
>estimate of center of mass. I am considering Albers Equal Area,
>Equidistant Conic, Azimuthal Equidistant, and Two-Point Equidistant.
An equidistant conic, central meridian at -92, reference latitude of 42,
and standard parallels around c. 37 and c. 47 degrees, should do very
nicely. Maximum areal distortion throughout this region is +-0.4%,
and--since there is no meridian distortion--maximum parallel scale
distortion is also +-0.4%. Maximum angular deviation is a quarter of a
degree. This all points to the potential for a highly accurate calculation.
An Albers equal-area projection with the same parameters has similar
amounts and types of distortion in the parallel scale. To become equal
area, though, it has to distort meridians, too, by the same amounts. This
makes the total scale distortion slightly worse than the equidistant
conic. This is reflected in the maximum angular deviation of about one and
a quarter degrees, realized in the southern corners of your region. These
are all good numbers for your application, but not as good as the
equidistant conic.
Another projection worth considering would be an oblique aspect of an
azimuthal equidistant projection centered near where you anticipate the
center of mass to be. (This is NOT the same as a polar azimuthal
equidistant projection with a reference latitude and central meridian set
near your region's center.) Distortion near the boundary would not be so
good, being off by a few percent perhaps, but it also wouldn't matter much,
because all distances and angles to the center of mass (which is all that
is needed for this kind of calculation) would be dead-on accurate.
I obtained these answers using the "Tissot" tool for ArcView 3.x that is
available on my web pages at quantdec.com.
--Bill Huber
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